LMFDB - Embedded newform 66.2.h.a.35.2

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			35.2
Root			$-0.245684 - 1.71454i$ of defining polynomial
Character	$\chi$	$=$	66.35
Dual form			66.2.h.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(1.70654 - 0.296161i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.01556 + 0.654895i) q^{5} +(0.245684 - 1.71454i) q^{6} +(-2.01556 + 2.77418i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.82458 - 1.01082i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(1.70654 - 0.296161i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.01556 + 0.654895i) q^{5} +(0.245684 - 1.71454i) q^{6} +(-2.01556 + 2.77418i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.82458 - 1.01082i) q^{9} +2.11929i q^{10} +(0.960858 - 3.17439i) q^{11} +(-1.55470 - 0.763481i) q^{12} +(-1.79505 - 0.583248i) q^{13} +(2.01556 + 2.77418i) q^{14} +(-3.24568 + 1.71454i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.59384 + 4.90534i) q^{17} +(-0.0885088 - 2.99869i) q^{18} +(-0.141616 - 0.194917i) q^{19} +(2.01556 + 0.654895i) q^{20} +(-2.61803 + 5.33119i) q^{21} +(-2.72210 - 1.89477i) q^{22} -4.97072i q^{23} +(-1.20654 + 1.24268i) q^{24} +(-0.411491 + 0.298966i) q^{25} +(-1.10940 + 1.52696i) q^{26} +(4.52089 - 2.56155i) q^{27} +(3.26124 - 1.05964i) q^{28} +(-3.37235 - 2.45016i) q^{29} +(0.627650 + 3.61665i) q^{30} +(2.02518 - 6.23285i) q^{31} +1.00000 q^{32} +(0.699614 - 5.70180i) q^{33} +5.15778 q^{34} +(2.24568 - 6.91151i) q^{35} +(-2.87928 - 0.842471i) q^{36} +(7.14052 + 5.18789i) q^{37} +(-0.229139 + 0.0744518i) q^{38} +(-3.23607 - 0.463712i) q^{39} +(1.24568 - 1.71454i) q^{40} +(-6.42001 + 4.66441i) q^{41} +(4.26124 + 4.13733i) q^{42} -6.51583i q^{43} +(-2.64321 + 2.00336i) q^{44} +(-5.03112 + 3.88718i) q^{45} +(-4.72744 - 1.53604i) q^{46} +(1.98077 + 2.72629i) q^{47} +(0.809017 + 1.53150i) q^{48} +(-1.47047 - 4.52566i) q^{49} +(0.157176 + 0.483737i) q^{50} +(4.17274 + 7.89915i) q^{51} +(1.10940 + 1.52696i) q^{52} +(5.91040 + 1.92040i) q^{53} +(-1.03914 - 5.09119i) q^{54} +(0.142225 + 7.02743i) q^{55} -3.42908i q^{56} +(-0.299400 - 0.290694i) q^{57} +(-3.37235 + 2.45016i) q^{58} +(-1.62931 + 2.24256i) q^{59} +(3.63359 + 0.520675i) q^{60} +(1.53975 - 0.500295i) q^{61} +(-5.30198 - 3.85211i) q^{62} +(-2.88889 + 9.87326i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +(-5.20654 - 2.42733i) q^{66} -9.98396 q^{67} +(1.59384 - 4.90534i) q^{68} +(-1.47214 - 8.48275i) q^{69} +(-5.87928 - 4.27155i) q^{70} +(-9.47214 + 3.07768i) q^{71} +(-1.69098 + 2.47802i) q^{72} +(-1.45756 + 2.00616i) q^{73} +(7.14052 - 5.18789i) q^{74} +(-0.613685 + 0.632066i) q^{75} +0.240931i q^{76} +(6.86966 + 9.06377i) q^{77} +(-1.44102 + 2.93439i) q^{78} +(10.7741 + 3.50072i) q^{79} +(-1.24568 - 1.71454i) q^{80} +(6.95647 - 5.71030i) q^{81} +(2.45223 + 7.54718i) q^{82} +(2.12232 + 6.53182i) q^{83} +(5.25163 - 2.77418i) q^{84} +(-6.42497 - 8.84322i) q^{85} +(-6.19693 - 2.01350i) q^{86} +(-6.48070 - 3.18254i) q^{87} +(1.08851 + 3.13291i) q^{88} -2.47254i q^{89} +(2.14222 + 5.98608i) q^{90} +(5.23607 - 3.80423i) q^{91} +(-2.92172 + 4.02140i) q^{92} +(1.61012 - 11.2364i) q^{93} +(3.20495 - 1.04135i) q^{94} +(0.413086 + 0.300124i) q^{95} +(1.70654 - 0.296161i) q^{96} +(-4.08582 + 12.5749i) q^{97} -4.75856 q^{98} +(-0.494732 - 9.93757i) 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 $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	1.70654	−	0.296161i	0.985273	−	0.170989i
$3$	1.70654	−	0.296161i	0.985273	−	0.170989i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−2.01556	+	0.654895i	−0.901386	+	0.292878i	−0.722809	−	0.691048i	$-0.757149\pi$
$5$	−2.01556	+	0.654895i	−0.901386	+	0.292878i	−0.178577	+	0.983926i	$0.557149\pi$
$6$	0.245684	−	1.71454i	0.100300	−	0.699957i
$7$	−2.01556	+	2.77418i	−0.761810	+	1.04854i	0.235251	+	0.971935i	$0.424409\pi$
$7$	−2.01556	+	2.77418i	−0.761810	+	1.04854i	−0.997061	+	0.0766070i	$0.975591\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	2.82458	−	1.01082i	0.941526	−	0.336941i
$10$			2.11929i			0.670177i
$11$	0.960858	−	3.17439i	0.289710	−	0.957115i
$11$	0.960858	−	3.17439i	0.289710	−	0.957115i
$12$	−1.55470	−	0.763481i	−0.448804	−	0.220398i
$13$	−1.79505	−	0.583248i	−0.497858	−	0.161764i	0.0493154	−	0.998783i	$-0.484296\pi$
$13$	−1.79505	−	0.583248i	−0.497858	−	0.161764i	−0.547173	+	0.837019i	$0.684296\pi$
$14$	2.01556	+	2.77418i	0.538681	+	0.741431i
$15$	−3.24568	+	1.71454i	−0.838032	+	0.442692i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.59384	+	4.90534i	0.386564	+	1.18972i	0.935340	+	0.353751i	$0.115094\pi$
$17$	1.59384	+	4.90534i	0.386564	+	1.18972i	−0.548776	+	0.835970i	$0.684906\pi$
$18$	−0.0885088	−	2.99869i	−0.0208617	−	0.706799i
$19$	−0.141616	−	0.194917i	−0.0324889	−	0.0447171i	0.792464	−	0.609919i	$-0.208798\pi$
$19$	−0.141616	−	0.194917i	−0.0324889	−	0.0447171i	−0.824952	+	0.565202i	$0.808798\pi$
$20$	2.01556	+	0.654895i	0.450693	+	0.146439i
$21$	−2.61803	+	5.33119i	−0.571302	+	1.16336i
$22$	−2.72210	−	1.89477i	−0.580354	−	0.403967i
$23$		−	4.97072i		−	1.03647i	−0.855239	−	0.518234i	$-0.826590\pi$
$23$		−	4.97072i		−	1.03647i	0.855239	−	0.518234i	$-0.173410\pi$
$24$	−1.20654	+	1.24268i	−0.246285	+	0.253661i
$25$	−0.411491	+	0.298966i	−0.0822982	+	0.0597932i
$26$	−1.10940	+	1.52696i	−0.217572	+	0.299462i
$27$	4.52089	−	2.56155i	0.870046	−	0.492970i
$28$	3.26124	−	1.05964i	0.616317	−	0.200254i
$29$	−3.37235	−	2.45016i	−0.626230	−	0.454982i	0.228862	−	0.973459i	$-0.426499\pi$
$29$	−3.37235	−	2.45016i	−0.626230	−	0.454982i	−0.855092	+	0.518476i	$0.826499\pi$
$30$	0.627650	+	3.61665i	0.114593	+	0.660307i
$31$	2.02518	−	6.23285i	0.363732	−	1.11945i	−0.587039	−	0.809559i	$-0.699706\pi$
$31$	2.02518	−	6.23285i	0.363732	−	1.11945i	0.950771	−	0.309894i	$-0.100294\pi$
$32$	1.00000			0.176777
$33$	0.699614	−	5.70180i	0.121787	−	0.992556i
$34$	5.15778			0.884553
$35$	2.24568	−	6.91151i	0.379590	−	1.16826i
$36$	−2.87928	−	0.842471i	−0.479880	−	0.140412i
$37$	7.14052	+	5.18789i	1.17389	+	0.852884i	0.991470	−	0.130335i	$-0.0416054\pi$
$37$	7.14052	+	5.18789i	1.17389	+	0.852884i	0.182425	+	0.983220i	$0.441605\pi$
$38$	−0.229139	+	0.0744518i	−0.0371713	+	0.0120777i
$39$	−3.23607	−	0.463712i	−0.518186	−	0.0742533i
$40$	1.24568	−	1.71454i	0.196960	−	0.271092i
$41$	−6.42001	+	4.66441i	−1.00264	+	0.728459i	−0.962652	−	0.270741i	$-0.912731\pi$
$41$	−6.42001	+	4.66441i	−1.00264	+	0.728459i	−0.0399856	+	0.999200i	$0.512731\pi$
$42$	4.26124	+	4.13733i	0.657524	+	0.638403i
$43$		−	6.51583i		−	0.993655i	−0.867849	−	0.496828i	$-0.834498\pi$
$43$		−	6.51583i		−	0.993655i	0.867849	−	0.496828i	$-0.165502\pi$
$44$	−2.64321	+	2.00336i	−0.398479	+	0.302017i
$45$	−5.03112	+	3.88718i	−0.749995	+	0.579466i
$46$	−4.72744	−	1.53604i	−0.697023	−	0.226476i
$47$	1.98077	+	2.72629i	0.288925	+	0.397671i	0.928664	−	0.370921i	$-0.120958\pi$
$47$	1.98077	+	2.72629i	0.288925	+	0.397671i	−0.639740	+	0.768591i	$0.720958\pi$
$48$	0.809017	+	1.53150i	0.116772	+	0.221053i
$49$	−1.47047	−	4.52566i	−0.210068	−	0.646522i
$50$	0.157176	+	0.483737i	0.0222280	+	0.0684107i
