LMFDB - Embedded newform 209.2.j.a.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(23,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.j (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			111.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	209.111
Dual form			209.2.j.a.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.673648 + 0.565258i) q^{2} +(1.87939 - 0.684040i) q^{3} +(-0.213011 - 1.20805i) q^{4} +(-0.286989 + 1.62760i) q^{5} +(1.65270 + 0.601535i) q^{6} +(0.0603074 + 0.104455i) q^{7} +(1.41875 - 2.45734i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.673648 + 0.565258i) q^{2} +(1.87939 - 0.684040i) q^{3} +(-0.213011 - 1.20805i) q^{4} +(-0.286989 + 1.62760i) q^{5} +(1.65270 + 0.601535i) q^{6} +(0.0603074 + 0.104455i) q^{7} +(1.41875 - 2.45734i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-1.11334 + 0.934204i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.22668 - 2.12467i) q^{12} +(4.29813 + 1.56439i) q^{13} +(-0.0184183 + 0.104455i) q^{14} +(0.573978 + 3.25519i) q^{15} +(0.0393628 - 0.0143269i) q^{16} +(-5.26991 - 4.42198i) q^{17} +0.879385 q^{18} +(-4.11721 + 1.43128i) q^{19} +2.02734 q^{20} +(0.184793 + 0.155059i) q^{21} +(-0.826352 + 0.300767i) q^{22} +(-0.726682 - 4.12122i) q^{23} +(0.985452 - 5.58878i) q^{24} +(2.13176 + 0.775897i) q^{25} +(2.01114 + 3.48340i) q^{26} +(-2.00000 + 3.46410i) q^{27} +(0.113341 - 0.0951042i) q^{28} +(-5.94356 + 4.98724i) q^{29} +(-1.45336 + 2.51730i) q^{30} +(3.08512 + 5.34359i) q^{31} +(-5.29813 - 1.92836i) q^{32} +(-0.347296 + 1.96962i) q^{33} +(-1.05051 - 5.95772i) q^{34} +(-0.187319 + 0.0681784i) q^{35} +(-0.939693 - 0.788496i) q^{36} -1.46791 q^{37} +(-3.58260 - 1.36310i) q^{38} +9.14796 q^{39} +(3.59240 + 3.01438i) q^{40} +(-2.09240 + 0.761570i) q^{41} +(0.0368366 + 0.208911i) q^{42} +(-1.75490 + 9.95253i) q^{43} +(1.15270 + 0.419550i) q^{44} +(0.826352 + 1.43128i) q^{45} +(1.84002 - 3.18701i) q^{46} +(5.54189 - 4.65020i) q^{47} +(0.0641778 - 0.0538515i) q^{48} +(3.49273 - 6.04958i) q^{49} +(0.997474 + 1.72768i) q^{50} +(-12.9290 - 4.70578i) q^{51} +(0.974308 - 5.52557i) q^{52} +(-2.11721 - 12.0073i) q^{53} +(-3.30541 + 1.20307i) q^{54} +(-1.26604 - 1.06234i) q^{55} +0.342244 q^{56} +(-6.75877 + 5.50627i) q^{57} -6.82295 q^{58} +(3.17752 + 2.66625i) q^{59} +(3.81016 - 1.38678i) q^{60} +(-1.54916 - 8.78574i) q^{61} +(-0.942219 + 5.34359i) q^{62} +(0.113341 + 0.0412527i) q^{63} +(-2.52094 - 4.36640i) q^{64} +(-3.77972 + 6.54666i) q^{65} +(-1.34730 + 1.13052i) q^{66} +(3.63429 - 3.04953i) q^{67} +(-4.21941 + 7.30823i) q^{68} +(-4.18479 - 7.24827i) q^{69} +(-0.164725 - 0.0599551i) q^{70} +(-0.0748553 + 0.424525i) q^{71} +(-0.492726 - 2.79439i) q^{72} +(5.36484 - 1.95264i) q^{73} +(-0.988856 - 0.829748i) q^{74} +4.53714 q^{75} +(2.60607 + 4.66890i) q^{76} -0.120615 q^{77} +(6.16250 + 5.17095i) q^{78} +(2.77972 - 1.01173i) q^{79} +(0.0120217 + 0.0681784i) q^{80} +(-1.91013 + 10.8329i) q^{81} +(-1.84002 - 0.669713i) q^{82} +(-1.54323 - 2.67296i) q^{83} +(0.147956 - 0.256267i) q^{84} +(8.70961 - 7.30823i) q^{85} +(-6.80793 + 5.71253i) q^{86} +(-7.75877 + 13.4386i) q^{87} +(1.41875 + 2.45734i) q^{88} +(9.90420 + 3.60483i) q^{89} +(-0.252374 + 1.43128i) q^{90} +(0.0957998 + 0.543308i) q^{91} +(-4.82383 + 1.75573i) q^{92} +(9.45336 + 7.93231i) q^{93} +6.36184 q^{94} +(-1.14796 - 7.11192i) q^{95} -11.2763 q^{96} +(4.25490 + 3.57029i) q^{97} +(5.77244 - 2.10100i) q^{98} +(0.173648 + 0.984808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8} - 3 q^{11} + 6 q^{12} + 12 q^{13} - 12 q^{14} - 12 q^{15} + 9 q^{16} - 3 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} - 6 q^{21} - 6 q^{22} + 9 q^{23} - 30 q^{24} + 18 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} + 18 q^{30} - 3 q^{31} - 18 q^{32} - 9 q^{34} + 21 q^{35} - 18 q^{37} - 15 q^{38} + 24 q^{39} + 18 q^{40} - 9 q^{41} + 24 q^{42} - 12 q^{43} + 9 q^{44} + 6 q^{45} - 9 q^{46} + 27 q^{47} - 18 q^{48} + 3 q^{49} + 21 q^{50} - 12 q^{51} - 24 q^{52} + 18 q^{53} - 24 q^{54} - 3 q^{55} + 30 q^{56} - 18 q^{57} - 6 q^{59} + 60 q^{60} - 21 q^{61} + 15 q^{62} - 6 q^{63} - 12 q^{64} + 3 q^{65} - 6 q^{66} + 12 q^{67} + 6 q^{68} - 18 q^{69} - 54 q^{70} - 42 q^{71} + 15 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} - 9 q^{76} - 12 q^{77} + 42 q^{78} - 9 q^{79} + 51 q^{80} + 9 q^{82} + 6 q^{83} - 30 q^{84} + 18 q^{85} - 30 q^{86} - 24 q^{87} + 6 q^{88} + 21 q^{89} - 18 q^{90} + 39 q^{91} - 45 q^{92} + 30 q^{93} + 72 q^{94} + 24 q^{95} + 27 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8 - 3 * q^11 + 6 * q^12 + 12 * q^13 - 12 * q^14 - 12 * q^15 + 9 * q^16 - 3 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 - 6 * q^21 - 6 * q^22 + 9 * q^23 - 30 * q^24 + 18 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 + 18 * q^30 - 3 * q^31 - 18 * q^32 - 9 * q^34 + 21 * q^35 - 18 * q^37 - 15 * q^38 + 24 * q^39 + 18 * q^40 - 9 * q^41 + 24 * q^42 - 12 * q^43 + 9 * q^44 + 6 * q^45 - 9 * q^46 + 27 * q^47 - 18 * q^48 + 3 * q^49 + 21 * q^50 - 12 * q^51 - 24 * q^52 + 18 * q^53 - 24 * q^54 - 3 * q^55 + 30 * q^56 - 18 * q^57 - 6 * q^59 + 60 * q^60 - 21 * q^61 + 15 * q^62 - 6 * q^63 - 12 * q^64 + 3 * q^65 - 6 * q^66 + 12 * q^67 + 6 * q^68 - 18 * q^69 - 54 * q^70 - 42 * q^71 + 15 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 - 9 * q^76 - 12 * q^77 + 42 * q^78 - 9 * q^79 + 51 * q^80 + 9 * q^82 + 6 * q^83 - 30 * q^84 + 18 * q^85 - 30 * q^86 - 24 * q^87 + 6 * q^88 + 21 * q^89 - 18 * q^90 + 39 * q^91 - 45 * q^92 + 30 * q^93 + 72 * q^94 + 24 * q^95 + 27 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	0.673648	+	0.565258i	0.476341	+	0.399698i	0.849101	−	0.528230i	$-0.177144\pi$
$2$	0.673648	+	0.565258i	0.476341	+	0.399698i	−0.372760	+	0.927928i	$0.621589\pi$
$3$	1.87939	−	0.684040i	1.08506	−	0.394931i	0.263274	−	0.964721i	$-0.415198\pi$
$3$	1.87939	−	0.684040i	1.08506	−	0.394931i	0.821790	+	0.569790i	$0.192976\pi$
$4$	−0.213011	−	1.20805i	−0.106506	−	0.604023i
$5$	−0.286989	+	1.62760i	−0.128345	+	0.727883i	0.850919	+	0.525297i	$0.176046\pi$
$5$	−0.286989	+	1.62760i	−0.128345	+	0.727883i	−0.979264	+	0.202586i	$0.935065\pi$
$6$	1.65270	+	0.601535i	0.674713	+	0.245576i
$7$	0.0603074	+	0.104455i	0.0227940	+	0.0394804i	0.877197	−	0.480130i	$-0.159410\pi$
$7$	0.0603074	+	0.104455i	0.0227940	+	0.0394804i	−0.854403	+	0.519610i	$0.826077\pi$
$8$	1.41875	−	2.45734i	0.501603	−	0.868802i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−1.11334	+	0.934204i	−0.352069	+	0.295421i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−1.22668	−	2.12467i	−0.354112	−	0.613341i
$13$	4.29813	+	1.56439i	1.19209	+	0.433884i	0.860456	−	0.509525i	$-0.170179\pi$
$13$	4.29813	+	1.56439i	1.19209	+	0.433884i	0.331632	+	0.943409i	$0.392401\pi$
$14$	−0.0184183	+	0.104455i	−0.00492250	+	0.0279169i
$15$	0.573978	+	3.25519i	0.148200	+	0.840487i
$16$	0.0393628	−	0.0143269i	0.00984071	−	0.00358173i
$17$	−5.26991	−	4.42198i	−1.27814	−	1.07249i	−0.993497	−	0.113855i	$-0.963680\pi$
$17$	−5.26991	−	4.42198i	−1.27814	−	1.07249i	−0.284645	−	0.958633i	$-0.591876\pi$
$18$	0.879385			0.207273
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$20$	2.02734			0.453327
$21$	0.184793	+	0.155059i	0.0403250	+	0.0338367i
$22$	−0.826352	+	0.300767i	−0.176179	+	0.0641238i
$23$	−0.726682	−	4.12122i	−0.151524	−	0.859333i	−0.961896	−	0.273417i	$-0.911846\pi$
$23$	−0.726682	−	4.12122i	−0.151524	−	0.859333i	0.810372	−	0.585916i	$-0.199265\pi$
$24$	0.985452	−	5.58878i	0.201155	−	1.14080i
$25$	2.13176	+	0.775897i	0.426352	+	0.155179i
$26$	2.01114	+	3.48340i	0.394418	+	0.683152i
$27$	−2.00000	+	3.46410i	−0.384900	+	0.666667i
$28$	0.113341	−	0.0951042i	0.0214194	−	0.0179730i
$29$	−5.94356	+	4.98724i	−1.10369	+	0.926108i	−0.997668	−	0.0682561i	$-0.978257\pi$
$29$	−5.94356	+	4.98724i	−1.10369	+	0.926108i	−0.106024	+	0.994364i	$0.533812\pi$
$30$	−1.45336	+	2.51730i	−0.265347	+	0.459594i
$31$	3.08512	+	5.34359i	0.554104	+	0.959737i	0.997973	+	0.0636448i	$0.0202725\pi$
$31$	3.08512	+	5.34359i	0.554104	+	0.959737i	−0.443868	+	0.896092i	$0.646394\pi$
$32$	−5.29813	−	1.92836i	−0.936587	−	0.340890i
$33$	−0.347296	+	1.96962i	−0.0604565	+	0.342866i
$34$	−1.05051	−	5.95772i	−0.180160	−	1.02174i
$35$	−0.187319	+	0.0681784i	−0.0316626	+	0.0115243i
$36$	−0.939693	−	0.788496i	−0.156615	−	0.131416i
$37$	−1.46791			−0.241323			−0.120662	−	0.992694i	$-0.538502\pi$
$37$	−1.46791			−0.241323			−0.120662	+	0.992694i	$0.538502\pi$
$38$	−3.58260	−	1.36310i	−0.581174	−	0.221125i
$39$	9.14796			1.46485
$40$	3.59240	+	3.01438i	0.568008	+	0.476615i
$41$	−2.09240	+	0.761570i	−0.326777	+	0.118937i	−0.500199	−	0.865910i	$-0.666740\pi$
$41$	−2.09240	+	0.761570i	−0.326777	+	0.118937i	0.173422	+	0.984848i	$0.444518\pi$
$42$	0.0368366	+	0.208911i	0.00568401	+	0.0322357i
$43$	−1.75490	+	9.95253i	−0.267620	+	1.51775i	0.493850	+	0.869547i	$0.335589\pi$
$43$	−1.75490	+	9.95253i	−0.267620	+	1.51775i	−0.761470	+	0.648200i	$0.775522\pi$
$44$	1.15270	+	0.419550i	0.173777	+	0.0632495i
$45$	0.826352	+	1.43128i	0.123185	+	0.213363i
$46$	1.84002	−	3.18701i	0.271297	−	0.469899i
$47$	5.54189	−	4.65020i	0.808368	−	0.678301i	−0.141850	−	0.989888i	$-0.545305\pi$
$47$	5.54189	−	4.65020i	0.808368	−	0.678301i	0.950218	+	0.311587i	$0.100861\pi$
$48$	0.0641778	−	0.0538515i	0.00926326	−	0.00777280i
$49$	3.49273	−	6.04958i	0.498961	−	0.864226i
$50$	0.997474	+	1.72768i	0.141064	+	0.244330i
$51$	−12.9290	−	4.70578i	−1.81042	−	0.658941i
$52$	0.974308	−	5.52557i	0.135112	−	0.766259i
$53$	−2.11721	−	12.0073i	−0.290821	−	1.64933i	−0.683717	−	0.729747i	$-0.739638\pi$
$53$	−2.11721	−	12.0073i	−0.290821	−	1.64933i	0.392896	−	0.919583i	$-0.371473\pi$
$54$	−3.30541	+	1.20307i	−0.449809	+	0.163717i
$55$	−1.26604	−	1.06234i	−0.170713	−	0.143246i
$56$	0.342244			0.0457343
$57$	−6.75877	+	5.50627i	−0.895221	+	0.729323i
$58$	−6.82295			−0.895897
$59$	3.17752	+	2.66625i	0.413678	+	0.347117i	0.825752	−	0.564033i	$-0.190751\pi$
$59$	3.17752	+	2.66625i	0.413678	+	0.347117i	−0.412074	+	0.911150i	$0.635196\pi$
$60$	3.81016	−	1.38678i	0.491889	−	0.179033i
$61$	−1.54916	−	8.78574i	−0.198350	−	1.12490i	−0.907567	−	0.419908i	$-0.862062\pi$
$61$	−1.54916	−	8.78574i	−0.198350	−	1.12490i	0.709217	−	0.704991i	$-0.249049\pi$
$62$	−0.942219	+	5.34359i	−0.119662	+	0.678636i
$63$	0.113341	+	0.0412527i	0.0142796	+	0.00519735i
$64$	−2.52094	−	4.36640i	−0.315118	−	0.545801i
$65$	−3.77972	+	6.54666i	−0.468816	+	0.812013i
$66$	−1.34730	+	1.13052i	−0.165841	+	0.139157i
$67$	3.63429	−	3.04953i	0.443999	−	0.372559i	−0.393205	−	0.919451i	$-0.628634\pi$
$67$	3.63429	−	3.04953i	0.443999	−	0.372559i	0.837203	+	0.546892i	$0.184189\pi$
$68$	−4.21941	+	7.30823i	−0.511678	+	0.886253i
$69$	−4.18479	−	7.24827i	−0.503790	−	0.872590i
$70$	−0.164725	−	0.0599551i	−0.0196884	−	0.00716601i
$71$	−0.0748553	+	0.424525i	−0.00888369	+	0.0503819i	−0.988927	−	0.148400i	$-0.952588\pi$
$71$	−0.0748553	+	0.424525i	−0.00888369	+	0.0503819i	0.980044	+	0.198782i	$0.0636987\pi$
$72$	−0.492726	−	2.79439i	−0.0580683	−	0.329322i
$73$	5.36484	−	1.95264i	0.627907	−	0.228539i	−0.00841323	−	0.999965i	$-0.502678\pi$
$73$	5.36484	−	1.95264i	0.627907	−	0.228539i	0.636320	+	0.771425i	$0.280456\pi$
$74$	−0.988856	−	0.829748i	−0.114952	−	0.0964563i
$75$	4.53714			0.523904
$76$	2.60607	+	4.66890i	0.298936	+	0.535560i
$77$	−0.120615			−0.0137453
$78$	6.16250	+	5.17095i	0.697766	+	0.585495i
$79$	2.77972	−	1.01173i	0.312742	−	0.113829i	−0.180880	−	0.983505i	$-0.557895\pi$
$79$	2.77972	−	1.01173i	0.312742	−	0.113829i	0.493623	+	0.869676i	$0.335672\pi$
$80$	0.0120217	+	0.0681784i	0.00134407	+	0.00762258i
$81$	−1.91013	+	10.8329i	−0.212237	+	1.20365i
$82$	−1.84002	−	0.669713i	−0.203196	−	0.0739575i
$83$	−1.54323	−	2.67296i	−0.169392	−	0.293395i	0.768814	−	0.639472i	$-0.220847\pi$
$83$	−1.54323	−	2.67296i	−0.169392	−	0.293395i	−0.938206	+	0.346077i	$0.887514\pi$
$84$	0.147956	−	0.256267i	0.0161433	−	0.0279610i
$85$	8.70961	−	7.30823i	0.944690	−	0.792689i
$86$	−6.80793	+	5.71253i	−0.734118	+	0.615998i
$87$	−7.75877	+	13.4386i	−0.831828	+	1.44077i
$88$	1.41875	+	2.45734i	0.151239	+	0.261954i
$89$	9.90420	+	3.60483i	1.04984	+	0.382112i	0.808604	−	0.588354i	$-0.200224\pi$
$89$	9.90420	+	3.60483i	1.04984	+	0.382112i	0.241240	+	0.970466i	$0.422446\pi$
$90$	−0.252374	+	1.43128i	−0.0266025	+	0.150871i
$91$	0.0957998	+	0.543308i	0.0100426	+	0.0569541i
$92$	−4.82383	+	1.75573i	−0.502919	+	0.183047i
$93$	9.45336	+	7.93231i	0.980268	+	0.822543i
$94$	6.36184			0.656174
$95$	−1.14796	−	7.11192i	−0.117778	−	0.729667i
$96$	−11.2763			−1.15088
$97$	4.25490	+	3.57029i	0.432020	+	0.362508i	0.832713	−	0.553705i	$-0.186786\pi$
$97$	4.25490	+	3.57029i	0.432020	+	0.362508i	−0.400693	+	0.916212i	$0.631231\pi$
$98$	5.77244	−	2.10100i	0.583105	−	0.212233i
$99$	0.173648	+	0.984808i	0.0174523	+	0.0989769i
$100$	0.483231	−	2.74054i	0.0483231	−	0.274054i
$101$	4.65910	+	1.69577i	0.463598	+	0.168736i	0.563250	−	0.826287i	$-0.309551\pi$
$101$	4.65910	+	1.69577i	0.463598	+	0.168736i	−0.0996522	+	0.995022i	$0.531773\pi$
$102$	−6.04963	−	10.4783i	−0.599003	−	1.03750i
$103$	1.17365	−	2.03282i	0.115643	−	0.200300i	−0.802394	−	0.596795i	$-0.796440\pi$
$103$	1.17365	−	2.03282i	0.115643	−	0.200300i	0.918037	+	0.396496i	$0.129774\pi$
$104$	9.94222	−	8.34251i	0.974915	−	0.818051i
$105$	−0.305407	+	0.256267i	−0.0298047	+	0.0250091i
$106$	5.36097	−	9.28547i	0.520703	−	0.901884i
$107$	2.27332	+	3.93750i	0.219770	+	0.380653i	0.954738	−	0.297449i	$-0.0961360\pi$
$107$	2.27332	+	3.93750i	0.219770	+	0.380653i	−0.734968	+	0.678102i	$0.762803\pi$
$108$	4.61081	+	1.67820i	0.443676	+	0.161485i
$109$	1.10741	−	6.28044i	0.106071	−	0.601557i	−0.884717	−	0.466129i	$-0.845648\pi$
$109$	1.10741	−	6.28044i	0.106071	−	0.601557i	0.990787	−	0.135428i	$-0.0432408\pi$
$110$	−0.252374	−	1.43128i	−0.0240629	−	0.136468i
$111$	−2.75877	+	1.00411i	−0.261851	+	0.0953059i
$112$	0.00387039	+	0.00324765i	0.000365718	+	0.000306874i
$113$	15.7101			1.47788			0.738940	−	0.673772i	$-0.235327\pi$
$113$	15.7101			1.47788			0.738940	+	0.673772i	$0.235327\pi$
$114$	−7.66550	−	0.111159i	−0.717940	−	0.0104110i
$115$	6.91622			0.644941
$116$	7.29086	+	6.11776i	0.676939	+	0.568020i
$117$	4.29813	−	1.56439i	0.397363	−	0.144628i