$51$	4.17274	+	7.89915i	0.584300	+	1.10610i
$52$	1.10940	+	1.52696i	0.153847	+	0.211752i
$53$	5.91040	+	1.92040i	0.811856	+	0.263788i	0.685384	−	0.728182i	$-0.259635\pi$
$53$	5.91040	+	1.92040i	0.811856	+	0.263788i	0.126472	+	0.991970i	$0.459635\pi$
$54$	−1.03914	−	5.09119i	−0.141409	−	0.692823i
$55$	0.142225	+	7.02743i	0.0191776	+	0.947579i
$56$		−	3.42908i		−	0.458229i
$57$	−0.299400	−	0.290694i	−0.0396566	−	0.0385033i
$58$	−3.37235	+	2.45016i	−0.442811	+	0.321721i
$59$	−1.62931	+	2.24256i	−0.212118	+	0.291956i	−0.901797	−	0.432160i	$-0.857752\pi$
$59$	−1.62931	+	2.24256i	−0.212118	+	0.291956i	0.689679	+	0.724115i	$0.257752\pi$
$60$	3.63359	+	0.520675i	0.469095	+	0.0672189i
$61$	1.53975	−	0.500295i	0.197145	−	0.0640563i	−0.208780	−	0.977963i	$-0.566949\pi$
$61$	1.53975	−	0.500295i	0.197145	−	0.0640563i	0.405925	+	0.913906i	$0.366949\pi$
$62$	−5.30198	−	3.85211i	−0.673352	−	0.489219i
$63$	−2.88889	+	9.87326i	−0.363967	+	1.24391i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	4.00000			0.496139
$66$	−5.20654	−	2.42733i	−0.640881	−	0.298783i
$67$	−9.98396			−1.21973			−0.609867	−	0.792504i	$-0.708777\pi$
$67$	−9.98396			−1.21973			−0.609867	+	0.792504i	$0.708777\pi$
$68$	1.59384	−	4.90534i	0.193282	−	0.594860i
$69$	−1.47214	−	8.48275i	−0.177224	−	1.02120i
$70$	−5.87928	−	4.27155i	−0.702708	−	0.510547i
$71$	−9.47214	+	3.07768i	−1.12414	+	0.365254i	−0.811345	−	0.584568i	$-0.801264\pi$
$71$	−9.47214	+	3.07768i	−1.12414	+	0.365254i	−0.312791	+	0.949822i	$0.601264\pi$
$72$	−1.69098	+	2.47802i	−0.199284	+	0.292037i
$73$	−1.45756	+	2.00616i	−0.170595	+	0.234803i	−0.885751	−	0.464162i	$-0.846356\pi$
$73$	−1.45756	+	2.00616i	−0.170595	+	0.234803i	0.715156	+	0.698965i	$0.246356\pi$
$74$	7.14052	−	5.18789i	0.830069	−	0.603080i
$75$	−0.613685	+	0.632066i	−0.0708623	+	0.0729847i
$76$			0.240931i			0.0276367i
$77$	6.86966	+	9.06377i	0.782871	+	1.03291i
$78$	−1.44102	+	2.93439i	−0.163163	+	0.332254i
$79$	10.7741	+	3.50072i	1.21218	+	0.393862i	0.844229	−	0.535982i	$-0.180059\pi$
$79$	10.7741	+	3.50072i	1.21218	+	0.393862i	0.367953	+	0.929844i	$0.380059\pi$
$80$	−1.24568	−	1.71454i	−0.139272	−	0.191691i
$81$	6.95647	−	5.71030i	0.772941	−	0.634478i
$82$	2.45223	+	7.54718i	0.270803	+	0.833447i
$83$	2.12232	+	6.53182i	0.232954	+	0.716960i	0.997386	+	0.0722554i	$0.0230197\pi$
$83$	2.12232	+	6.53182i	0.232954	+	0.716960i	−0.764432	+	0.644705i	$0.776980\pi$
$84$	5.25163	−	2.77418i	0.573000	−	0.302688i
$85$	−6.42497	−	8.84322i	−0.696886	−	0.959181i
$86$	−6.19693	−	2.01350i	−0.668232	−	0.217122i
$87$	−6.48070	−	3.18254i	−0.694804	−	0.341204i
$88$	1.08851	+	3.13291i	0.116035	+	0.333970i
$89$		−	2.47254i		−	0.262088i	−0.991377	−	0.131044i	$-0.958167\pi$
$89$		−	2.47254i		−	0.262088i	0.991377	−	0.131044i	$-0.0418330\pi$
$90$	2.14222	+	5.98608i	0.225810	+	0.630989i
$91$	5.23607	−	3.80423i	0.548889	−	0.398791i
$92$	−2.92172	+	4.02140i	−0.304610	+	0.419260i
$93$	1.61012	−	11.2364i	0.166962	−	1.16516i
$94$	3.20495	−	1.04135i	0.330565	−	0.107407i
$95$	0.413086	+	0.300124i	0.0423817	+	0.0307921i
$96$	1.70654	−	0.296161i	0.174173	−	0.0302268i
$97$	−4.08582	+	12.5749i	−0.414852	+	1.27678i	0.497531	+	0.867446i	$0.334240\pi$
$97$	−4.08582	+	12.5749i	−0.414852	+	1.27678i	−0.912383	+	0.409338i	$0.865760\pi$
$98$	−4.75856			−0.480687
$99$	−0.494732	−	9.93757i	−0.0497225	−	0.998763i
$100$	0.508631			0.0508631
$101$	0.760259	−	2.33984i	0.0756486	−	0.232822i	−0.906081	−	0.423105i	$-0.860940\pi$
$101$	0.760259	−	2.33984i	0.0756486	−	0.232822i	0.981729	+	0.190282i	$0.0609403\pi$
$102$	8.80198	−	1.52754i	0.871526	−	0.151249i
$103$	3.72914	+	2.70938i	0.367443	+	0.266963i	0.756150	−	0.654399i	$-0.227078\pi$
$103$	3.72914	+	2.70938i	0.367443	+	0.266963i	−0.388707	+	0.921361i	$0.627078\pi$
$104$	1.79505	−	0.583248i	0.176019	−	0.0571921i
$105$	1.78544	−	12.4599i	0.174241	−	1.21596i
$106$	3.65283	−	5.02768i	0.354794	−	0.488332i
$107$	14.6716	−	10.6596i	1.41836	−	1.03050i	0.426322	−	0.904572i	$-0.359809\pi$
$107$	14.6716	−	10.6596i	1.41836	−	1.03050i	0.992039	−	0.125928i	$-0.0401909\pi$
$108$	−5.16312	−	0.584981i	−0.496821	−	0.0562898i
$109$			0.702783i			0.0673144i	0.999433	+	0.0336572i	$0.0107154\pi$
$109$			0.702783i			0.0673144i	−0.999433	+	0.0336572i	$0.989285\pi$
$110$	6.72744	+	2.03633i	0.641436	+	0.194157i
$111$	13.7221	+	6.73861i	1.30244	+	0.639601i
$112$	−3.26124	−	1.05964i	−0.308159	−	0.100127i
$113$	2.51821	+	3.46601i	0.236893	+	0.326055i	0.910867	−	0.412700i	$-0.135414\pi$
$113$	2.51821	+	3.46601i	0.236893	+	0.326055i	−0.673974	+	0.738755i	$0.735414\pi$
$114$	−0.368986	+	0.194917i	−0.0345587	+	0.0182557i
$115$	3.25530	+	10.0188i	0.303558	+	0.934257i
$116$	1.28812	+	3.96443i	0.119599	+	0.368089i
$117$	−5.65982	+	0.167054i	−0.523251	+	0.0154442i
$118$	1.62931	+	2.24256i	0.149990	+	0.206444i
$119$	−16.8208	−	5.46541i	−1.54196	−	0.501013i
$120$	1.61803	−	3.29486i	0.147706	−	0.300778i
$121$	−9.15350	−	6.10028i	−0.832137	−	0.554571i
$122$		−	1.61899i		−	0.146576i
$123$	−9.57461	+	9.86138i	−0.863314	+	0.889171i
$124$	−5.30198	+	3.85211i	−0.476132	+	0.345930i
$125$	6.86202	−	9.44475i	0.613757	−	0.844765i
$126$	8.49731	+	5.79851i	0.757001	+	0.516572i
$127$	−16.6803	+	5.41975i	−1.48013	+	0.480925i	−0.934153	−	0.356872i	$-0.883843\pi$
$127$	−16.6803	+	5.41975i	−1.48013	+	0.480925i	−0.545982	+	0.837797i	$0.683843\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−1.92974	−	11.1195i	−0.169904	−	0.979022i
$130$	1.23607	−	3.80423i	0.108410	−	0.333653i
$131$	4.82298			0.421386			0.210693	−	0.977552i	$-0.432428\pi$
$131$	4.82298			0.421386			0.210693	+	0.977552i	$0.432428\pi$
$132$	−3.91743	+	4.20163i	−0.340969	+	0.365705i
$133$	0.826171			0.0716381
$134$	−3.08521	+	9.49531i	−0.266522	+	0.820270i
$135$	−7.43459	+	8.12366i	−0.639868	+	0.699173i
$136$	−4.17274	−	3.03167i	−0.357809	−	0.259964i
$137$	−17.1743	+	5.58026i	−1.46730	+	0.476754i	−0.930291	−	0.366823i	$-0.880445\pi$
$137$	−17.1743	+	5.58026i	−1.46730	+	0.476754i	−0.537008	+	0.843577i	$0.680445\pi$
$138$	−8.52249	−	1.22123i	−0.725482	−	0.103958i
$139$	0.581539	−	0.800420i	0.0493255	−	0.0678907i	−0.783642	−	0.621213i	$-0.786640\pi$
$139$	0.581539	−	0.800420i	0.0493255	−	0.0678907i	0.832967	+	0.553322i	$0.186640\pi$
$140$	−5.87928	+	4.27155i	−0.496890	+	0.361012i
$141$	4.18769	+	4.06591i	0.352667	+	0.342411i
$142$			9.95959i			0.835790i
$143$	−3.57625	+	5.13778i	−0.299061	+	0.429642i
$144$	1.83419	+	2.37397i	0.152849	+	0.197831i
$145$	8.40177	+	2.72990i	0.697729	+	0.226706i
$146$	1.45756	+	2.00616i	0.120629	+	0.166031i
$147$	−3.84975	−	7.28773i	−0.317522	−	0.601082i
$148$	−2.72744	−	8.39419i	−0.224194	−	0.689998i
$149$	−4.32227	−	13.3026i	−0.354094	−	1.08979i	−0.956533	−	0.291624i	$-0.905804\pi$
$149$	−4.32227	−	13.3026i	−0.354094	−	1.08979i	0.602439	−	0.798165i	$-0.294196\pi$
$150$	0.411491	+	0.778968i	0.0335981	+	0.0636025i
$151$	−3.71979	−	5.11985i	−0.302712	−	0.416648i	0.630379	−	0.776288i	$-0.282900\pi$
$151$	−3.71979	−	5.11985i	−0.302712	−	0.416648i	−0.933091	+	0.359640i	$0.882900\pi$
$152$	0.229139	+	0.0744518i	0.0185856	+	0.00603884i
$153$	9.46037	+	12.2444i	0.764826	+	0.989903i
$154$	10.7430	−	3.73258i	0.865695	−	0.300780i
$155$			13.8890i			1.11559i
$156$	2.34547	+	2.27726i	0.187788	+	0.182327i
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$	6.65877	−	9.16501i	0.529743	−	0.729129i
$159$	10.6551	+	1.52682i	0.845004	+	0.121085i
$160$	−2.01556	+	0.654895i	−0.159344	+	0.0517740i
$161$	13.7897	+	10.0188i	1.08678	+	0.789591i
$162$	−3.28115	−	8.38057i	−0.257792	−	0.658440i
$163$	2.64222	−	8.13193i	0.206955	−	0.636942i	−0.792672	−	0.609648i	$-0.791311\pi$
$163$	2.64222	−	8.13193i	0.206955	−	0.636942i	0.999627	−	0.0272943i	$-0.00868912\pi$
$164$	7.93557			0.619664
$165$	2.32397	+	11.9505i	0.180921	+	0.930345i
$166$	6.86796			0.533057
$167$	0.508631	−	1.56541i	0.0393591	−	0.121135i	−0.929446	−	0.368957i	$-0.879715\pi$
$167$	0.508631	−	1.56541i	0.0393591	−	0.121135i	0.968805	+	0.247822i	$0.0797149\pi$
$168$	−1.01556	−	5.85186i	−0.0783521	−	0.451481i
$169$	−7.63519	−	5.54729i	−0.587322	−	0.426715i
$170$	−10.3958	+	3.37781i	−0.797323	+	0.259066i
$171$	−0.597032	−	0.407411i	−0.0456562	−	0.0311555i
$172$	−3.82991	+	5.27142i	−0.292028	+	0.401942i
$173$	2.83854	−	2.06232i	0.215810	−	0.156795i	−0.474628	−	0.880186i	$-0.657418\pi$
$173$	2.83854	−	2.06232i	0.215810	−	0.156795i	0.690439	+	0.723391i	$0.257418\pi$
$174$	−5.02942	+	5.18005i	−0.381279	+	0.392699i
$175$		−	1.74413i		−	0.131844i
$176$	3.31595	−	0.0671098i	0.249949	−	0.00505859i
$177$	−2.11633	+	4.30956i	−0.159073	+	0.323926i
$178$	−2.35152	−	0.764056i	−0.176254	−	0.0572684i
$179$	−7.80160	−	10.7380i	−0.583119	−	0.802595i	0.410914	−	0.911674i	$-0.365210\pi$
$179$	−7.80160	−	10.7380i	−0.583119	−	0.802595i	−0.994033	+	0.109079i	$0.965210\pi$
$180$	6.35509	−	0.187575i	0.473680	−	0.0139810i
$181$	−2.29709	−	7.06971i	−0.170741	−	0.525488i	0.828672	−	0.559734i	$-0.189097\pi$
$181$	−2.29709	−	7.06971i	−0.170741	−	0.525488i	−0.999413	+	0.0342467i	$0.989097\pi$
$182$	−2.00000	−	6.15537i	−0.148250	−	0.456266i
$183$	2.47948	−	1.30979i	0.183289	−	0.0968225i
$184$	2.92172	+	4.02140i	0.215392	+	0.296461i
$185$	−17.7897	−	5.78022i	−1.30792	−	0.424970i
$186$	−10.1889	−	5.00356i	−0.747087	−	0.366879i
$187$	17.1029	−	0.346138i	1.25069	−	0.0253121i
$188$		−	3.36988i		−	0.245774i
$189$	−2.00594	+	17.7047i	−0.145911	+	1.28783i
$190$	0.413086	−	0.300124i	0.0299684	−	0.0217733i
$191$	−1.52249	+	2.09553i	−0.110163	+	0.151627i	−0.860539	−	0.509385i	$-0.829873\pi$
$191$	−1.52249	+	2.09553i	−0.110163	+	0.151627i	0.750375	+	0.661012i	$0.229873\pi$
$192$	0.245684	−	1.71454i	0.0177307	−	0.123736i
$193$	18.5702	−	6.03383i	1.33671	−	0.434325i	0.448511	−	0.893777i	$-0.351954\pi$
$193$	18.5702	−	6.03383i	1.33671	−	0.434325i	0.888202	+	0.459453i	$0.151954\pi$
$194$	10.6968	+	7.77169i	0.767987	+	0.557975i
$195$	6.82617	−	1.18465i	0.488832	−	0.0848342i
$196$	−1.47047	+	4.52566i	−0.105034	+	0.323261i
$197$	5.38713			0.383817			0.191908	−	0.981413i	$-0.438532\pi$
$197$	5.38713			0.383817			0.191908	+	0.981413i	$0.438532\pi$
$198$	−9.60407	−	2.60036i	−0.682531	−	0.184799i
$199$	7.38713			0.523659			0.261830	−	0.965114i	$-0.415674\pi$
$199$	7.38713			0.523659			0.261830	+	0.965114i	$0.415674\pi$
$200$	0.157176	−	0.483737i	0.0111140	−	0.0342054i
$201$	−17.0380	+	2.95686i	−1.20177	+	0.208561i
$202$	−1.99038	−	1.44610i	−0.140043	−	0.101747i
$203$	13.5943	−	4.41707i	0.954136	−	0.310018i
$204$	1.26719	−	8.84322i	0.0887209	−	0.619149i
$205$	9.88522	−	13.6058i	0.690414	−	0.950273i
$206$	3.72914	−	2.70938i	0.259821	−	0.188771i
$207$	−5.02453	−	14.0402i	−0.349229	−	0.975860i
$208$		−	1.88743i		−	0.130870i
$209$	−0.754817	+	0.262256i	−0.0522118	+	0.0181406i
$210$	−11.2983	−	5.54836i	−0.779657	−	0.382873i
$211$	−8.14317	−	2.64588i	−0.560599	−	0.182150i	0.0149917	−	0.999888i	$-0.495228\pi$
$211$	−8.14317	−	2.64588i	−0.560599	−	0.182150i	−0.575591	+	0.817738i	$0.695228\pi$
$212$	−3.65283	−	5.02768i	−0.250877	−	0.345303i
$213$	−15.2531	+	8.05748i	−1.04513	+	0.552089i
$214$	−5.60407	−	17.2475i	−0.383086	−	1.17902i
$215$	4.26719	+	13.1331i	0.291020	+	0.895667i
$216$	−2.15184	+	4.72965i	−0.146414	+	0.321812i
$217$	13.2092	+	18.1809i	0.896698	+	1.23420i
$218$	0.668387	+	0.217172i	0.0452689	+	0.0147087i
$219$	−1.89324	+	3.85527i	−0.127934	+	0.260515i
$220$	4.01556	−	5.76891i	0.270729	−	0.388940i
$221$		−	9.73495i		−	0.654844i
$222$	10.6492	−	10.9681i	0.714724	−	0.736131i
$223$	−0.0407361	+	0.0295965i	−0.00272789	+	0.00198193i	−0.589148	−	0.808025i	$-0.700537\pi$
$223$	−0.0407361	+	0.0295965i	−0.00272789	+	0.00198193i	0.586420	+	0.810007i	$0.300537\pi$
$224$	−2.01556	+	2.77418i	−0.134670	+	0.185358i
$225$	−0.860086	+	1.26040i	−0.0573391	+	0.0840265i
$226$	4.07454	−	1.32390i	0.271035	−	0.0880645i
$227$	−11.5589	−	8.39806i	−0.767194	−	0.557399i	0.133914	−	0.990993i	$-0.457245\pi$
$227$	−11.5589	−	8.39806i	−0.767194	−	0.557399i	−0.901108	+	0.433594i	$0.857245\pi$
$228$	0.0713545	+	0.411159i	0.00472557	+	0.0272297i
$229$	−9.34547	+	28.7624i	−0.617566	+	1.90067i	−0.271783	+	0.962359i	$0.587613\pi$
$229$	−9.34547	+	28.7624i	−0.617566	+	1.90067i	−0.345783	+	0.938314i	$0.612387\pi$
$230$	10.5344			0.694616
$231$	14.4077	+	13.4332i	0.947958	+	0.883838i
$232$	4.16845			0.273672
$233$	−0.874011	+	2.68993i	−0.0572583	+	0.176223i	−0.975595	−	0.219576i	$-0.929532\pi$
$233$	−0.874011	+	2.68993i	−0.0572583	+	0.176223i	0.918337	+	0.395799i	$0.129532\pi$
$234$	−1.59010	+	5.43443i	−0.103948	+	0.355260i
$235$	−5.77779	−	4.19781i	−0.376901	−	0.273835i
$236$	2.63628	−	0.856580i	0.171607	−	0.0557586i
$237$	19.4233	+	2.78326i	1.26168	+	0.180792i
$238$	−10.3958	+	14.3086i	−0.673861	+	0.927490i
$239$	−0.918528	+	0.667349i	−0.0594146	+	0.0431672i	−0.617096	−	0.786888i	$-0.711691\pi$
$239$	−0.918528	+	0.667349i	−0.0594146	+	0.0431672i	0.557682	+	0.830055i	$0.311691\pi$
$240$	−2.63359	−	2.55701i	−0.169998	−	0.165054i
$241$		−	15.0464i		−	0.969223i	−0.874730	−	0.484611i	$-0.838961\pi$
$241$		−	15.0464i		−	0.969223i	0.874730	−	0.484611i	$-0.161039\pi$
$242$	−8.63030	+	6.82041i	−0.554777	+	0.438432i
$243$	10.1803	−	11.8051i	0.653069	−	0.757298i
$244$	−1.53975	−	0.500295i	−0.0985724	−	0.0320281i
$245$	5.92766	+	8.15872i	0.378704	+	0.521242i
$246$	6.42001	+	12.1533i	0.409325	+	0.774868i
$247$	0.140523	+	0.432484i	0.00894124	+	0.0275183i
$248$	2.02518	+	6.23285i	0.128599	+	0.395786i
$249$	5.55630	+	10.5183i	0.352116	+	0.666569i
$250$	−6.86202	−	9.44475i	−0.433992	−	0.597339i
$251$	9.16478	+	2.97782i	0.578476	+	0.187958i	0.583618	−	0.812029i	$-0.301637\pi$
$251$	9.16478	+	2.97782i	0.578476	+	0.187958i	−0.00514185	+	0.999987i	$0.501637\pi$
$252$	8.14052	−	6.28959i	0.512805	−	0.396207i
$253$	−15.7790	−	4.77616i	−0.992018	−	0.300275i
$254$			17.5387i			1.10047i
$255$	−13.5835	−	13.1885i	−0.850632	−	0.825896i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−7.85036	+	10.8051i	−0.489692	+	0.674003i	−0.980331	−	0.197360i	$-0.936763\pi$
$257$	−7.85036	+	10.8051i	−0.489692	+	0.674003i	0.490639	+	0.871363i	$0.336763\pi$
$258$	−11.1716	−	1.60084i	−0.695516	−	0.0996639i
$259$	−28.7843	+	9.35259i	−1.78857	+	0.581141i
$260$	−3.23607	−	2.35114i	−0.200692	−	0.145812i
$261$	−12.0021	−	3.51180i	−0.742914	−	0.217375i
$262$	1.49038	−	4.58693i	0.0920762	−	0.283381i