$118$	0.633408	+	3.59224i	0.0583099	+	0.330692i
$119$	0.144086	−	0.817150i	0.0132083	−	0.0749080i
$120$	8.81345	+	3.20783i	0.804554	+	0.292834i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	3.92262	−	6.79417i	0.355137	−	0.615116i
$123$	−3.41147	+	2.86257i	−0.307602	+	0.258109i
$124$	5.79813	−	4.86521i	0.520688	−	0.436909i
$125$	−6.00640	+	10.4034i	−0.537228	+	0.930507i
$126$	0.0530334	+	0.0918566i	0.00472459	+	0.00818323i
$127$	−15.8157	−	5.75643i	−1.40341	−	0.510801i	−0.474224	−	0.880404i	$-0.657271\pi$
$127$	−15.8157	−	5.75643i	−1.40341	−	0.510801i	−0.929190	+	0.369603i	$0.879494\pi$
$128$	−1.18820	+	6.73859i	−0.105023	+	0.595613i
$129$	3.50980	+	19.9051i	0.309021	+	1.75254i
$130$	−6.24675	+	2.27363i	−0.547876	+	0.199411i
$131$	−3.75490	−	3.15074i	−0.328067	−	0.275281i	0.463845	−	0.885917i	$-0.346470\pi$
$131$	−3.75490	−	3.15074i	−0.328067	−	0.275281i	−0.791912	+	0.610636i	$0.790914\pi$
$132$	2.45336			0.213538
$133$	−0.397804	−	0.343748i	−0.0344939	−	0.0298067i
$134$	4.17200			0.360406
$135$	−5.06418	−	4.24935i	−0.435855	−	0.365726i
$136$	−18.3430	+	6.67631i	−1.57290	+	0.572489i
$137$	−2.24170	−	12.7133i	−0.191521	−	1.08617i	−0.917287	−	0.398228i	$-0.869625\pi$
$137$	−2.24170	−	12.7133i	−0.191521	−	1.08617i	0.725766	−	0.687942i	$-0.241486\pi$
$138$	1.27807	−	7.24827i	0.108796	−	0.617014i
$139$	7.89693	+	2.87425i	0.669809	+	0.243790i	0.654465	−	0.756092i	$-0.272894\pi$
$139$	7.89693	+	2.87425i	0.669809	+	0.243790i	0.0153431	+	0.999882i	$0.495116\pi$
$140$	0.122264	+	0.211767i	0.0103332	+	0.0178976i
$141$	7.23442	−	12.5304i	0.609248	−	1.05525i
$142$	−0.290393	+	0.243668i	−0.0243692	+	0.0204482i
$143$	−3.50387	+	2.94010i	−0.293008	+	0.245863i
$144$	0.0209445	−	0.0362770i	0.00174538	−	0.00302308i
$145$	−6.41147	−	11.1050i	−0.532444	−	0.922220i
$146$	4.71776	+	1.71712i	0.390444	+	0.142110i
$147$	2.42602	−	13.7587i	0.200095	−	1.13479i
$148$	0.312681	+	1.77330i	0.0257022	+	0.145765i
$149$	−5.27972	+	1.92166i	−0.432531	+	0.157428i	−0.549105	−	0.835754i	$-0.685031\pi$
$149$	−5.27972	+	1.92166i	−0.432531	+	0.157428i	0.116574	+	0.993182i	$0.462809\pi$
$150$	3.05644	+	2.56466i	0.249557	+	0.209403i
$151$	9.23442			0.751487			0.375743	−	0.926724i	$-0.377387\pi$
$151$	9.23442			0.751487			0.375743	+	0.926724i	$0.377387\pi$
$152$	−2.32413	+	12.1480i	−0.188512	+	0.985336i
$153$	−6.87939			−0.556165
$154$	−0.0812519	−	0.0681784i	−0.00654747	−	0.00549398i
$155$	−9.58260	+	3.48778i	−0.769693	+	0.280145i
$156$	−1.94862	−	11.0511i	−0.156014	−	0.884800i
$157$	−1.53074	+	8.68128i	−0.122167	+	0.692842i	0.860784	+	0.508971i	$0.169974\pi$
$157$	−1.53074	+	8.68128i	−0.122167	+	0.692842i	−0.982950	+	0.183871i	$0.941137\pi$
$158$	2.44444	+	0.889704i	0.194469	+	0.0707810i
$159$	−12.1925	−	21.1181i	−0.966931	−	1.67477i
$160$	4.65910	−	8.06980i	0.368334	−	0.637974i
$161$	0.386659	−	0.324446i	0.0304730	−	0.0255699i
$162$	−7.41013	+	6.21784i	−0.582195	+	0.488519i
$163$	−10.0496	+	17.4065i	−0.787148	+	1.36338i	0.140560	+	0.990072i	$0.455110\pi$
$163$	−10.0496	+	17.4065i	−0.787148	+	1.36338i	−0.927708	+	0.373308i	$0.878224\pi$
$164$	1.36571	+	2.36549i	0.106644	+	0.184714i
$165$	−3.10607	−	1.13052i	−0.241807	−	0.0880105i
$166$	0.471315	−	2.67296i	0.0365811	−	0.207462i
$167$	0.162504	+	0.921605i	0.0125749	+	0.0713159i	0.990449	−	0.137876i	$-0.0440277\pi$
$167$	0.162504	+	0.921605i	0.0125749	+	0.0713159i	−0.977875	+	0.209192i	$0.932917\pi$
$168$	0.643208	−	0.234109i	0.0496246	−	0.0180619i
$169$	6.06805	+	5.09170i	0.466773	+	0.391669i
$170$	9.99825			0.766830
$171$	−2.23396	+	3.74292i	−0.170835	+	0.286228i
$172$	12.3969			0.945257
$173$	−2.51707	−	2.11208i	−0.191370	−	0.160578i	0.542069	−	0.840334i	$-0.317641\pi$
$173$	−2.51707	−	2.11208i	−0.191370	−	0.160578i	−0.733438	+	0.679756i	$0.762086\pi$
$174$	−12.8229	+	4.66717i	−0.972105	+	0.353817i
$175$	0.0475142	+	0.269466i	0.00359173	+	0.0203697i
$176$	−0.00727396	+	0.0412527i	−0.000548295	+	0.00310954i
$177$	7.79561	+	2.83737i	0.585954	+	0.213270i
$178$	4.63429	+	8.02682i	0.347354	+	0.601635i
$179$	−10.9081	+	18.8933i	−0.815307	+	1.41215i	0.0937994	+	0.995591i	$0.470099\pi$
$179$	−10.9081	+	18.8933i	−0.815307	+	1.41215i	−0.909107	+	0.416563i	$0.863235\pi$
$180$	1.55303	−	1.30315i	0.115756	−	0.0971310i
$181$	19.5685	−	16.4199i	1.45452	−	1.22048i	0.525316	−	0.850907i	$-0.323947\pi$
$181$	19.5685	−	16.4199i	1.45452	−	1.22048i	0.929200	−	0.369577i	$-0.120497\pi$
$182$	−0.242574	+	0.420150i	−0.0179808	+	0.0311436i
$183$	−8.92127	−	15.4521i	−0.659480	−	1.14225i
$184$	−11.1582	−	4.06126i	−0.822595	−	0.299400i
$185$	0.421274	−	2.38917i	0.0309727	−	0.175655i
$186$	1.88444	+	10.6872i	0.138174	+	0.783622i
$187$	6.46451	−	2.35289i	0.472732	−	0.172060i
$188$	−6.79813	−	5.70431i	−0.495805	−	0.416030i
$189$	−0.482459			−0.0350937
$190$	3.24675	−	5.43982i	0.235544	−	0.394646i
$191$	−17.7811			−1.28659			−0.643296	−	0.765617i	$-0.722434\pi$
$191$	−17.7811			−1.28659			−0.643296	+	0.765617i	$0.722434\pi$
$192$	−7.72462	−	6.48173i	−0.557477	−	0.467778i
$193$	16.4757	−	5.99665i	1.18594	−	0.431648i	0.327646	−	0.944801i	$-0.393745\pi$
$193$	16.4757	−	5.99665i	1.18594	−	0.431648i	0.858297	+	0.513152i	$0.171522\pi$
$194$	0.848174	+	4.81023i	0.0608953	+	0.345355i
$195$	−2.62536	+	14.8892i	−0.188006	+	1.06624i
$196$	−8.05216	−	2.93075i	−0.575154	−	0.209339i
$197$	−0.0282185	−	0.0488759i	−0.00201048	−	0.00348226i	0.865018	−	0.501740i	$-0.167307\pi$
$197$	−0.0282185	−	0.0488759i	−0.00201048	−	0.00348226i	−0.867029	+	0.498258i	$0.833973\pi$
$198$	−0.439693	+	0.761570i	−0.0312476	+	0.0541224i
$199$	−10.4645	+	8.78076i	−0.741809	+	0.622452i	−0.933323	−	0.359038i	$-0.883105\pi$
$199$	−10.4645	+	8.78076i	−0.741809	+	0.622452i	0.191514	+	0.981490i	$0.438660\pi$
$200$	4.93107	−	4.13766i	0.348680	−	0.292577i
$201$	4.74422	−	8.21723i	0.334632	−	0.579599i
$202$	2.18004	+	3.77595i	0.153387	+	0.265675i
$203$	−0.879385	−	0.320070i	−0.0617207	−	0.0224645i
$204$	−2.93077	+	16.6212i	−0.205195	+	1.16372i
$205$	−0.639033	−	3.62414i	−0.0446320	−	0.253121i
$206$	1.93969	−	0.705990i	0.135145	−	0.0491887i
$207$	−3.20574	−	2.68993i	−0.222814	−	0.186963i
$208$	0.191600			0.0132850
$209$	0.819078	−	4.28125i	0.0566568	−	0.296140i
$210$	−0.350594			−0.0241933
$211$	−3.94356	−	3.30904i	−0.271486	−	0.227804i	0.496872	−	0.867824i	$-0.334482\pi$
$211$	−3.94356	−	3.30904i	−0.271486	−	0.227804i	−0.768358	+	0.640020i	$0.778926\pi$
$212$	−14.0544	+	5.11538i	−0.965259	+	0.351325i
$213$	0.149711	+	0.849051i	0.0102580	+	0.0581760i
$214$	−0.694288	+	3.93750i	−0.0474606	+	0.269162i
$215$	−15.6951	−	5.71253i	−1.07039	−	0.389592i
$216$	5.67499	+	9.82938i	0.386134	+	0.668804i
$217$	−0.372111	+	0.644516i	−0.0252606	+	0.0437526i
$218$	4.29607	−	3.60483i	0.290967	−	0.244150i
$219$	8.74691	−	7.33953i	0.591061	−	0.495959i
$220$	−1.01367	+	1.75573i	−0.0683417	+	0.118371i
$221$	−15.7331	−	27.2505i	−1.05832	−	1.83307i
$222$	−2.42602	−	0.883000i	−0.162824	−	0.0592631i
$223$	3.23143	−	18.3263i	0.216393	−	1.22722i	−0.662081	−	0.749432i	$-0.730327\pi$
$223$	3.23143	−	18.3263i	0.216393	−	1.22722i	0.878474	−	0.477791i	$-0.158562\pi$