$263$	−9.33677			−0.575730			−0.287865	−	0.957671i	$-0.592945\pi$
$263$	−9.33677			−0.575730			−0.287865	+	0.957671i	$0.592945\pi$
$264$	2.78544	+	5.02408i	0.171432	+	0.309211i
$265$	−13.1704			−0.809053
$266$	0.255301	−	0.785736i	0.0156535	−	0.0481765i
$267$	−0.732270	−	4.21949i	−0.0448142	−	0.258229i
$268$	8.07719	+	5.86842i	0.493393	+	0.358471i
$269$	12.9581	−	4.21035i	0.790071	−	0.256710i	0.113937	−	0.993488i	$-0.463654\pi$
$269$	12.9581	−	4.21035i	0.790071	−	0.256710i	0.676134	+	0.736778i	$0.263654\pi$
$270$	5.42865	+	9.58106i	0.330377	+	0.583085i
$271$	2.75734	−	3.79515i	0.167496	−	0.230539i	−0.717015	−	0.697058i	$-0.754492\pi$
$271$	2.75734	−	3.79515i	0.167496	−	0.230539i	0.884511	+	0.466519i	$0.154492\pi$
$272$	−4.17274	+	3.03167i	−0.253009	+	0.183822i
$273$	7.80891	−	8.04280i	0.472617	−	0.486772i
$274$			18.0581i			1.09093i
$275$	0.553649	+	1.59350i	0.0333863	+	0.0960915i
$276$	−3.79505	+	7.72799i	−0.228435	+	0.465170i
$277$	−7.87652	−	2.55924i	−0.473254	−	0.153770i	0.0626723	−	0.998034i	$-0.480038\pi$
$277$	−7.87652	−	2.55924i	−0.473254	−	0.153770i	−0.535927	+	0.844264i	$0.680038\pi$
$278$	−0.581539	−	0.800420i	−0.0348784	−	0.0480060i
$279$	−0.580052	−	19.6523i	−0.0347268	−	1.17655i
$280$	2.24568	+	6.91151i	0.134205	+	0.413041i
$281$	−3.91369	−	12.0451i	−0.233471	−	0.718551i	−0.997320	−	0.0731563i	$-0.976693\pi$
$281$	−3.91369	−	12.0451i	−0.233471	−	0.718551i	0.763849	−	0.645395i	$-0.223307\pi$
$282$	5.16097	−	2.72629i	0.307332	−	0.162348i
$283$	13.2896	+	18.2916i	0.789985	+	1.08732i	0.994110	+	0.108377i	$0.0345652\pi$
$283$	13.2896	+	18.2916i	0.789985	+	1.08732i	−0.204125	+	0.978945i	$0.565435\pi$
$284$	9.47214	+	3.07768i	0.562068	+	0.182627i
$285$	0.793834	+	0.389835i	0.0470226	+	0.0230918i
$286$	3.78119	+	4.98887i	0.223587	+	0.294998i
$287$		−	27.2117i		−	1.60625i
$288$	2.82458	−	1.01082i	0.166440	−	0.0595634i
$289$	−7.76878	+	5.64435i	−0.456987	+	0.332021i
$290$	5.19258	−	7.14697i	0.304919	−	0.419685i
$291$	−3.24844	+	22.6696i	−0.190427	+	1.32892i
$292$	2.35838	−	0.766285i	0.138014	−	0.0448435i
$293$	−20.2998	−	14.7487i	−1.18593	−	0.861626i	−0.193099	−	0.981179i	$-0.561854\pi$
$293$	−20.2998	−	14.7487i	−1.18593	−	0.861626i	−0.992828	+	0.119553i	$0.961854\pi$
$294$	−8.12068	+	1.40930i	−0.473608	+	0.0821921i
$295$	1.81534	−	5.58703i	0.105693	−	0.325290i
$296$	−8.82617			−0.513011
$297$	−3.78741	−	16.8124i	−0.219768	−	0.975552i
$298$	−13.9871			−0.810254
$299$	−2.89916	+	8.92270i	−0.167663	+	0.516013i
$300$	0.868001	−	0.150637i	0.0501140	−	0.00869703i
$301$	18.0761	+	13.1331i	1.04189	+	0.756977i
$302$	−6.01875	+	1.95561i	−0.346340	+	0.112533i
$303$	0.604445	−	4.21819i	0.0347245	−	0.242329i
$304$	0.141616	−	0.194917i	0.00812222	−	0.0111793i
$305$	−2.77582	+	2.01675i	−0.158943	+	0.115479i
$306$	14.5686	−	5.21361i	0.832829	−	0.298042i
$307$		−	16.0682i		−	0.917058i	−0.888679	−	0.458529i	$-0.848377\pi$
$307$		−	16.0682i		−	0.917058i	0.888679	−	0.458529i	$-0.151623\pi$
$308$	−0.230125	−	11.3706i	−0.0131126	−	0.647902i
$309$	7.16635	+	3.51924i	0.407679	+	0.200203i
$310$	13.2092	+	4.29193i	0.750232	+	0.243765i
$311$	5.65772	+	7.78718i	0.320820	+	0.441571i	0.938717	−	0.344688i	$-0.112015\pi$
$311$	5.65772	+	7.78718i	0.320820	+	0.441571i	−0.617897	+	0.786259i	$0.712015\pi$
$312$	2.89060	−	1.52696i	0.163648	−	0.0864472i
$313$	6.21555	+	19.1295i	0.351324	+	1.08126i	0.958111	+	0.286399i	$0.0924581\pi$
$313$	6.21555	+	19.1295i	0.351324	+	1.08126i	−0.606787	+	0.794865i	$0.707542\pi$
$314$	−1.14590	−	3.52671i	−0.0646668	−	0.199024i
$315$	−0.643210	−	21.7921i	−0.0362408	−	1.22784i
$316$	−6.65877	−	9.16501i	−0.374585	−	0.515572i
$317$	17.5481	+	5.70172i	0.985599	+	0.320241i	0.757097	−	0.653303i	$-0.226617\pi$
$317$	17.5481	+	5.70172i	0.985599	+	0.320241i	0.228503	+	0.973543i	$0.426617\pi$
$318$	4.74470	−	9.66179i	0.266070	−	0.541806i
$319$	−11.0181	+	8.35090i	−0.616895	+	0.467561i
$320$			2.11929i			0.118472i
$321$	21.8808	−	22.5362i	1.22127	−	1.25785i
$322$	13.7897	−	10.0188i	0.768469	−	0.558325i
$323$	0.730424	−	1.00534i	0.0406419	−	0.0559387i
$324$	−8.98433	+	0.530822i	−0.499130	+	0.0294901i
$325$	0.913019	−	0.296658i	0.0506452	−	0.0164556i
$326$	−6.91743	−	5.02581i	−0.383121	−	0.278354i
$327$	0.208137	+	1.19933i	0.0115100	+	0.0663231i
$328$	2.45223	−	7.54718i	0.135402	−	0.416723i
$329$	−11.5556			−0.637080
$330$	12.0837	+	1.48268i	0.665188	+	0.0816189i
$331$	−5.03641			−0.276826			−0.138413	−	0.990375i	$-0.544200\pi$
$331$	−5.03641			−0.276826			−0.138413	+	0.990375i	$0.544200\pi$
$332$	2.12232	−	6.53182i	0.116477	−	0.358480i
$333$	25.4130	+	7.43579i	1.39262	+	0.407479i
$334$	−1.33161	−	0.967474i	−0.0728626	−	0.0529378i
$335$	20.1233	−	6.53844i	1.09945	−	0.357233i
$336$	−5.87928	−	0.842471i	−0.320741	−	0.0459605i
$337$	10.3769	−	14.2826i	0.565267	−	0.778024i	−0.426717	−	0.904385i	$-0.640330\pi$
$337$	10.3769	−	14.2826i	0.565267	−	0.778024i	0.991984	+	0.126361i	$0.0403299\pi$
$338$	−7.63519	+	5.54729i	−0.415299	+	0.301733i
$339$	5.32393	+	5.16911i	0.289156	+	0.280747i
$340$			10.9308i			0.592807i
$341$	−17.8396	−	12.4176i	−0.966068	−	0.672450i
$342$	−0.571964	+	0.441914i	−0.0309282	+	0.0238960i
$343$	−7.30989	−	2.37513i	−0.394697	−	0.128245i
$344$	3.82991	+	5.27142i	0.206495	+	0.284216i
$345$	8.52249	+	16.1334i	0.458835	+	0.868593i
$346$	−1.08423	−	3.33691i	−0.0582884	−	0.179393i
$347$	4.64355	+	14.2914i	0.249279	+	0.767201i	0.994903	+	0.100834i	$0.0321512\pi$
$347$	4.64355	+	14.2914i	0.249279	+	0.767201i	−0.745625	+	0.666366i	$0.767849\pi$
$348$	3.37235	+	6.38399i	0.180777	+	0.342218i
$349$	2.05443	+	2.82768i	0.109971	+	0.151362i	0.860455	−	0.509527i	$-0.170179\pi$
$349$	2.05443	+	2.82768i	0.109971	+	0.151362i	−0.750484	+	0.660889i	$0.770179\pi$
$350$	−1.65877	−	0.538967i	−0.0886650	−	0.0288090i
$351$	−9.60925	+	1.96131i	−0.512904	+	0.104687i
$352$	0.960858	−	3.17439i	0.0512139	−	0.169196i
$353$			25.2674i			1.34485i	0.740167	+	0.672423i	$0.234747\pi$
$353$			25.2674i			1.34485i	−0.740167	+	0.672423i	$0.765253\pi$
$354$	3.44465	+	3.34448i	0.183081	+	0.177757i
$355$	17.0761	−	12.4065i	0.906305	−	0.658469i
$356$	−1.45332	+	2.00032i	−0.0770258	+	0.106017i
$357$	−30.3241	−	4.34528i	−1.60492	−	0.229977i
$358$	−12.6233	+	4.10155i	−0.667160	+	0.216773i
$359$	15.6095	+	11.3409i	0.823836	+	0.598552i	0.917809	−	0.397023i	$-0.129957\pi$
$359$	15.6095	+	11.3409i	0.823836	+	0.598552i	−0.0939725	+	0.995575i	$0.529957\pi$
$360$	1.78544	−	6.10201i	0.0941007	−	0.321604i
$361$	5.85339	−	18.0149i	0.308073	−	0.948151i
$362$	−7.43354			−0.390698
$363$	−17.4275	−	7.69947i	−0.914707	−	0.404117i
$364$	−6.47214			−0.339232
$365$	1.62398	−	4.99809i	0.0850029	−	0.261612i
$366$	−0.479482	−	2.76288i	−0.0250629	−	0.144418i
$367$	0.726385	+	0.527749i	0.0379170	+	0.0275483i	0.606582	−	0.795021i	$-0.292540\pi$
$367$	0.726385	+	0.527749i	0.0379170	+	0.0275483i	−0.568665	+	0.822569i	$0.692540\pi$
$368$	4.72744	−	1.53604i	0.246435	−	0.0800715i
$369$	−13.4189	+	19.6645i	−0.698561	+	1.02369i
$370$	−10.9946	+	15.1328i	−0.571583	+	0.786717i
$371$	−17.2403	+	12.5258i	−0.895072	+	0.650308i
$372$	−7.90721	+	8.14404i	−0.409970	+	0.422249i
$373$			26.3407i			1.36387i	0.731413	+	0.681935i	$0.238861\pi$
$373$			26.3407i			1.36387i	−0.731413	+	0.681935i	$0.761139\pi$
$374$	4.95590	−	16.3728i	0.256264	−	0.846618i
$375$	8.91315	−	18.1501i	0.460273	−	0.937269i
$376$	−3.20495	−	1.04135i	−0.165283	−	0.0537036i
$377$	4.62449	+	6.36507i	0.238174	+	0.327818i
$378$	16.2183	+	7.37883i	0.834180	+	0.379526i
$379$	−0.823525	−	2.53455i	−0.0423016	−	0.130191i	0.927675	−	0.373388i	$-0.121804\pi$
$379$	−0.823525	−	2.53455i	−0.0423016	−	0.130191i	−0.969977	+	0.243197i	$0.921804\pi$
$380$	−0.157785	−	0.485611i	−0.00809418	−	0.0249113i
$381$	−26.8605	+	14.1891i	−1.37610	+	0.726929i
$382$	1.52249	+	2.09553i	0.0778973	+	0.107216i
$383$	31.1072	+	10.1073i	1.58950	+	0.516461i	0.964483	−	0.264146i	$-0.0850901\pi$
$383$	31.1072	+	10.1073i	1.58950	+	0.516461i	0.625022	+	0.780607i	$0.285090\pi$
$384$	−1.55470	−	0.763481i	−0.0793380	−	0.0389612i
$385$	−19.7820	−	13.7697i	−1.00819	−	0.701767i
$386$		−	19.5259i		−	0.993841i
$387$	−6.58636	−	18.4045i	−0.334804	−	0.935552i
$388$	10.6968	−	7.77169i	0.543049	−	0.394548i
$389$	−0.990218	+	1.36292i	−0.0502060	+	0.0691027i	−0.833382	−	0.552698i	$-0.813598\pi$
$389$	−0.990218	+	1.36292i	−0.0502060	+	0.0691027i	0.783176	+	0.621800i	$0.213598\pi$
$390$	0.982738	−	6.85815i	0.0497629	−	0.347276i
$391$	24.3831	−	7.92255i	1.23311	−	0.400661i
$392$	3.84975	+	2.79701i	0.194442	+	0.141270i
$393$	8.23063	−	1.42838i	0.415180	−	0.0720523i
$394$	1.66471	−	5.12346i	0.0838671	−	0.258116i
$395$	−24.0085			−1.20800
$396$	−5.44091	+	8.33046i	−0.273416	+	0.418621i
$397$	−8.89235			−0.446294			−0.223147	−	0.974785i	$-0.571633\pi$
$397$	−8.89235			−0.446294			−0.223147	+	0.974785i	$0.571633\pi$
$398$	2.28275	−	7.02557i	0.114424	−	0.352160i
$399$	1.40990	−	0.244680i	0.0705831	−	0.0122493i
$400$	−0.411491	−	0.298966i	−0.0205746	−	0.0149483i
$401$	18.6014	−	6.04398i	0.928912	−	0.301822i	0.194794	−	0.980844i	$-0.437596\pi$
$401$	18.6014	−	6.04398i	0.928912	−	0.301822i	0.734118	+	0.679022i	$0.237596\pi$
$402$	−2.45290	+	17.1179i	−0.122340	+	0.853762i
$403$	−7.27059	+	10.0071i	−0.362174	+	0.498490i
$404$	−1.99038	+	1.44610i	−0.0990253	+	0.0719461i
$405$	−10.2815	+	16.0652i	−0.510893	+	0.798287i
$406$		−	14.2939i		−	0.709396i
$407$	23.3294	−	17.6820i	1.15640	−	0.876463i
$408$	−8.01882	−	3.93787i	−0.396991	−	0.194954i
$409$	23.5359	+	7.64727i	1.16377	+	0.378133i	0.826315	−	0.563208i	$-0.190433\pi$
$409$	23.5359	+	7.64727i	1.16377	+	0.378133i	0.337458	+	0.941341i	$0.390433\pi$
$410$	−9.88522	−	13.6058i	−0.488196	−	0.671945i
$411$	−27.6560	+	14.6093i	−1.36417	+	0.720625i
$412$	−1.42440	−	4.38387i	−0.0701754	−	0.215978i
$413$	−2.93728	−	9.04001i	−0.144534	−	0.444830i
$414$	−14.9057	+	0.439953i	−0.732574	+	0.0216225i
$415$	−8.55531	−	11.7754i	−0.419964	−	0.578030i
$416$	−1.79505	−	0.583248i	−0.0880096	−	0.0285961i
$417$	0.755368	−	1.53818i	0.0369905	−	0.0753250i
$418$	0.0161689	+	0.798915i	0.000790845	+	0.0390762i
$419$			34.8462i			1.70235i	0.524883	+	0.851174i	$0.324109\pi$
$419$			34.8462i			1.70235i	−0.524883	+	0.851174i	$0.675891\pi$
$420$	−8.76817	+	9.03079i	−0.427843	+	0.440657i
$421$	−14.1996	+	10.3166i	−0.692045	+	0.502800i	−0.877332	−	0.479884i	$-0.840679\pi$
$421$	−14.1996	+	10.3166i	−0.692045	+	0.502800i	0.185287	+	0.982684i	$0.440679\pi$
$422$	−5.03276	+	6.92699i	−0.244991	+	0.337201i
$423$	8.35063	+	5.69841i	0.406022	+	0.277066i
$424$	−5.91040	+	1.92040i	−0.287034	+	0.0932631i
$425$	−2.12238	−	1.54200i	−0.102951	−	0.0747981i
$426$	2.94965	+	16.9965i	0.142911	+	0.823482i
$427$	−1.71555	+	5.27992i	−0.0830213	+	0.255513i
$428$	−18.1351			−0.876595
$429$	−4.58141	+	9.82698i	−0.221192	+	0.474451i
$430$	13.8089			0.665925
$431$	−10.3275	+	31.7846i	−0.497456	+	1.53101i	0.315638	+	0.948880i	$0.397782\pi$
$431$	−10.3275	+	31.7846i	−0.497456	+	1.53101i	−0.813094	+	0.582133i	$0.802218\pi$
$432$	3.83321	+	3.50806i	0.184425	+	0.168782i
$433$	−21.9952	−	15.9805i	−1.05702	−	0.767973i	−0.0834881	−	0.996509i	$-0.526606\pi$
$433$	−21.9952	−	15.9805i	−1.05702	−	0.767973i	−0.973535	+	0.228536i	$0.926606\pi$
$434$	21.3729	−	6.94448i	1.02593	−	0.333346i
$435$	15.1465	+	2.17041i	0.726217	+	0.104063i
$436$	0.413086	−	0.568564i	0.0197832	−	0.0272293i
$437$	−0.968880	+	0.703933i	−0.0463478	+	0.0336737i
$438$	3.08154	+	2.99193i	0.147242	+	0.142960i
$439$		−	13.4068i		−	0.639873i	−0.947439	−	0.319936i	$-0.896338\pi$
$439$		−	13.4068i		−	0.639873i	0.947439	−	0.319936i	$-0.103662\pi$
$440$	−4.24568	−	5.60172i	−0.202405	−	0.267051i
$441$	−8.72811	−	11.2967i	−0.415624	−	0.537937i
$442$	−9.25849	−	3.00827i	−0.440381	−	0.143089i
$443$	−10.8348	−	14.9128i	−0.514777	−	0.708530i	0.469939	−	0.882699i	$-0.344276\pi$
$443$	−10.8348	−	14.9128i	−0.514777	−	0.708530i	−0.984716	+	0.174169i	$0.944276\pi$
$444$	−7.14052	−	13.5173i	−0.338874	−	0.641502i
$445$	1.61925	+	4.98355i	0.0767599	+	0.236243i
$446$	0.0155598	+	0.0478882i	0.000736779	+	0.00226757i
$447$	−11.3158	−	21.4213i	−0.535221	−	1.01319i
$448$	2.01556	+	2.77418i	0.0952263	+	0.131068i
$449$	28.8836	+	9.38485i	1.36310	+	0.442898i	0.897077	−	0.441874i	$-0.145686\pi$
$449$	28.8836	+	9.38485i	1.36310	+	0.442898i	0.466024	+	0.884772i	$0.345686\pi$
$450$	0.932928	+	1.20748i	0.0439786	+	0.0569209i
$451$	8.63794	+	24.8615i	0.406745	+	1.17068i
$452$		−	4.28423i		−	0.201513i
$453$	−7.86429	−	7.63559i	−0.369496	−	0.358751i
$454$	−11.5589	+	8.39806i	−0.542488	+	0.394141i
$455$	−8.06224	+	11.0967i	−0.377964	+	0.520222i
$456$	0.413086	+	0.0591931i	0.0193445	+	0.00277197i
$457$	32.9901	−	10.7191i	1.54321	−	0.501419i	0.590950	−	0.806708i	$-0.298753\pi$
$457$	32.9901	−	10.7191i	1.54321	−	0.501419i	0.952260	+	0.305289i	$0.0987530\pi$
$458$	24.4668	+	17.7761i	1.14326	+	0.830625i
$459$	19.7709	+	18.0938i	0.922825	+	0.844548i
$460$	3.25530	−	10.0188i	0.151779	−	0.467128i
$461$	20.8777			0.972370			0.486185	−	0.873856i	$-0.338388\pi$
$461$	20.8777			0.972370			0.486185	+	0.873856i	$0.338388\pi$
$462$	17.2279	−	9.55147i	0.801516	−	0.444374i
$463$	6.14371			0.285522			0.142761	−	0.989757i	$-0.454402\pi$
$463$	6.14371			0.285522			0.142761	+	0.989757i	$0.454402\pi$
$464$	1.28812	−	3.96443i	0.0597996	−	0.184044i
$465$	4.11338	+	23.7021i	0.190753	+	1.09916i
$466$	2.28819	+	1.66247i	0.105998	+	0.0770123i
$467$	−33.1013	+	10.7553i	−1.53174	+	0.497694i	−0.949084	−	0.315022i	$-0.897988\pi$
$467$	−33.1013	+	10.7553i	−1.53174	+	0.497694i	−0.582660	+	0.812716i	$0.697988\pi$
$468$	4.67708	+	3.19161i	0.216198	+	0.147532i
$469$	20.1233	−	27.6973i	0.929206	−	1.27894i
$470$	−5.77779	+	4.19781i	−0.266510	+	0.193631i
$471$	4.47411	−	4.60811i	0.206156	−	0.212331i
$472$		−	2.77195i		−	0.127589i
$473$	−20.6838	−	6.26079i	−0.951042	−	0.287872i
$474$	8.64915	−	17.6126i	0.397269	−	0.808971i
$475$	0.116547	+	0.0378685i	0.00534756	+	0.00173753i
$476$	10.3958	+	14.3086i	0.476492	+	0.655835i
$477$	18.6356	−	0.550043i	0.853264	−	0.0251848i
$478$	0.350846	+	1.07979i	0.0160473	+	0.0493886i
$479$	−10.7639	−	33.1280i	−0.491817	−	1.51366i	−0.821860	−	0.569690i	$-0.807063\pi$
$479$	−10.7639	−	33.1280i	−0.491817	−	1.51366i	0.330043	−	0.943966i	$-0.392937\pi$
$480$	−3.24568	+	1.71454i	−0.148145	+	0.0782576i