$224$	−0.118089	−	0.669713i	−0.00789012	−	0.0447471i
$225$	2.13176	−	0.775897i	0.142117	−	0.0517265i
$226$	10.5831	+	8.88024i	0.703975	+	0.590705i
$227$	−20.8007			−1.38059			−0.690294	−	0.723529i	$-0.742519\pi$
$227$	−20.8007			−1.38059			−0.690294	+	0.723529i	$0.742519\pi$
$228$	8.09152	+	6.99201i	0.535874	+	0.463057i
$229$	1.10338			0.0729133			0.0364567	−	0.999335i	$-0.488393\pi$
$229$	1.10338			0.0729133			0.0364567	+	0.999335i	$0.488393\pi$
$230$	4.65910	+	3.90945i	0.307212	+	0.257781i
$231$	−0.226682	+	0.0825054i	−0.0149146	+	0.00542845i
$232$	3.82295	+	21.6810i	0.250989	+	1.42343i
$233$	−4.72715	+	26.8090i	−0.309686	+	1.75632i	0.290898	+	0.956754i	$0.406046\pi$
$233$	−4.72715	+	26.8090i	−0.309686	+	1.75632i	−0.600584	+	0.799561i	$0.705065\pi$
$234$	3.77972	+	1.37570i	0.247088	+	0.0899326i
$235$	5.97818	+	10.3545i	0.389973	+	0.675454i
$236$	2.54411	−	4.40653i	0.165607	−	0.286841i
$237$	4.53209	−	3.80287i	0.294391	−	0.247023i
$238$	0.558963	−	0.469026i	0.0362322	−	0.0304024i
$239$	5.83750	−	10.1108i	0.377596	−	0.654016i	−0.613116	−	0.789993i	$-0.710084\pi$
$239$	5.83750	−	10.1108i	0.377596	−	0.654016i	0.990712	+	0.135977i	$0.0434174\pi$
$240$	0.0692302	+	0.119910i	0.00446879	+	0.00774017i
$241$	−24.0920	−	8.76877i	−1.55190	−	0.564846i	−0.583039	−	0.812444i	$-0.698136\pi$
$241$	−24.0920	−	8.76877i	−1.55190	−	0.564846i	−0.968863	+	0.247599i	$0.920359\pi$
$242$	0.152704	−	0.866025i	0.00981616	−	0.0556702i
$243$	1.73648	+	9.84808i	0.111395	+	0.631754i
$244$	−10.2836	+	3.74292i	−0.658339	+	0.239616i
$245$	8.84389	+	7.42091i	0.565016	+	0.474104i
$246$	−3.91622			−0.249689
$247$	−19.9354	−	0.289088i	−1.26846	−	0.0183942i
$248$	17.5080			1.11176
$249$	−4.72874	−	3.96788i	−0.299672	−	0.251454i
$250$	−9.92679	+	3.61306i	−0.627826	+	0.228510i
$251$	0.115867	+	0.657115i	0.00731346	+	0.0414767i	0.988246	−	0.152871i	$-0.0488520\pi$
$251$	0.115867	+	0.657115i	0.00731346	+	0.0414767i	−0.980933	+	0.194348i	$0.937741\pi$
$252$	0.0256923	−	0.145708i	0.00161846	−	0.00917875i
$253$	3.93242	+	1.43128i	0.247229	+	0.0899840i
$254$	−7.40033	−	12.8177i	−0.464338	−	0.804257i
$255$	11.3696	−	19.6927i	0.711991	−	1.23320i
$256$	−12.3341	+	10.3495i	−0.770881	+	0.646846i
$257$	7.94949	−	6.67042i	0.495876	−	0.416089i	−0.360251	−	0.932856i	$-0.617309\pi$
$257$	7.94949	−	6.67042i	0.495876	−	0.416089i	0.856126	+	0.516766i	$0.172864\pi$
$258$	−8.88713	+	15.3930i	−0.553288	+	0.958323i
$259$	−0.0885259	−	0.153331i	−0.00550073	−	0.00952754i
$260$	8.71378	+	3.17156i	0.540406	+	0.196692i
$261$	−1.34730	+	7.64090i	−0.0833956	+	0.472960i
$262$	−0.748503	−	4.24497i	−0.0462427	−	0.262255i
$263$	−0.299011	+	0.108831i	−0.0184378	+	0.00671081i	−0.351223	−	0.936292i	$-0.614234\pi$
$263$	−0.299011	+	0.108831i	−0.0184378	+	0.00671081i	0.332785	+	0.943003i	$0.392012\pi$
$264$	4.34730	+	3.64781i	0.267558	+	0.224507i
$265$	20.1506			1.23784
$266$	−0.0736733	−	0.456427i	−0.00451720	−	0.0279853i
$267$	21.0797			1.29005
$268$	−4.45811	−	3.74080i	−0.272322	−	0.228506i
$269$	−11.7788	+	4.28715i	−0.718168	+	0.261392i	−0.675148	−	0.737682i	$-0.735920\pi$
$269$	−11.7788	+	4.28715i	−0.718168	+	0.261392i	−0.0430204	+	0.999074i	$0.513698\pi$
$270$	−1.00950	−	5.72513i	−0.0614359	−	0.348421i
$271$	−2.70233	+	15.3257i	−0.164155	+	0.930970i	0.785776	+	0.618511i	$0.212264\pi$
$271$	−2.70233	+	15.3257i	−0.164155	+	0.930970i	−0.949931	+	0.312459i	$0.898847\pi$
$272$	−0.270792	−	0.0985603i	−0.0164192	−	0.00597610i
$273$	0.551689	+	0.955554i	0.0333898	+	0.0578327i
$274$	5.67617	−	9.83142i	0.342910	−	0.593938i
$275$	−1.73783	+	1.45821i	−0.104795	+	0.0879333i
$276$	−7.86484	+	6.59938i	−0.473408	+	0.397236i
$277$	7.07057	−	12.2466i	0.424830	−	0.735827i	−0.571575	−	0.820550i	$-0.693667\pi$
$277$	7.07057	−	12.2466i	0.424830	−	0.735827i	0.996405	+	0.0847234i	$0.0270007\pi$
$278$	3.69506	+	6.40003i	0.221615	+	0.383848i
$279$	5.79813	+	2.11035i	0.347125	+	0.126343i
$280$	−0.0982202	+	0.557035i	−0.00586978	+	0.0332892i
$281$	1.13697	+	6.44810i	0.0678262	+	0.384661i	0.999757	+	0.0220262i	$0.00701173\pi$
$281$	1.13697	+	6.44810i	0.0678262	+	0.384661i	−0.931931	+	0.362635i	$0.881877\pi$
$282$	11.9564	−	4.35176i	0.711991	−	0.259143i
$283$	−5.34208	−	4.48254i	−0.317554	−	0.266459i	0.470052	−	0.882639i	$-0.344235\pi$
$283$	−5.34208	−	4.48254i	−0.317554	−	0.266459i	−0.787606	+	0.616179i	$0.788680\pi$
$284$	0.528791			0.0313780
$285$	−7.02229	−	12.5808i	−0.415964	−	0.745221i
$286$	−4.02229			−0.237843
$287$	−0.205737	−	0.172634i	−0.0121443	−	0.0101903i
$288$	−5.29813	+	1.92836i	−0.312196	+	0.113630i
$289$	5.26604	+	29.8652i	0.309767	+	1.75678i
$290$	1.95811	−	11.1050i	0.114984	−	0.652108i
$291$	10.4388	+	3.79942i	0.611934	+	0.222726i
$292$	−3.50165	−	6.06503i	−0.204919	−	0.354929i
$293$	9.42989	−	16.3331i	0.550900	−	0.954187i	−0.447310	−	0.894379i	$-0.647618\pi$
$293$	9.42989	−	16.3331i	0.550900	−	0.954187i	0.998210	−	0.0598080i	$-0.0190488\pi$
$294$	9.41147	−	7.89716i	0.548888	−	0.460572i
$295$	−5.25150	+	4.40653i	−0.305754	+	0.256558i
$296$	−2.08260	+	3.60716i	−0.121048	+	0.209662i
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$	−4.64290	−	1.68988i	−0.268956	−	0.0978920i
$299$	3.32383	−	18.8504i	0.192222	−	1.09014i
$300$	−0.966461	−	5.48107i	−0.0557987	−	0.316450i
$301$	−1.14543	+	0.416902i	−0.0660215	+	0.0240298i
$302$	6.22075	+	5.21983i	0.357964	+	0.300367i
$303$	9.91622			0.569672
$304$	−0.141559	+	0.115326i	−0.00811898	+	0.00661442i
$305$	14.7442			0.844252
$306$	−4.63429	−	3.88863i	−0.264924	−	0.222298i
$307$	4.21688	−	1.53482i	0.240670	−	0.0875968i	−0.218869	−	0.975754i	$-0.570237\pi$
$307$	4.21688	−	1.53482i	0.240670	−	0.0875968i	0.459539	+	0.888157i	$0.348015\pi$
$308$	0.0256923	+	0.145708i	0.00146395	+	0.00830249i
$309$	0.815207	−	4.62327i	0.0463755	−	0.263009i
$310$	−8.42679	−	3.06710i	−0.478610	−	0.174200i
$311$	−9.32042	−	16.1434i	−0.528513	−	0.915411i	−0.999447	−	0.0332427i	$-0.989417\pi$
$311$	−9.32042	−	16.1434i	−0.528513	−	0.915411i	0.470935	−	0.882168i	$-0.343917\pi$
$312$	12.9786	−	22.4797i	0.734771	−	1.27266i
$313$	−5.94150	+	4.98551i	−0.335834	+	0.281798i	−0.795072	−	0.606515i	$-0.792567\pi$
$313$	−5.94150	+	4.98551i	−0.335834	+	0.281798i	0.459238	+	0.888313i	$0.348122\pi$
$314$	−5.93835	+	4.98287i	−0.335120	+	0.281199i
$315$	−0.0996702	+	0.172634i	−0.00561578	+	0.00972682i
$316$	−1.81433	−	3.14251i	−0.102064	−	0.176780i
$317$	15.9008	+	5.78742i	0.893078	+	0.325054i	0.747475	−	0.664289i	$-0.231266\pi$
$317$	15.9008	+	5.78742i	0.893078	+	0.325054i	0.145602	+	0.989343i	$0.453488\pi$
$318$	3.72369	−	21.1181i	0.208814	−	1.18424i
$319$	−1.34730	−	7.64090i	−0.0754341	−	0.427808i
$320$	7.83022	−	2.84997i	0.437723	−	0.159318i
$321$	6.96585	+	5.84504i	0.388796	+	0.326239i
$322$	0.443868			0.0247358
$323$	28.0265	+	10.6635i	1.55943	+	0.593333i
$324$	13.4935			0.749639
$325$	7.94878	+	6.66982i	0.440919	+	0.369975i
$326$	−16.6091	+	6.04520i	−0.919891	+	0.334813i
$327$	−2.21482	−	12.5609i	−0.122480	−	0.694618i
$328$	−1.09714	+	6.22221i	−0.0605796	+	0.343564i
$329$	0.819955	+	0.298439i	0.0452056	+	0.0164535i
$330$	−1.45336	−	2.51730i	−0.0800050	−	0.138573i
$331$	−3.65136	+	6.32434i	−0.200697	+	0.347617i	−0.948753	−	0.316018i	$-0.897654\pi$
$331$	−3.65136	+	6.32434i	−0.200697	+	0.347617i	0.748056	+	0.663635i	$0.230987\pi$
$332$	−2.90033	+	2.43367i	−0.159176	+	0.133565i
$333$	−1.12449	+	0.943555i	−0.0616214	+	0.0517065i
$334$	−0.411474	+	0.712694i	−0.0225149	+	0.0389969i
$335$	3.92040	+	6.79033i	0.214194	+	0.370995i
$336$	0.00949548	+	0.00345607i	0.000518021	+	0.000188544i
$337$	−4.99407	+	28.3228i	−0.272044	+	1.54284i	0.476152	+	0.879363i	$0.342031\pi$
$337$	−4.99407	+	28.3228i	−0.272044	+	1.54284i	−0.748196	+	0.663477i	$0.769080\pi$
$338$	1.20961	+	6.86002i	0.0657940	+	0.373136i
$339$	29.5253	−	10.7463i	1.60359	−	0.583660i
$340$	−10.6839	−	8.96487i	−0.579417	−	0.486188i
$341$	−6.17024			−0.334137
$342$	−3.62061	+	1.25865i	−0.195780	+	0.0680600i
$343$	1.68685			0.0910814
$344$	21.9670	+	18.4325i	1.18438	+	0.993815i
$345$	12.9982	−	4.73097i	0.699802	−	0.254707i
$346$	−0.501755	−	2.84559i	−0.0269745	−	0.152980i
$347$	−5.17546	+	29.3515i	−0.277833	+	1.57567i	0.451983	+	0.892027i	$0.350717\pi$
$347$	−5.17546	+	29.3515i	−0.277833	+	1.57567i	−0.729816	+	0.683644i	$0.760394\pi$
$348$	17.8871	+	6.51038i	0.958851	+	0.348993i
$349$	−8.06031	−	13.9609i	−0.431458	−	0.747308i	0.565541	−	0.824720i	$-0.308667\pi$
$349$	−8.06031	−	13.9609i	−0.431458	−	0.747308i	−0.996999	+	0.0774125i	$0.975334\pi$
$350$	−0.120310	+	0.208383i	−0.00643084	+	0.0111385i
$351$	−14.0155	+	11.7604i	−0.748091	+	0.627723i
$352$	4.31908	−	3.62414i	0.230208	−	0.193167i
$353$	17.9500	−	31.0902i	0.955380	−	1.65477i	0.221884	−	0.975073i	$-0.428779\pi$
$353$	17.9500	−	31.0902i	0.955380	−	1.65477i	0.733496	−	0.679693i	$-0.237887\pi$
$354$	3.64765	+	6.31792i	0.193870	+	0.335794i
$355$	−0.669473	−	0.243668i	−0.0355319	−	0.0129326i
$356$	2.24510	−	12.7326i	0.118990	−	0.674826i
$357$	−0.288171	−	1.63430i	−0.0152516	−	0.0864963i
$358$	−18.0278	+	6.56159i	−0.952799	+	0.346791i
$359$	9.26857	+	7.77725i	0.489176	+	0.410468i	0.853731	−	0.520714i	$-0.174334\pi$
$359$	9.26857	+	7.77725i	0.489176	+	0.410468i	−0.364555	+	0.931182i	$0.618779\pi$
$360$	4.68954			0.247160
$361$	14.9029	−	11.7858i	0.784361	−	0.620305i
$362$	22.4638			1.18067
$363$	−1.53209	−	1.28558i	−0.0804138	−	0.0674752i
$364$	0.635934	−	0.231461i	0.0333320	−	0.0121319i
$365$	1.63846	+	9.29217i	0.0857609	+	0.486374i
$366$	2.72462	−	15.4521i	0.142418	−	0.807694i
$367$	13.0239	+	4.74033i	0.679844	+	0.247443i	0.658781	−	0.752335i	$-0.271073\pi$
$367$	13.0239	+	4.74033i	0.679844	+	0.247443i	0.0210635	+	0.999778i	$0.493295\pi$
$368$	−0.0876485	−	0.151812i	−0.00456900	−	0.00791373i
$369$	−1.11334	+	1.92836i	−0.0579582	+	0.100387i
$370$	1.63429	−	1.37133i	0.0849624	−	0.0712920i
$371$	1.12654	−	0.945283i	0.0584873	−	0.0490767i
$372$	7.56893	−	13.1098i	0.392431	−	0.679710i
$373$	15.1468	+	26.2350i	0.784270	+	1.35840i	0.929434	+	0.368988i	$0.120296\pi$
$373$	15.1468	+	26.2350i	0.784270	+	1.35840i	−0.145164	+	0.989408i	$0.546371\pi$
$374$	5.68479	+	2.06910i	0.293954	+	0.106990i
$375$	−4.17200	+	23.6606i	−0.215441	+	1.22183i
$376$	−3.56459	−	20.2158i	−0.183830	−	1.04255i
$377$	−33.3482	+	12.1378i	−1.71752	+	0.625127i
$378$	−0.325008	−	0.272714i	−0.0167166	−	0.0140269i
$379$	−35.5526			−1.82622			−0.913108	−	0.407718i	$-0.866325\pi$
$379$	−35.5526			−1.82622			−0.913108	+	0.407718i	$0.866325\pi$
$380$	−8.34699	+	2.90170i	−0.428192	+	0.148854i
$381$	−33.6614			−1.72452
$382$	−11.9782	−	10.0509i	−0.612857	−	0.514248i
$383$	7.46538	−	2.71718i	0.381463	−	0.138841i	−0.144169	−	0.989553i	$-0.546051\pi$
$383$	7.46538	−	2.71718i	0.381463	−	0.138841i	0.525632	+	0.850712i	$0.323829\pi$
$384$	2.37639	+	13.4772i	0.121270	+	0.687755i
$385$	0.0346151	−	0.196312i	0.00176415	−	0.0100050i
$386$	14.4884	+	5.27336i	0.737442	+	0.268407i
$387$	5.05303	+	8.75211i	0.256860	+	0.444895i
$388$	3.40673	−	5.90062i	0.172950	−	0.299559i
$389$	−1.48499	+	1.24605i	−0.0752917	+	0.0631773i	−0.679657	−	0.733530i	$-0.737871\pi$
$389$	−1.48499	+	1.24605i	−0.0752917	+	0.0631773i	0.604365	+	0.796708i	$0.293427\pi$
$390$	−10.1848	+	8.54606i	−0.515727	+	0.432746i
$391$	−14.3944	+	24.9318i	−0.727956	+	1.26086i
$392$	−9.91060	−	17.1657i	−0.500561	−	0.866997i
$393$	−9.21213	−	3.35294i	−0.464691	−	0.169134i
$394$	0.00861813	−	0.0488759i	0.000434175	−	0.00246233i
$395$	0.848945	+	4.81461i	0.0427151	+	0.242249i
$396$	1.15270	−	0.419550i	0.0579255	−	0.0210832i
$397$	20.7463	+	17.4082i	1.04123	+	0.873692i	0.992144	−	0.125102i	$-0.0399259\pi$
$397$	20.7463	+	17.4082i	1.04123	+	0.873692i	0.0490822	+	0.998795i	$0.484370\pi$
$398$	−12.0128			−0.602147
$399$	−0.982764	−	0.373922i	−0.0491997	−	0.0187195i
$400$	0.0950283			0.00475142
$401$	−12.0478	−	10.1093i	−0.601639	−	0.504835i	0.290333	−	0.956926i	$-0.406234\pi$
$401$	−12.0478	−	10.1093i	−0.601639	−	0.504835i	−0.891972	+	0.452090i	$0.850678\pi$
$402$	7.84079	−	2.85382i	0.391063	−	0.142335i
$403$	4.90080	+	27.7938i	0.244126	+	1.38451i
$404$	1.05613	−	5.98962i	0.0525445	−	0.297995i
$405$	−17.0834	−	6.21784i	−0.848879	−	0.308967i
$406$	−0.411474	−	0.712694i	−0.0204211	−	0.0353704i
$407$	0.733956	−	1.27125i	0.0363808	−	0.0630134i
$408$	−29.9067	+	25.0947i	−1.48060	+	1.24237i
$409$	−10.9042	+	9.14971i	−0.539178	+	0.452424i	−0.871257	−	0.490828i	$-0.836694\pi$
$409$	−10.9042	+	9.14971i	−0.539178	+	0.452424i	0.332079	+	0.943252i	$0.392250\pi$
$410$	1.61809	−	2.80261i	0.0799117	−	0.138411i
$411$	−12.9094	−	22.3598i	−0.636774	−	1.10293i
$412$	−2.70574	−	0.984808i	−0.133302	−	0.0485180i
$413$	−0.0868770	+	0.492704i	−0.00427494	+	0.0242444i
$414$	−0.639033	−	3.62414i	−0.0314068	−	0.178117i
$415$	4.79339	−	1.74465i	0.235298	−	0.0856415i
$416$	−19.7554	−	16.5767i	−0.968587	−	0.812741i
$417$	16.8075			0.823065
$418$	2.97178	−	2.42107i	0.145355	−	0.118418i
$419$	−25.0051			−1.22158			−0.610788	−	0.791794i	$-0.709147\pi$
$419$	−25.0051			−1.22158			−0.610788	+	0.791794i	$0.709147\pi$
$420$	0.374638	+	0.314358i	0.0182804	+	0.0153391i
$421$	−31.1587	+	11.3408i	−1.51858	+	0.552719i	−0.960794	−	0.277265i	$-0.910572\pi$
$421$	−31.1587	+	11.3408i	−1.51858	+	0.552719i	−0.557788	+	0.829983i	$0.688350\pi$
$422$	−0.786112	−	4.45826i	−0.0382673	−	0.217025i
$423$	1.25624	−	7.12452i	0.0610807	−	0.346406i
$424$	−32.5099	−	11.8326i	−1.57882	−	0.574643i
$425$	−7.80319	−	13.5155i	−0.378510	−	0.655599i
$426$	−0.379081	+	0.656587i	−0.0183665	+	0.0318117i
$427$	0.824292	−	0.691663i	0.0398903	−	0.0334719i
$428$	4.27244	−	3.58500i	0.206516	−	0.173288i
$429$	−4.57398	+	7.92236i	−0.220834	+	0.382495i
$430$	−7.34389	−	12.7200i	−0.354154	−	0.613413i
$431$	20.6065	+	7.50016i	0.992582	+	0.361270i	0.786719	−	0.617311i	$-0.211778\pi$
$431$	20.6065	+	7.50016i	0.992582	+	0.361270i	0.205862	+	0.978581i	$0.434000\pi$
$432$	−0.0290958	+	0.165011i	−0.00139987	+	0.00793908i
$433$	−3.69001	−	20.9271i	−0.177330	−	1.00569i	−0.935419	−	0.353540i	$-0.884978\pi$
$433$	−3.69001	−	20.9271i	−0.177330	−	1.00569i	0.758089	−	0.652151i	$-0.226133\pi$
$434$	−0.614990	+	0.223838i	−0.0295204	+	0.0107446i
$435$	−19.6459	−	16.4849i	−0.941949	−	0.790389i
$436$	−7.82295			−0.374651