$481$	−9.79178	−	13.4772i	−0.446467	−	0.614509i
$482$	−14.3100	−	4.64959i	−0.651801	−	0.211783i
$483$	26.4999	+	13.0135i	1.20578	+	0.592136i
$484$	3.81969	+	10.3155i	0.173622	+	0.468887i
$485$		−	28.0212i		−	1.27238i
$486$	−8.08143	−	13.3301i	−0.366581	−	0.604664i
$487$	4.66471	−	3.38911i	0.211378	−	0.153575i	−0.477059	−	0.878871i	$-0.658297\pi$
$487$	4.66471	−	3.38911i	0.211378	−	0.153575i	0.688437	+	0.725296i	$0.258297\pi$
$488$	−0.951618	+	1.30979i	−0.0430777	+	0.0592914i
$489$	2.10071	−	14.6600i	0.0949972	−	0.662949i
$490$	9.59116	−	3.11636i	0.433284	−	0.140783i
$491$	−8.42871	−	6.12382i	−0.380382	−	0.276364i	0.381121	−	0.924525i	$-0.375538\pi$
$491$	−8.42871	−	6.12382i	−0.380382	−	0.276364i	−0.761503	+	0.648161i	$0.775538\pi$
$492$	13.5424	−	2.35021i	0.610538	−	0.105956i
$493$	6.64386	−	20.4477i	0.299224	−	0.920918i
$494$	0.454741			0.0204597
$495$	7.50523	+	19.7058i	0.337335	+	0.885708i
$496$	6.55361			0.294266
$497$	10.5536	−	32.4807i	0.473394	−	1.45696i
$498$	11.7205	−	2.03402i	0.525207	−	0.0911468i
$499$	17.7151	+	12.8708i	0.793038	+	0.576176i	0.908864	−	0.417094i	$-0.136951\pi$
$499$	17.7151	+	12.8708i	0.793038	+	0.576176i	−0.115825	+	0.993270i	$0.536951\pi$
$500$	−11.1030	+	3.60758i	−0.496540	+	0.161336i
$501$	0.404388	−	2.82207i	0.0180667	−	0.126081i
$502$	5.66415	−	7.79603i	0.252803	−	0.347954i
$503$	−15.8347	+	11.5045i	−0.706032	+	0.512962i	−0.881891	−	0.471453i	$-0.843730\pi$
$503$	−15.8347	+	11.5045i	−0.706032	+	0.512962i	0.175859	+	0.984415i	$0.443730\pi$
$504$	−3.46619	−	9.68569i	−0.154396	−	0.431435i
$505$			5.21397i			0.232019i
$506$	−9.41838	+	13.5308i	−0.418698	+	0.601518i
$507$	−14.6727	−	7.20544i	−0.651636	−	0.320005i
$508$	16.6803	+	5.41975i	0.740067	+	0.240462i
$509$	−21.3064	−	29.3257i	−0.944389	−	1.29984i	−0.953975	−	0.299886i	$-0.903051\pi$
$509$	−21.3064	−	29.3257i	−0.944389	−	1.29984i	0.00958605	−	0.999954i	$-0.496949\pi$
$510$	−16.7405	+	8.84322i	−0.741284	+	0.391584i
$511$	−2.62765	−	8.08708i	−0.116240	−	0.357751i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.13952	−	0.518446i	−0.0503110	−	0.0228899i
$514$	7.85036	+	10.8051i	0.346265	+	0.476592i
$515$	−9.29066	−	3.01872i	−0.409395	−	0.133021i
$516$	−4.97472	+	10.1302i	−0.219000	+	0.445956i
$517$	10.5575	−	3.66815i	0.464321	−	0.161325i
$518$			30.2656i			1.32979i
$519$	4.23331	−	4.36011i	0.185822	−	0.191387i
$520$	−3.23607	+	2.35114i	−0.141911	+	0.103104i
$521$	10.6363	−	14.6396i	0.465985	−	0.641373i	−0.509751	−	0.860322i	$-0.670263\pi$
$521$	10.6363	−	14.6396i	0.465985	−	0.641373i	0.975736	+	0.218948i	$0.0702626\pi$
$522$	−7.04878	+	10.3295i	−0.308517	+	0.452110i
$523$	−23.8450	+	7.74771i	−1.04267	+	0.338784i	−0.779787	−	0.626045i	$-0.784673\pi$
$523$	−23.8450	+	7.74771i	−1.04267	+	0.338784i	−0.262881	+	0.964828i	$0.584673\pi$
$524$	−3.90187	−	2.83488i	−0.170454	−	0.123842i
$525$	−0.516545	−	2.97644i	−0.0225439	−	0.129902i
$526$	−2.88522	+	8.87980i	−0.125802	+	0.387178i
$527$	33.8021			1.47244
$528$	5.63893	−	1.09658i	0.245403	−	0.0477226i
$529$	−1.70807			−0.0742639
$530$	−4.06988	+	12.5258i	−0.176785	+	0.544087i
$531$	−2.33529	+	7.98122i	−0.101343	+	0.346355i
$532$	−0.668387	−	0.485611i	−0.0289782	−	0.0210539i
$533$	14.2448	−	4.62840i	0.617009	−	0.200478i
$534$	−4.23926	−	0.607464i	−0.183451	−	0.0262875i
$535$	−22.5907	+	31.0934i	−0.976680	+	1.34428i
$536$	8.07719	−	5.86842i	0.348881	−	0.253477i
$537$	−16.4939	−	16.0143i	−0.711766	−	0.691068i
$538$		−	13.6250i		−	0.587415i
$539$	−15.7791	+	0.319346i	−0.679655	+	0.0137552i
$540$	10.7897	−	2.20224i	0.464314	−	0.0947692i
$541$	−37.4648	−	12.1730i	−1.61074	−	0.523360i	−0.641006	−	0.767536i	$-0.721483\pi$
$541$	−37.4648	−	12.1730i	−1.61074	−	0.523360i	−0.969731	+	0.244176i	$0.921483\pi$
$542$	−2.75734	−	3.79515i	−0.118438	−	0.163016i
$543$	−6.01386	−	11.3845i	−0.258079	−	0.488554i
$544$	1.59384	+	4.90534i	0.0683355	+	0.210315i
$545$	−0.460249	−	1.41650i	−0.0197149	−	0.0606763i
$546$	−5.23607	−	9.91207i	−0.224083	−	0.424198i
$547$	1.05599	+	1.45344i	0.0451507	+	0.0621446i	0.830995	−	0.556279i	$-0.187772\pi$
$547$	1.05599	+	1.45344i	0.0451507	+	0.0621446i	−0.785845	+	0.618424i	$0.787772\pi$
$548$	17.1743	+	5.58026i	0.733649	+	0.238377i
$549$	3.84343	−	2.96954i	0.164034	−	0.126737i
$550$	1.68659	−	0.0341341i	0.0719166	−	0.00145548i
$551$			1.00431i			0.0427851i
$552$	6.17702	+	5.99739i	0.262911	+	0.255266i
$553$	−31.4275	+	22.8334i	−1.33643	+	0.970976i
$554$	−4.86796	+	6.70017i	−0.206820	+	0.284663i
$555$	−32.0707	−	4.59557i	−1.36133	−	0.195071i
$556$	−0.940950	+	0.305733i	−0.0399052	+	0.0129660i
$557$	34.6574	+	25.1801i	1.46848	+	1.06691i	0.981051	+	0.193750i	$0.0620652\pi$
$557$	34.6574	+	25.1801i	1.46848	+	1.06691i	0.487429	+	0.873163i	$0.337935\pi$
$558$	−18.8697	−	5.52122i	−0.798816	−	0.233732i
$559$	−3.80034	+	11.6963i	−0.160737	+	0.494699i
$560$	7.26719			0.307095
$561$	29.0844	−	5.65593i	1.22794	−	0.238794i
$562$	−12.6650			−0.534240
$563$	−5.33623	+	16.4232i	−0.224895	+	0.692157i	0.773407	+	0.633910i	$0.218551\pi$
$563$	−5.33623	+	16.4232i	−0.224895	+	0.692157i	−0.998302	+	0.0582467i	$0.981449\pi$
$564$	−0.998029	−	5.75085i	−0.0420246	−	0.242154i
$565$	−7.34547	−	5.33680i	−0.309026	−	0.224521i
$566$	21.5030	−	6.98676i	0.903840	−	0.293675i
$567$	1.82023	+	30.8080i	0.0764424	+	1.29381i
$568$	5.85410	−	8.05748i	0.245633	−	0.338084i
$569$	−4.41418	+	3.20709i	−0.185052	+	0.134448i	−0.676454	−	0.736484i	$-0.736484\pi$
$569$	−4.41418	+	3.20709i	−0.185052	+	0.134448i	0.491402	+	0.870933i	$0.336484\pi$
$570$	0.616063	−	0.634515i	0.0258040	−	0.0265769i
$571$			18.8259i			0.787838i	0.919145	+	0.393919i	$0.128881\pi$
$571$			18.8259i			0.787838i	−0.919145	+	0.393919i	$0.871119\pi$
$572$	5.91315	−	2.05448i	0.247241	−	0.0859023i
$573$	−1.97758	+	4.02701i	−0.0826145	+	0.168231i
$574$	−25.8798	−	8.40887i	−1.08020	−	0.350980i
$575$	1.48608	+	2.04541i	0.0619736	+	0.0852994i
$576$	−0.0885088	−	2.99869i	−0.00368787	−	0.124946i
$577$	4.84849	+	14.9221i	0.201845	+	0.621216i	0.999828	+	0.0185361i	$0.00590056\pi$
$577$	4.84849	+	14.9221i	0.201845	+	0.621216i	−0.797983	+	0.602680i	$0.794099\pi$
$578$	2.96741	+	9.13275i	0.123428	+	0.379872i
$579$	29.9039	−	15.7968i	1.24276	−	0.656491i
$580$	−5.19258	−	7.14697i	−0.215610	−	0.296762i
$581$	−22.3981	−	7.27758i	−0.929230	−	0.301925i
$582$	20.5563	+	10.0947i	0.852084	+	0.418441i
$583$	11.7752	−	16.9167i	0.487678	−	0.700617i
$584$		−	2.47975i		−	0.102613i
$585$	11.2983	−	4.04330i	0.467128	−	0.167170i
$586$	−20.2998	+	14.7487i	−0.838577	+	0.609262i
$587$	−1.74399	+	2.40039i	−0.0719821	+	0.0990748i	−0.843490	−	0.537145i	$-0.819503\pi$
$587$	−1.74399	+	2.40039i	−0.0719821	+	0.0990748i	0.771508	+	0.636220i	$0.219503\pi$
$588$	−1.16910	+	8.15872i	−0.0482130	+	0.336460i
$589$	−1.50169	+	0.487928i	−0.0618760	+	0.0201047i
$590$	−4.75261	−	3.45298i	−0.195662	−	0.142157i
$591$	9.19336	−	1.59546i	0.378164	−	0.0656284i
$592$	−2.72744	+	8.39419i	−0.112097	+	0.344999i
$593$	−43.4839			−1.78567			−0.892836	−	0.450383i	$-0.851288\pi$
$593$	−43.4839			−1.78567			−0.892836	+	0.450383i	$0.851288\pi$
$594$	−17.1599	−	1.59327i	−0.704078	−	0.0653726i
$595$	37.4826			1.53664
$596$	−4.32227	+	13.3026i	−0.177047	+	0.544894i
$597$	12.6064	−	2.18778i	0.515948	−	0.0895399i
$598$	7.59010	+	5.51453i	0.310382	+	0.225506i
$599$	24.7770	−	8.05055i	1.01236	−	0.328936i	0.244567	−	0.969632i	$-0.421354\pi$
$599$	24.7770	−	8.05055i	1.01236	−	0.328936i	0.767795	+	0.640696i	$0.221354\pi$
$600$	0.124963	−	0.872067i	0.00510158	−	0.0356020i
$601$	−27.1211	+	37.3290i	−1.10629	+	1.52268i	−0.279529	+	0.960137i	$0.590178\pi$
$601$	−27.1211	+	37.3290i	−1.10629	+	1.52268i	−0.826766	+	0.562546i	$0.809822\pi$
$602$	18.0761	−	13.1331i	0.736727	−	0.535263i
$603$	−28.2005	+	10.0920i	−1.14841	+	0.410979i
$604$			6.32849i			0.257502i
$605$	22.4445	+	6.30089i	0.912498	+	0.256168i
$606$	−3.82495	−	1.87835i	−0.155378	−	0.0763029i
$607$	−9.07413	−	2.94836i	−0.368307	−	0.119670i	0.119015	−	0.992892i	$-0.462026\pi$
$607$	−9.07413	−	2.94836i	−0.368307	−	0.119670i	−0.487322	+	0.873222i	$0.662026\pi$
$608$	−0.141616	−	0.194917i	−0.00574328	−	0.00790495i
$609$	21.8912	−	11.5640i	0.887075	−	0.468599i
$610$	1.06027	+	3.26317i	0.0429290	+	0.132122i
$611$	−1.96548	−	6.04911i	−0.0795146	−	0.244721i
$612$	−0.456510	−	15.4666i	−0.0184533	−	0.625201i
$613$	−6.16173	−	8.48089i	−0.248870	−	0.342540i	0.666245	−	0.745733i	$-0.267900\pi$
$613$	−6.16173	−	8.48089i	−0.248870	−	0.342540i	−0.915115	+	0.403193i	$0.867900\pi$
$614$	−15.2817	−	4.96533i	−0.616720	−	0.200384i
$615$	12.8400	−	26.1466i	0.517760	−	1.05433i
$616$	−10.8852	−	3.29486i	−0.438578	−	0.132754i
$617$			26.7867i			1.07839i	0.842180	+	0.539196i	$0.181272\pi$
$617$			26.7867i			1.07839i	−0.842180	+	0.539196i	$0.818728\pi$
$618$	5.56152	−	5.72810i	0.223717	−	0.230418i
$619$	6.51821	−	4.73575i	0.261989	−	0.190346i	−0.449035	−	0.893514i	$-0.648232\pi$
$619$	6.51821	−	4.73575i	0.261989	−	0.190346i	0.711023	+	0.703168i	$0.248232\pi$
$620$	8.16373	−	11.2364i	0.327863	−	0.451265i
$621$	−12.7327	−	22.4721i	−0.510947	−	0.901775i
$622$	9.15438	−	2.97444i	0.367057	−	0.119264i
$623$	6.85926	+	4.98355i	0.274811	+	0.199662i
$624$	−0.558984	−	3.22098i	−0.0223773	−	0.128942i
$625$	−6.85960	+	21.1117i	−0.274384	+	0.844467i
$626$	20.1139			0.803915
$627$	−1.21046	+	0.671098i	−0.0483410	+	0.0268011i
$628$	−3.70820			−0.147973
$629$	−14.0675	+	43.2954i	−0.560909	+	1.72630i
$630$	−20.9243	−	6.12239i	−0.833642	−	0.243922i
$631$	16.5719	+	12.0402i	0.659718	+	0.479313i	0.866568	−	0.499060i	$-0.166321\pi$
$631$	16.5719	+	12.0402i	0.659718	+	0.479313i	−0.206850	+	0.978373i	$0.566321\pi$
$632$	−10.7741	+	3.50072i	−0.428571	+	0.139251i
$633$	−14.6803	−	2.10361i	−0.583488	−	0.0836109i
$634$	10.8453	−	14.9273i	0.430723	−	0.592839i
$635$	30.0707	−	21.8477i	1.19332	−	0.866998i
$636$	−7.72271	−	7.49813i	−0.306225	−	0.297320i
$637$			8.98144i			0.355858i
$638$	4.53740	+	13.0594i	0.179637	+	0.517027i
$639$	−23.6438	+	18.2678i	−0.935333	+	0.722664i
$640$	2.01556	+	0.654895i	0.0796720	+	0.0258870i
$641$	1.82529	+	2.51229i	0.0720946	+	0.0992296i	0.843541	−	0.537064i	$-0.180467\pi$
$641$	1.82529	+	2.51229i	0.0720946	+	0.0992296i	−0.771447	+	0.636294i	$0.780467\pi$
$642$	−14.6716	−	27.7740i	−0.579044	−	1.09615i
$643$	−12.1432	−	37.3728i	−0.478880	−	1.47384i	−0.840653	−	0.541574i	$-0.817828\pi$
$643$	−12.1432	−	37.3728i	−0.478880	−	1.47384i	0.361773	−	0.932266i	$-0.382172\pi$
$644$	−5.26719	−	16.2107i	−0.207556	−	0.638793i
$645$	11.1716	+	21.1483i	0.439883	+	0.832715i
$646$	−0.730424	−	1.00534i	−0.0287381	−	0.0395547i
$647$	−34.1070	−	11.0820i	−1.34088	−	0.435680i	−0.451268	−	0.892388i	$-0.649028\pi$
$647$	−34.1070	−	11.0820i	−1.34088	−	0.435680i	−0.889616	+	0.456709i	$0.849028\pi$
$648$	−2.27147	+	8.70864i	−0.0892318	+	0.342108i
$649$	5.55321	+	7.32685i	0.217982	+	0.287604i
$650$		−	0.960005i		−	0.0376545i
$651$	27.9265	+	27.1144i	1.09453	+	1.06270i
$652$	−6.91743	+	5.02581i	−0.270908	+	0.196826i
$653$	1.38621	−	1.90795i	0.0542465	−	0.0746639i	−0.781032	−	0.624491i	$-0.785306\pi$
$653$	1.38621	−	1.90795i	0.0542465	−	0.0746639i	0.835278	+	0.549827i	$0.185306\pi$
$654$	1.20495	+	0.172663i	0.0471172	+	0.00675166i
$655$	−9.72101	+	3.15855i	−0.379831	+	0.123415i
$656$	−6.42001	−	4.66441i	−0.250659	−	0.182115i
$657$	−2.08912	+	7.13990i	−0.0815043	+	0.278554i
$658$	−3.57087	+	10.9900i	−0.139207	+	0.428435i
$659$	−8.51039			−0.331518			−0.165759	−	0.986166i	$-0.553007\pi$
$659$	−8.51039			−0.331518			−0.165759	+	0.986166i	$0.553007\pi$
$660$	5.14420	−	11.0341i	0.200238	−	0.429504i
$661$	42.4546			1.65129			0.825646	−	0.564189i	$-0.190811\pi$
$661$	42.4546			1.65129			0.825646	+	0.564189i	$0.190811\pi$
$662$	−1.55634	+	4.78991i	−0.0604888	+	0.186165i
$663$	−2.88312	−	16.6131i	−0.111971	−	0.645200i
$664$	−5.55630	−	4.03689i	−0.215626	−	0.156662i
$665$	−1.66520	+	0.541056i	−0.0645736	+	0.0209812i
$666$	14.9249	−	21.8714i	0.578328	−	0.847500i
$667$	−12.1790	+	16.7630i	−0.471574	+	0.649066i
$668$	−1.33161	+	0.967474i	−0.0515217	+	0.0374327i
$669$	−0.0607526	+	0.0625722i	−0.00234883	+	0.00241918i
$670$		−	21.1588i		−	0.817438i
$671$	−0.108650	−	5.36848i	−0.00419439	−	0.207248i
$672$	−2.61803	+	5.33119i	−0.100993	+	0.205655i
$673$	45.4817	+	14.7779i	1.75319	+	0.569646i	0.996459	−	0.0840801i	$-0.0267952\pi$
$673$	45.4817	+	14.7779i	1.75319	+	0.569646i	0.756731	+	0.653726i	$0.226795\pi$
$674$	−10.3769	−	14.2826i	−0.399704	−	0.550146i
$675$	−1.09449	+	2.40565i	−0.0421271	+	0.0925934i
$676$	2.91638	+	8.97570i	0.112169	+	0.345219i
$677$	1.70016	+	5.23254i	0.0653423	+	0.201103i	0.978397	−	0.206734i	$-0.0662833\pi$
$677$	1.70016	+	5.23254i	0.0653423	+	0.201103i	−0.913055	+	0.407837i	$0.866283\pi$
$678$	6.56130	−	3.46601i	0.251985	−	0.133111i
$679$	−26.6497	−	36.6802i	−1.02272	−	1.40766i
$680$	10.3958	+	3.37781i	0.398662	+	0.129533i
$681$	−22.2130	−	10.9083i	−0.851205	−	0.418009i
$682$	−17.3226	+	13.1292i	−0.663315	+	0.502744i
$683$		−	40.1110i		−	1.53480i	−0.641166	−	0.767402i	$-0.721549\pi$
$683$		−	40.1110i		−	1.53480i	0.641166	−	0.767402i	$-0.278451\pi$
$684$	0.243539	+	0.680529i	0.00931195	+	0.0260207i
$685$	30.9613	−	22.4947i	1.18297	−	0.859479i
$686$	−4.51776	+	6.21817i	−0.172489	+	0.237411i
$687$	−7.43013	+	51.8520i	−0.283477	+	1.97828i
$688$	6.19693	−	2.01350i	0.236256	−	0.0767641i
$689$	−9.48940	−	6.89445i	−0.361517	−	0.262658i
$690$	17.9774	−	3.11988i	0.684386	−	0.118772i
$691$	9.77418	−	30.0818i	0.371827	−	1.14437i	−0.573767	−	0.819019i	$-0.694518\pi$
$691$	9.77418	−	30.0818i	0.371827	−	1.14437i	0.945594	−	0.325348i	$-0.105482\pi$
$692$	−3.50863			−0.133378
$693$	28.5658	+	18.6573i	1.08512	+	0.708732i
$694$	15.0268			0.570411
$695$	−0.647936	+	1.99414i	−0.0245776	+	0.0756421i
$696$	7.11364	−	1.23454i	0.269642	−	0.0467949i
$697$	−33.1131	−	24.0580i	−1.25425	−	0.911263i
$698$	3.32413	−	1.08008i	0.125820	−	0.0408815i
$699$	−0.694884	+	4.84933i	−0.0262829	+	0.183418i
$700$	−1.02518	+	1.41103i	−0.0387480	+	0.0533321i
$701$	12.7136	−	9.23696i	0.480185	−	0.348875i	−0.321212	−	0.947007i	$-0.604090\pi$
$701$	12.7136	−	9.23696i	0.480185	−	0.348875i	0.801397	+	0.598132i	$0.204090\pi$
$702$	−1.10411	+	9.74502i	−0.0416719	+	0.367802i
$703$		−	2.12650i		−	0.0802025i
$704$	−2.72210	−	1.89477i	−0.102593	−	0.0714119i