$437$	8.89053	+	15.9278i	0.425292	+	0.761931i
$438$	10.0411			0.479781
$439$	−7.13429	−	5.98638i	−0.340501	−	0.285714i	0.456461	−	0.889743i	$-0.349117\pi$
$439$	−7.13429	−	5.98638i	−0.340501	−	0.285714i	−0.796962	+	0.604029i	$0.793561\pi$
$440$	−4.40673	+	1.60392i	−0.210082	+	0.0764638i
$441$	−1.21301	−	6.87933i	−0.0577624	−	0.327587i
$442$	4.80500	−	27.2505i	0.228550	−	1.29617i
$443$	17.1420	+	6.23919i	0.814442	+	0.296433i	0.715458	−	0.698656i	$-0.246218\pi$
$443$	17.1420	+	6.23919i	0.814442	+	0.296433i	0.0989847	+	0.995089i	$0.468441\pi$
$444$	1.80066	+	3.11883i	0.0854555	+	0.148013i
$445$	−8.70961	+	15.0855i	−0.412875	+	0.715120i
$446$	12.5360	−	10.5189i	0.593595	−	0.498085i
$447$	−8.60813	+	7.22308i	−0.407150	+	0.341640i
$448$	0.304063	−	0.526653i	0.0143656	−	0.0248820i
$449$	−0.496130	−	0.859322i	−0.0234138	−	0.0405539i	0.854081	−	0.520140i	$-0.174120\pi$
$449$	−0.496130	−	0.859322i	−0.0234138	−	0.0405539i	−0.877495	+	0.479586i	$0.840787\pi$
$450$	1.87464	+	0.682312i	0.0883713	+	0.0321645i
$451$	0.386659	−	2.19285i	0.0182071	−	0.103257i
$452$	−3.34642	−	18.9785i	−0.157402	−	0.892673i
$453$	17.3550	−	6.31672i	0.815411	−	0.296785i
$454$	−14.0123	−	11.7577i	−0.657631	−	0.551818i
$455$	−0.911779			−0.0427449
$456$	3.94181	+	24.4206i	0.184592	+	1.14360i
$457$	−16.3746			−0.765973			−0.382987	−	0.923754i	$-0.625104\pi$
$457$	−16.3746			−0.765973			−0.382987	+	0.923754i	$0.625104\pi$
$458$	0.743289	+	0.623693i	0.0347316	+	0.0291433i
$459$	25.8580	−	9.41155i	1.20695	−	0.439294i
$460$	−1.47323	−	8.35511i	−0.0686898	−	0.389559i
$461$	6.81773	−	38.6653i	0.317534	−	1.80082i	−0.240115	−	0.970745i	$-0.577185\pi$
$461$	6.81773	−	38.6653i	0.317534	−	1.80082i	0.557648	−	0.830077i	$-0.311704\pi$
$462$	−0.199340	−	0.0725540i	−0.00927416	−	0.00337552i
$463$	21.0167	+	36.4019i	0.976727	+	1.69174i	0.674113	+	0.738628i	$0.264526\pi$
$463$	21.0167	+	36.4019i	0.976727	+	1.69174i	0.302614	+	0.953113i	$0.402141\pi$
$464$	−0.162504	+	0.281465i	−0.00754405	+	0.0130667i
$465$	−15.6236	+	13.1098i	−0.724527	+	0.607951i
$466$	−18.3384	+	15.3878i	−0.849511	+	0.712825i
$467$	−20.6434	+	35.7554i	−0.955261	+	1.65456i	−0.221492	+	0.975162i	$0.571093\pi$
$467$	−20.6434	+	35.7554i	−0.955261	+	1.65456i	−0.733769	+	0.679399i	$0.762241\pi$
$468$	−2.80541	−	4.85911i	−0.129680	−	0.224612i
$469$	0.537714	+	0.195712i	0.0248293	+	0.00903713i
$470$	−1.82578	+	10.3545i	−0.0842169	+	0.477618i
$471$	3.06149	+	17.3626i	0.141066	+	0.800025i
$472$	11.0600	−	4.02551i	0.509078	−	0.185289i
$473$	−7.74170	−	6.49605i	−0.355964	−	0.298689i
$474$	5.20264			0.238965
$475$	−9.88743	−	0.143380i	−0.453666	−	0.00657872i
$476$	−1.01785			−0.0466529
$477$	−9.34002	−	7.83721i	−0.427650	−	0.358841i
$478$	9.64765	−	3.51146i	0.441273	−	0.160610i
$479$	2.26692	+	12.8564i	0.103578	+	0.587422i	0.991779	+	0.127965i	$0.0408446\pi$
$479$	2.26692	+	12.8564i	0.103578	+	0.587422i	−0.888200	+	0.459456i	$0.848044\pi$
$480$	3.23618	−	18.3533i	0.147711	−	0.837708i
$481$	−6.30928	−	2.29639i	−0.287678	−	0.104706i
$482$	−11.2729	−	19.5252i	−0.513467	−	0.889351i
$483$	0.504748	−	0.874249i	0.0229668	−	0.0397797i
$484$	−0.939693	+	0.788496i	−0.0427133	+	0.0358407i
$485$	−7.03209	+	5.90062i	−0.319311	+	0.267933i
$486$	−4.39693	+	7.61570i	−0.199449	+	0.345455i
$487$	−10.9907	−	19.0364i	−0.498035	−	0.862621i	0.501963	−	0.864889i	$-0.332611\pi$
$487$	−10.9907	−	19.0364i	−0.498035	−	0.862621i	−0.999997	+	0.00226791i	$0.999278\pi$
$488$	−23.7875	−	8.65793i	−1.07681	−	0.391926i
$489$	−6.98040	+	39.5878i	−0.315665	+	1.79022i
$490$	1.76295	+	9.99816i	0.0796418	+	0.451671i
$491$	12.7785	−	4.65101i	0.576687	−	0.209897i	−0.0371769	−	0.999309i	$-0.511837\pi$
$491$	12.7785	−	4.65101i	0.576687	−	0.209897i	0.613864	+	0.789412i	$0.289614\pi$
$492$	4.18479	+	3.51146i	0.188665	+	0.158309i
$493$	53.3756			2.40391
$494$	−13.2660	−	11.4634i	−0.596868	−	0.515762i
$495$	−1.65270			−0.0742835
$496$	0.197996	+	0.166139i	0.00889030	+	0.00745984i
$497$	−0.0488583	+	0.0177830i	−0.00219160	+	0.000797676i
$498$	−0.942629	−	5.34592i	−0.0422402	−	0.239556i
$499$	−0.646774	+	3.66804i	−0.0289536	+	0.164204i	−0.995856	−	0.0909417i	$-0.971012\pi$
$499$	−0.646774	+	3.66804i	−0.0289536	+	0.164204i	0.966903	+	0.255146i	$0.0821234\pi$
$500$	13.8472	+	5.03997i	0.619265	+	0.225394i
$501$	0.935822	+	1.62089i	0.0418095	+	0.0724161i
$502$	−0.293386	+	0.508159i	−0.0130944	+	0.0226802i
$503$	20.5431	−	17.2377i	0.915970	−	0.768590i	−0.0572751	−	0.998358i	$-0.518241\pi$
$503$	20.5431	−	17.2377i	0.915970	−	0.768590i	0.973245	+	0.229768i	$0.0737968\pi$
$504$	0.262174	−	0.219990i	0.0116782	−	0.00979914i
$505$	−4.09714	+	7.09646i	−0.182321	+	0.315788i
$506$	1.84002	+	3.18701i	0.0817990	+	0.141680i
$507$	14.8871	+	5.41847i	0.661160	+	0.240643i
$508$	−3.58512	+	20.3322i	−0.159064	+	0.902097i
$509$	−1.15539	−	6.55255i	−0.0512118	−	0.290437i	0.948436	−	0.316968i	$-0.102665\pi$
$509$	−1.15539	−	6.55255i	−0.0512118	−	0.290437i	−0.999648	+	0.0265315i	$0.991554\pi$
$510$	18.7906	−	6.83920i	0.832060	−	0.302845i
$511$	0.527503	+	0.442628i	0.0233354	+	0.0195807i
$512$	−0.473897			−0.0209435
$513$	3.27631	−	17.1250i	0.144653	−	0.756087i
$514$	9.12567			0.402516
$515$	2.97178	+	2.49362i	0.130952	+	0.109882i
$516$	23.2986	−	8.48000i	1.02566	−	0.373311i
$517$	1.25624	+	7.12452i	0.0552496	+	0.313336i
$518$	0.0270364	−	0.153331i	0.00118791	−	0.00673699i
$519$	−6.17530	−	2.24762i	−0.271065	−	0.0986598i
$520$	10.7249	+	18.5761i	0.470319	+	0.814617i
$521$	2.41740	−	4.18707i	0.105908	−	0.183439i	−0.808201	−	0.588907i	$-0.799558\pi$
$521$	2.41740	−	4.18707i	0.105908	−	0.183439i	0.914109	+	0.405469i	$0.132892\pi$
$522$	−5.22668	+	4.38571i	−0.228766	+	0.191957i
$523$	19.7512	−	16.5733i	0.863662	−	0.724698i	−0.0990919	−	0.995078i	$-0.531594\pi$
$523$	19.7512	−	16.5733i	0.863662	−	0.724698i	0.962754	+	0.270380i	$0.0871493\pi$
$524$	−3.00640	+	5.20723i	−0.131335	+	0.227479i
$525$	0.273623	+	0.473929i	0.0119419	+	0.0206840i
$526$	−0.262946	−	0.0957044i	−0.0114650	−	0.00417291i
$527$	7.37093	−	41.8026i	0.321083	−	1.82095i
$528$	0.0145479	+	0.0825054i	0.000633117	+	0.00359058i
$529$	5.15657	−	1.87684i	0.224199	−	0.0816017i
$530$	13.5744	+	11.3903i	0.589636	+	0.494764i
$531$	4.14796			0.180006
$532$	−0.330527	+	0.553787i	−0.0143302	+	0.0240097i
$533$	−10.1848			−0.441152
$534$	14.2003	+	11.9154i	0.614506	+	0.515632i
$535$	−7.06108	+	2.57002i	−0.305277	+	0.111112i
$536$	−2.33760	−	13.2572i	−0.100969	−	0.572624i
$537$	−7.57667	+	42.9694i	−0.326957	+	1.85427i
$538$	−10.3581	−	3.77005i	−0.446571	−	0.162539i
$539$	3.49273	+	6.04958i	0.150442	+	0.260574i
$540$	−4.05468	+	7.02292i	−0.174486	+	0.302218i
$541$	−5.57604	+	4.67885i	−0.239733	+	0.201160i	−0.754736	−	0.656029i	$-0.772235\pi$
$541$	−5.57604	+	4.67885i	−0.239733	+	0.201160i	0.515003	+	0.857188i	$0.327791\pi$
$542$	−10.4834	+	8.79661i	−0.450300	+	0.377847i
$543$	25.5449	−	44.2450i	1.09624	−	1.89874i
$544$	19.3935	+	33.5906i	0.831490	+	1.44018i
$545$	9.90420	+	3.60483i	0.424249	+	0.154414i
$546$	−0.168490	+	0.955554i	−0.00721070	+	0.0408939i
$547$	−4.89037	−	27.7347i	−0.209097	−	1.18585i	−0.890861	−	0.454276i	$-0.849898\pi$