$705$	−11.1033	−	5.45258i	−0.418174	−	0.205356i
$706$	24.0307	+	7.80805i	0.904407	+	0.293860i
$707$	4.95878	+	6.82517i	0.186494	+	0.256687i
$708$	4.24524	−	2.24256i	0.159546	−	0.0842804i
$709$	1.83617	+	5.65115i	0.0689588	+	0.212233i	0.979597	−	0.200971i	$-0.0644096\pi$
$709$	1.83617	+	5.65115i	0.0689588	+	0.212233i	−0.910638	+	0.413204i	$0.864410\pi$
$710$	−6.52249	−	20.0742i	−0.244785	−	0.753370i
$711$	33.9709	−	1.00268i	1.27401	−	0.0376034i
$712$	1.45332	+	2.00032i	0.0544655	+	0.0749653i
$713$	−30.9818	−	10.0666i	−1.16028	−	0.376997i
$714$	−13.5033	+	27.4971i	−0.505347	+	1.02905i
$715$	3.84343	−	12.6976i	0.143736	−	0.474862i
$716$			13.2729i			0.496031i
$717$	−1.36986	+	1.41089i	−0.0511585	+	0.0526908i
$718$	15.6095	−	11.3409i	0.582540	−	0.423240i
$719$	18.1483	−	24.9789i	0.676816	−	0.931557i	−0.323075	−	0.946373i	$-0.604716\pi$
$719$	18.1483	−	24.9789i	0.676816	−	0.931557i	0.999890	+	0.0148168i	$0.00471649\pi$
$720$	−5.25163	−	3.58367i	−0.195717	−	0.133556i
$721$	−15.0326	+	4.88439i	−0.559844	+	0.181904i
$722$	−15.3244	−	11.1338i	−0.570314	−	0.414357i
$723$	−4.45616	−	25.6773i	−0.165726	−	0.954949i
$724$	−2.29709	+	7.06971i	−0.0853706	+	0.262744i
$725$	2.12020			0.0787424
$726$	−12.7080	+	14.1953i	−0.471639	+	0.526836i
$727$	−23.3566			−0.866249			−0.433124	−	0.901334i	$-0.642589\pi$
$727$	−23.3566			−0.866249			−0.433124	+	0.901334i	$0.642589\pi$
$728$	−2.00000	+	6.15537i	−0.0741249	+	0.228133i
$729$	13.8770	−	23.1610i	0.513962	−	0.857813i
$730$	−4.25163	−	3.08899i	−0.157360	−	0.114329i
$731$	31.9624	−	10.3852i	1.18217	−	0.384111i
$732$	−2.77582	−	0.397761i	−0.102597	−	0.0147017i
$733$	24.3752	−	33.5495i	0.900317	−	1.23918i	−0.0700499	−	0.997543i	$-0.522316\pi$
$733$	24.3752	−	33.5495i	0.900317	−	1.23918i	0.970367	−	0.241636i	$-0.0776842\pi$
$734$	0.726385	−	0.527749i	0.0268114	−	0.0194796i
$735$	12.5321	+	12.1677i	0.462254	+	0.448811i
$736$		−	4.97072i		−	0.183223i
$737$	−9.59317	+	31.6930i	−0.353369	+	1.16743i
$738$	14.5554	+	18.8388i	0.535791	+	0.693466i
$739$	29.5635	+	9.60577i	1.08751	+	0.353354i	0.797284	−	0.603604i	$-0.206269\pi$
$739$	29.5635	+	9.60577i	1.08751	+	0.353354i	0.290227	+	0.956958i	$0.406269\pi$
$740$	10.9946	+	15.1328i	0.404170	+	0.556293i
$741$	0.367893	+	0.696435i	0.0135149	+	0.0255842i
$742$	6.58521	+	20.2672i	0.241751	+	0.744032i
$743$	−9.47940	−	29.1746i	−0.347765	−	1.07031i	−0.960087	−	0.279703i	$-0.909764\pi$
$743$	−9.47940	−	29.1746i	−0.347765	−	1.07031i	0.612321	−	0.790609i	$-0.290236\pi$
$744$	5.30198	+	10.0368i	0.194380	+	0.367969i
$745$	17.4236	+	23.9815i	0.638350	+	0.878614i
$746$	25.0515	+	8.13972i	0.917200	+	0.298016i
$747$	12.5972	+	16.3043i	0.460906	+	0.596544i
$748$	−14.0400	−	9.77282i	−0.513354	−	0.357330i
$749$			62.1868i			2.27226i
$750$	−14.5075	−	14.0856i	−0.529739	−	0.514334i
$751$	6.03982	−	4.38818i	0.220396	−	0.160127i	−0.472109	−	0.881540i	$-0.656507\pi$
$751$	6.03982	−	4.38818i	0.220396	−	0.160127i	0.692505	+	0.721413i	$0.256507\pi$
$752$	−1.98077	+	2.72629i	−0.0722311	+	0.0994176i
$753$	16.5220	+	2.36752i	0.602095	+	0.0862772i
$754$	7.48259	−	2.43124i	0.272500	−	0.0885406i
$755$	10.8504	+	7.88330i	0.394888	+	0.286903i
$756$	12.0294	−	13.1444i	0.437506	−	0.478056i
$757$	−7.21548	+	22.2070i	−0.262251	+	0.807126i	0.730063	+	0.683380i	$0.239491\pi$
$757$	−7.21548	+	22.2070i	−0.262251	+	0.807126i	−0.992314	+	0.123746i	$0.960509\pi$
$758$	−2.66498			−0.0967965
$759$	−28.3421	−	3.47759i	−1.02875	−	0.126228i
$760$	−0.510602			−0.0185215
$761$	−2.97052	+	9.14231i	−0.107681	+	0.331408i	−0.990350	−	0.138586i	$-0.955744\pi$
$761$	−2.97052	+	9.14231i	−0.107681	+	0.331408i	0.882669	+	0.469995i	$0.155744\pi$
$762$	5.19428	+	29.9305i	0.188169	+	1.08427i
$763$	−1.94965	−	1.41650i	−0.0705820	−	0.0512808i
$764$	2.46344	−	0.800420i	0.0891241	−	0.0289582i
$765$	−27.0868	−	18.4838i	−0.979324	−	0.668284i

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.70654 - 0.296161i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.01556 + 0.654895i) q^{5} +(0.245684 - 1.71454i) q^{6} +(-2.01556 + 2.77418i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.82458 - 1.01082i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.70654 - 0.296161i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.01556 + 0.654895i) q^{5} +(0.245684 - 1.71454i) q^{6} +(-2.01556 + 2.77418i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(2.82458 - 1.01082i) q^{9} +2.11929i q^{10} +(0.960858 - 3.17439i) q^{11} +(-1.55470 - 0.763481i) q^{12} +(-1.79505 - 0.583248i) q^{13} +(2.01556 + 2.77418i) q^{14} +(-3.24568 + 1.71454i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.59384 + 4.90534i) q^{17} +(-0.0885088 - 2.99869i) q^{18} +(-0.141616 - 0.194917i) q^{19} +(2.01556 + 0.654895i) q^{20} +(-2.61803 + 5.33119i) q^{21} +(-2.72210 - 1.89477i) q^{22} -4.97072i q^{23} +(-1.20654 + 1.24268i) q^{24} +(-0.411491 + 0.298966i) q^{25} +(-1.10940 + 1.52696i) q^{26} +(4.52089 - 2.56155i) q^{27} +(3.26124 - 1.05964i) q^{28} +(-3.37235 - 2.45016i) q^{29} +(0.627650 + 3.61665i) q^{30} +(2.02518 - 6.23285i) q^{31} +1.00000 q^{32} +(0.699614 - 5.70180i) q^{33} +5.15778 q^{34} +(2.24568 - 6.91151i) q^{35} +(-2.87928 - 0.842471i) q^{36} +(7.14052 + 5.18789i) q^{37} +(-0.229139 + 0.0744518i) q^{38} +(-3.23607 - 0.463712i) q^{39} +(1.24568 - 1.71454i) q^{40} +(-6.42001 + 4.66441i) q^{41} +(4.26124 + 4.13733i) q^{42} -6.51583i q^{43} +(-2.64321 + 2.00336i) q^{44} +(-5.03112 + 3.88718i) q^{45} +(-4.72744 - 1.53604i) q^{46} +(1.98077 + 2.72629i) q^{47} +(0.809017 + 1.53150i) q^{48} +(-1.47047 - 4.52566i) q^{49} +(0.157176 + 0.483737i) q^{50} +(4.17274 + 7.89915i) q^{51} +(1.10940 + 1.52696i) q^{52} +(5.91040 + 1.92040i) q^{53} +(-1.03914 - 5.09119i) q^{54} +(0.142225 + 7.02743i) q^{55} -3.42908i q^{56} +(-0.299400 - 0.290694i) q^{57} +(-3.37235 + 2.45016i) q^{58} +(-1.62931 + 2.24256i) q^{59} +(3.63359 + 0.520675i) q^{60} +(1.53975 - 0.500295i) q^{61} +(-5.30198 - 3.85211i) q^{62} +(-2.88889 + 9.87326i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +(-5.20654 - 2.42733i) q^{66} -9.98396 q^{67} +(1.59384 - 4.90534i) q^{68} +(-1.47214 - 8.48275i) q^{69} +(-5.87928 - 4.27155i) q^{70} +(-9.47214 + 3.07768i) q^{71} +(-1.69098 + 2.47802i) q^{72} +(-1.45756 + 2.00616i) q^{73} +(7.14052 - 5.18789i) q^{74} +(-0.613685 + 0.632066i) q^{75} +0.240931i q^{76} +(6.86966 + 9.06377i) q^{77} +(-1.44102 + 2.93439i) q^{78} +(10.7741 + 3.50072i) q^{79} +(-1.24568 - 1.71454i) q^{80} +(6.95647 - 5.71030i) q^{81} +(2.45223 + 7.54718i) q^{82} +(2.12232 + 6.53182i) q^{83} +(5.25163 - 2.77418i) q^{84} +(-6.42497 - 8.84322i) q^{85} +(-6.19693 - 2.01350i) q^{86} +(-6.48070 - 3.18254i) q^{87} +(1.08851 + 3.13291i) q^{88} -2.47254i q^{89} +(2.14222 + 5.98608i) q^{90} +(5.23607 - 3.80423i) q^{91} +(-2.92172 + 4.02140i) q^{92} +(1.61012 - 11.2364i) q^{93} +(3.20495 - 1.04135i) q^{94} +(0.413086 + 0.300124i) q^{95} +(1.70654 - 0.296161i) q^{96} +(-4.08582 + 12.5749i) q^{97} -4.75856 q^{98} +(-0.494732 - 9.93757i) 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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