$547$	−4.89037	−	27.7347i	−0.209097	−	1.18585i	0.681764	−	0.731572i	$-0.261213\pi$
$548$	−14.8807	+	5.41614i	−0.635673	+	0.231366i
$549$	−6.83409	−	5.73448i	−0.291672	−	0.244742i
$550$	−1.99495			−0.0850648
$551$	17.3327	−	29.0404i	0.738400	−	1.23716i
$552$	−23.7487			−1.01081
$553$	0.273318	+	0.229341i	0.0116227	+	0.00975259i
$554$	11.6856	−	4.25320i	0.496472	−	0.180701i
$555$	−0.842549	−	4.77833i	−0.0357642	−	0.202829i
$556$	1.79009	−	10.1521i	0.0759166	−	0.430545i
$557$	−2.37716	−	0.865217i	−0.100724	−	0.0366604i	0.291167	−	0.956672i	$-0.405957\pi$
$557$	−2.37716	−	0.865217i	−0.100724	−	0.0366604i	−0.391890	+	0.920012i	$0.628179\pi$
$558$	2.71301	+	4.69907i	0.114851	+	0.198928i
$559$	−23.1125	+	40.0320i	−0.977553	+	1.69317i
$560$	−0.00639661	+	0.00536740i	−0.000270306	+	0.000226814i
$561$	10.5398	−	8.84397i	0.444992	−	0.373393i
$562$	−2.87892	+	4.98643i	−0.121440	+	0.210340i
$563$	4.81861	+	8.34608i	0.203080	+	0.351745i	0.949519	−	0.313708i	$-0.101571\pi$
$563$	4.81861	+	8.34608i	0.203080	+	0.351745i	−0.746439	+	0.665454i	$0.768238\pi$
$564$	−16.6783	−	6.07040i	−0.702283	−	0.255610i
$565$	−4.50862	+	25.5696i	−0.189679	+	1.07572i
$566$	−1.06489	−	6.03931i	−0.0447608	−	0.253851i
$567$	−1.24675	+	0.453779i	−0.0523585	+	0.0190569i
$568$	0.937004	+	0.786240i	0.0393158	+	0.0329899i
$569$	−24.2790			−1.01783			−0.508914	−	0.860817i	$-0.669953\pi$
$569$	−24.2790			−1.01783			−0.508914	+	0.860817i	$0.669953\pi$
$570$	2.38084	−	12.4444i	0.0997222	−	0.521240i
$571$	15.0743			0.630839			0.315420	−	0.948952i	$-0.397855\pi$
$571$	15.0743			0.630839			0.315420	+	0.948952i	$0.397855\pi$
$572$	4.29813	+	3.60656i	0.179714	+	0.150798i
$573$	−33.4175	+	12.1630i	−1.39603	+	0.508115i
$574$	−0.0410117	−	0.232589i	−0.00171180	−	0.00970808i
$575$	1.64853	−	9.34927i	0.0687484	−	0.389892i
$576$	−4.73783	−	1.72443i	−0.197409	−	0.0718512i
$577$	10.2221	+	17.7052i	0.425551	+	0.737077i	0.996472	−	0.0839288i	$-0.0267468\pi$
$577$	10.2221	+	17.7052i	0.425551	+	0.737077i	−0.570920	+	0.821005i	$0.693413\pi$
$578$	−13.3341	+	23.0953i	−0.554625	+	0.960639i
$579$	26.8621	−	22.5400i	1.11635	−	0.936731i
$580$	−12.0496	+	10.1108i	−0.500334	+	0.419830i
$581$	0.186137	−	0.322398i	0.00772225	−	0.0133753i
$582$	4.88444	+	8.46009i	0.202466	+	0.350682i
$583$	11.4572	+	4.17009i	0.474510	+	0.172708i
$584$	2.81304	−	15.9536i	0.116405	−	0.660163i
$585$	1.31268	+	7.44459i	0.0542727	+	0.307796i
$586$	15.5848	−	5.67241i	0.643803	−	0.234325i
$587$	27.8259	+	23.3487i	1.14850	+	0.963706i	0.999683	−	0.0251594i	$-0.00800932\pi$
$587$	27.8259	+	23.3487i	1.14850	+	0.963706i	0.148816	+	0.988865i	$0.452454\pi$
$588$	−17.1379			−0.706753
$589$	−20.3503	−	17.5850i	−0.838519	−	0.724577i
$590$	−6.02849			−0.248189
$591$	−0.0864665	−	0.0725540i	−0.00355676	−	0.00298447i
$592$	−0.0577812	+	0.0210306i	−0.00237479	+	0.000864353i
$593$	−3.87598	−	21.9818i	−0.159167	−	0.902684i	−0.954876	−	0.297004i	$-0.904012\pi$
$593$	−3.87598	−	21.9818i	−0.159167	−	0.902684i	0.795709	−	0.605680i	$-0.207099\pi$
$594$	0.610815	−	3.46410i	0.0250620	−	0.142134i
$595$	1.28864	+	0.469026i	0.0528290	+	0.0192282i
$596$	3.44609	+	5.96880i	0.141157	+	0.244492i
$597$	−13.6604	+	23.6606i	−0.559085	+	0.968363i
$598$	12.8944	−	10.8197i	0.527291	−	0.442450i
$599$	8.96039	−	7.51866i	0.366112	−	0.307204i	−0.441110	−	0.897453i	$-0.645415\pi$
$599$	8.96039	−	7.51866i	0.366112	−	0.307204i	0.807221	+	0.590249i	$0.200971\pi$
$600$	6.43706	−	11.1493i	0.262792	−	0.455169i
$601$	−18.9650	−	32.8483i	−0.773597	−	1.33991i	−0.935579	−	0.353116i	$-0.885122\pi$
$601$	−18.9650	−	32.8483i	−0.773597	−	1.33991i	0.161982	−	0.986794i	$-0.448211\pi$
$602$	−1.00727	−	0.366618i	−0.0410534	−	0.0149422i
$603$	0.823826	−	4.67215i	0.0335488	−	0.190265i
$604$	−1.96703	−	11.1556i	−0.0800375	−	0.453915i
$605$	1.55303	−	0.565258i	0.0631398	−	0.0229810i
$606$	6.68004	+	5.60522i	0.271358	+	0.227697i
$607$	9.23442			0.374814			0.187407	−	0.982282i	$-0.439992\pi$
$607$	9.23442			0.374814			0.187407	+	0.982282i	$0.439992\pi$
$608$	24.5736	+	0.356347i	0.996590	+	0.0144518i
$609$	−1.87164			−0.0758429
$610$	9.93242	+	8.33429i	0.402152	+	0.337445i
$611$	31.0945	−	11.3175i	1.25795	−	0.457856i
$612$	1.46538	+	8.31061i	0.0592347	+	0.335937i
$613$	−1.06805	+	6.05720i	−0.0431381	+	0.244648i	−0.998750	−	0.0499794i	$-0.984084\pi$
$613$	−1.06805	+	6.05720i	−0.0431381	+	0.244648i	0.955612	+	0.294627i	$0.0951956\pi$
$614$	3.70826	+	1.34970i	0.149653	+	0.0544694i
$615$	−3.68004	−	6.37402i	−0.148394	−	0.257025i
$616$	−0.171122	+	0.296392i	−0.00689470	+	0.0119420i
$617$	−20.5685	+	17.2590i	−0.828057	+	0.694823i	−0.954844	−	0.297107i	$-0.903978\pi$
$617$	−20.5685	+	17.2590i	−0.828057	+	0.694823i	0.126787	+	0.991930i	$0.459534\pi$
$618$	3.16250	−	2.65366i	0.127215	−	0.106746i
$619$	17.3787	−	30.1007i	0.698508	−	1.20985i	−0.270476	−	0.962727i	$-0.587181\pi$
$619$	17.3787	−	30.1007i	0.698508	−	1.20985i	0.968984	−	0.247124i	$-0.0794856\pi$
$620$	6.25460	+	10.8333i	0.251191	+	0.435075i
$621$	15.7297	+	5.72513i	0.631210	+	0.229742i
$622$	2.84652	−	16.1434i	0.114135	−	0.647293i
$623$	0.220752	+	1.25195i	0.00884423	+	0.0501581i
$624$	0.360090	−	0.131062i	0.0144151	−	0.00524667i
$625$	−6.51960	−	5.47059i	−0.260784	−	0.218824i
$626$	−6.82058			−0.272605
$627$	−1.38919	−	8.60640i	−0.0554787	−	0.343707i
$628$	10.8135			0.431504
$629$	7.73577	+	6.49108i	0.308445	+	0.258816i
$630$	−0.164725	+	0.0599551i	−0.00656281	+	0.00238867i
$631$	−5.80659	−	32.9308i	−0.231157	−	1.31095i	−0.850558	−	0.525880i	$-0.823736\pi$
$631$	−5.80659	−	32.9308i	−0.231157	−	1.31095i	0.619402	−	0.785074i	$-0.287375\pi$
$632$	1.45754	−	8.26611i	0.0579778	−	0.328808i
$633$	−9.67499	−	3.52141i	−0.384546	−	0.139963i
$634$	7.44016	+	12.8867i	0.295486	+	0.511798i
$635$	13.9081	−	24.0895i	0.551925	−	0.955962i
$636$	−22.9145	+	19.2275i	−0.908618	+	0.762421i
$637$	24.4761	−	20.5379i	0.969779	−	0.813741i
$638$	3.41147	−	5.90885i	0.135062	−	0.233933i
$639$	0.215537	+	0.373321i	0.00852652	+	0.0147684i
$640$	−10.6267	−	3.86780i	−0.420057	−	0.152888i
$641$	−5.79648	+	32.8735i	−0.228947	+	1.29843i	0.626046	+	0.779786i	$0.284672\pi$
$641$	−5.79648	+	32.8735i	−0.228947	+	1.29843i	−0.854993	+	0.518639i	$0.826439\pi$
$642$	1.38858	+	7.87501i	0.0548027	+	0.310802i
$643$	−30.9488	+	11.2644i	−1.22050	+	0.444226i	−0.870334	−	0.492462i	$-0.836097\pi$
$643$	−30.9488	+	11.2644i	−1.22050	+	0.444226i	−0.350166	+	0.936687i	$0.613875\pi$
$644$	−0.474308	−	0.397991i	−0.0186903	−	0.0156831i
$645$	−33.4047			−1.31531
$646$	12.8523	+	23.0256i	0.505669	+	0.905931i
$647$	−31.6979			−1.24617			−0.623086	−	0.782153i	$-0.714121\pi$
$647$	−31.6979			−1.24617			−0.623086	+	0.782153i	$0.714121\pi$
$648$	23.9101	+	20.0630i	0.939279	+	0.788148i
$649$	−3.89780	+	1.41868i	−0.153002	+	0.0556882i
$650$	1.58451	+	8.98622i	0.0621497	+	0.352469i
$651$	−0.258466	+	1.46583i	−0.0101301	+	0.0574505i
$652$	23.1685	+	8.43264i	0.907348	+	0.330248i
$653$	4.17840	+	7.23719i	0.163513	+	0.283213i	0.936126	−	0.351664i	$-0.114384\pi$
$653$	4.17840	+	7.23719i	0.163513	+	0.283213i	−0.772613	+	0.634877i	$0.781051\pi$
$654$	5.60813	−	9.71356i	0.219295	−	0.379830i
$655$	6.20574	−	5.20723i	0.242478	−	0.203463i
$656$	−0.0714517	+	0.0599551i	−0.00278972	+	0.00234085i
$657$	2.85457	−	4.94426i	0.111367	−	0.192894i
$658$	0.383666	+	0.664529i	0.0149569	+	0.0259060i
$659$	6.41147	+	2.33359i	0.249756	+	0.0909036i	0.463864	−	0.885906i	$-0.346462\pi$
$659$	6.41147	+	2.33359i	0.249756	+	0.0909036i	−0.214109	+	0.976810i	$0.568685\pi$
$660$	−0.704088	+	3.99308i	−0.0274066	+	0.155431i
$661$	−1.29102	−	7.32175i	−0.0502149	−	0.284783i	0.949352	−	0.314215i	$-0.101741\pi$
$661$	−1.29102	−	7.32175i	−0.0502149	−	0.284783i	−0.999567	+	0.0294320i	$0.990630\pi$
$662$	−6.03462	+	2.19642i	−0.234542	+	0.0853663i
$663$	−48.2089	−	40.4521i	−1.87228	−	1.57103i
$664$	−8.75784			−0.339870
$665$	0.673648	−	0.548811i	0.0261230	−	0.0212820i
$666$	−1.29086			−0.0500198
$667$	24.8726	+	20.8706i	0.963070	+	0.808112i
$668$	1.07873	−	0.392624i	0.0417372	−	0.0151911i
$669$	−6.46286	−	36.6527i	−0.249869	−	1.41707i
$670$	−1.19732	+	6.79033i	−0.0462564	+	0.262333i
$671$	8.38326	+	3.05126i	0.323632	+	0.117792i
$672$	−0.680045	−	1.17787i	−0.0262333	−	0.0454374i
$673$	−15.6446	+	27.0972i	−0.603053	+	1.04452i	0.389303	+	0.921110i	$0.372716\pi$
$673$	−15.6446	+	27.0972i	−0.603053	+	1.04452i	−0.992356	+	0.123409i	$0.960617\pi$
$674$	−19.3739	+	16.2567i	−0.746256	+	0.626183i
$675$	−6.95130	+	5.83284i	−0.267556	+	0.224506i
$676$	4.85844	−	8.41507i	0.186863	−	0.323656i
$677$	20.3824	+	35.3033i	0.783358	+	1.35682i	0.929975	+	0.367623i	$0.119828\pi$
$677$	20.3824	+	35.3033i	0.783358	+	1.35682i	−0.146616	+	0.989193i	$0.546838\pi$
$678$	25.9641	+	9.45016i	0.997145	+	0.362931i
$679$	−0.116334	+	0.659762i	−0.00446448	+	0.0253193i
$680$	−5.60209	−	31.7710i	−0.214830	−	1.21836i
$681$	−39.0925	+	14.2285i	−1.49803	+	0.545237i
$682$	−4.15657	−	3.48778i	−0.159163	−	0.133554i
$683$	−27.7320			−1.06114			−0.530568	−	0.847642i	$-0.678022\pi$
$683$	−27.7320			−1.06114			−0.530568	+	0.847642i	$0.678022\pi$
$684$	4.99747	+	1.90144i	0.191083	+	0.0727033i
$685$	21.3354			0.815185
$686$	1.13634	+	0.953506i	0.0433858	+	0.0364050i
$687$	2.07367	−	0.754755i	0.0791156	−	0.0287957i
$688$	0.0735111	+	0.416902i	0.00280259	+	0.0158943i
$689$	9.68408	−	54.9211i	0.368934	−	2.09233i
$690$	11.4305	+	4.16035i	0.435150	+	0.158382i
$691$	18.5906	+	32.1999i	0.707221	+	1.22494i	0.965884	+	0.258976i	$0.0833849\pi$
$691$	18.5906	+	32.1999i	0.707221	+	1.22494i	−0.258663	+	0.965968i	$0.583282\pi$
$692$	−2.01532	+	3.49064i	−0.0766110	+	0.132694i
$693$	−0.0923963	+	0.0775297i	−0.00350984	+	0.00294511i
$694$	−20.0776	+	16.8471i	−0.762135	+	0.639507i
$695$	−6.94444	+	12.0281i	−0.263418	+	0.456253i
$696$	22.0155	+	38.1319i	0.834495	+	1.44539i
$697$	14.3944	+	5.23913i	0.545227	+	0.198446i
$698$	2.46168	−	13.9609i	0.0931758	−	0.528426i
$699$	9.45430	+	53.6180i	0.357594	+	2.02802i
$700$	0.315406	−	0.114799i	0.0119212	−	0.00433898i
$701$	2.05896	+	1.72768i	0.0777660	+	0.0652534i	0.680842	−	0.732430i	$-0.261614\pi$
$701$	2.05896	+	1.72768i	0.0777660	+	0.0652534i	−0.603076	+	0.797684i	$0.706058\pi$
$702$	−16.0892			−0.607246
$703$	6.04370	−	2.10100i	0.227942	−	0.0792406i
$704$	5.04189			0.190023
$705$	18.3182	+	15.3708i	0.689903	+	0.578898i
$706$	29.6660	−	10.7975i	1.11649	−	0.406370i
$707$	0.103845	+	0.588936i	0.00390551	+	0.0221492i
$708$	1.76712	−	10.0218i	0.0664125	−	0.376644i
$709$	−32.7520	−	11.9207i	−1.23003	−	0.447693i	−0.356419	−	0.934326i	$-0.616003\pi$
$709$	−32.7520	−	11.9207i	−1.23003	−	0.447693i	−0.873606	+	0.486633i	$0.838225\pi$
$710$	−0.313254	−	0.542572i	−0.0117562	−	0.0203624i
$711$	1.47906	−	2.56180i	0.0554689	−	0.0960750i
$712$	22.9099	−	19.2237i	0.858584	−	0.720438i
$713$	19.7802	−	16.5975i	0.740774	−	0.621583i
$714$	0.729675	−	1.26383i	0.0273074	−	0.0472978i
$715$	−3.77972	−	6.54666i	−0.141353	−	0.244831i
$716$	25.1475	+	9.15296i	0.939808	+	0.342062i
$717$	4.05468	−	22.9952i	0.151425	−	0.858773i
$718$	1.84760	+	10.4783i	0.0689519	+	0.391045i
$719$	−1.28787	+	0.468745i	−0.0480293	+	0.0174812i	−0.365923	−	0.930645i	$-0.619247\pi$
$719$	−1.28787	+	0.468745i	−0.0480293	+	0.0174812i	0.317894	+	0.948126i	$0.397024\pi$
$720$	0.0530334	+	0.0445003i	0.00197644	+	0.00165843i
$721$	0.283119			0.0105439
$722$	16.7013	+	0.484481i	0.621558	+	0.0180305i
$723$	−51.2763			−1.90699
$724$	−24.0043	−	20.1420i	−0.892114	−	0.748573i
$725$	−16.5398	+	6.02001i	−0.614274	+	0.223577i
$726$	−0.305407	−	1.73205i	−0.0113347	−	0.0642824i
$727$	−1.27955	+	7.25671i	−0.0474560	+	0.269136i	−0.999298	−	0.0374512i	$-0.988076\pi$
$727$	−1.27955	+	7.25671i	−0.0474560	+	0.269136i	0.951842	+	0.306588i	$0.0991872\pi$
$728$	1.47101	+	0.535404i	0.0545193	+	0.0198434i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$	−4.14873	+	7.18581i	−0.153551	+	0.265959i
$731$	53.2581	−	44.6889i	1.96982	−	1.65288i
$732$	−16.7665	+	14.0688i	−0.619708	+	0.519997i
$733$	15.3469	−	26.5816i	0.566850	−	0.981813i	−0.430025	−	0.902817i	$-0.641495\pi$
$733$	15.3469	−	26.5816i	0.566850	−	0.981813i	0.996875	−	0.0789962i	$-0.0251715\pi$
$734$	6.09405	+	10.5552i	0.224935	+	0.389599i
$735$	21.6973	+	7.89716i	0.800316	+	0.291291i
$736$	−4.09714	+	23.2361i	−0.151023	+	0.856492i
$737$	0.823826	+	4.67215i	0.0303460	+	0.172101i
$738$	−1.84002	+	0.669713i	−0.0677322	+	0.0246525i
$739$	32.0526	+	26.8953i	1.17907	+	0.989361i	0.999985	+	0.00552854i	$0.00175980\pi$
$739$	32.0526	+	26.8953i	1.17907	+	0.989361i	0.179090	+	0.983833i	$0.442685\pi$
$740$	−2.97596			−0.109398
$741$	−37.6641	+	13.0933i	−1.38362	+	0.480995i
$742$	1.29322			0.0474757
$743$	−20.2683	−	17.0071i	−0.743573	−	0.623932i	0.190222	−	0.981741i	$-0.439079\pi$
$743$	−20.2683	−	17.0071i	−0.743573	−	0.623932i	−0.933795	+	0.357810i	$0.883524\pi$
$744$	32.9044	−	11.9762i	1.20633	−	0.439069i
$745$	−1.61246	−	9.14473i	−0.0590761	−	0.335037i
$746$	−4.62594	+	26.2350i	−0.169368	+	0.960531i
$747$	−2.90033	−	1.05563i	−0.106118	−	0.0386236i
$748$	−4.21941	−	7.30823i	−0.154277	−	0.267215i
$749$	−0.274196	+	0.474921i	−0.0100189	+	0.0173532i
$750$	−16.1848	+	13.5807i	−0.590985	+	0.495895i
$751$	17.9342	−	15.0486i	0.654429	−	0.549131i	−0.253982	−	0.967209i	$-0.581740\pi$
$751$	17.9342	−	15.0486i	0.654429	−	0.549131i	0.908411	+	0.418078i	$0.137296\pi$
$752$	0.151522	−	0.262443i	0.00552542	−	0.00957032i
$753$	0.667252	+	1.15571i	0.0243160	+	0.0421165i
$754$	−29.3259	−	10.6738i	−1.06799	−	0.388716i
$755$	−2.65018	+	15.0299i	−0.0964498	+	0.546994i
$756$	0.102769	+	0.582832i	0.00373768	+	0.0211974i
$757$	−8.53761	+	3.10744i	−0.310305	+	0.112942i	−0.492478	−	0.870325i	$-0.663909\pi$
$757$	−8.53761	+	3.10744i	−0.310305	+	0.112942i	0.182174	+	0.983266i	$0.441687\pi$
$758$	−23.9500	−	20.0964i	−0.869902	−	0.729934i
$759$	8.36959			0.303797
$760$	−19.1051	−	7.26910i	−0.693014	−	0.263678i
$761$	−18.0196			−0.653210			−0.326605	−	0.945161i	$-0.605905\pi$
$761$	−18.0196			−0.653210			−0.326605	+	0.945161i	$0.605905\pi$
$762$	−22.6759	−	19.0274i	−0.821462	−	0.689289i
$763$	0.722811	−	0.263082i	0.0261675	−	0.00952420i
$764$	3.78

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.673648 + 0.565258i) q^{2} +(1.87939 - 0.684040i) q^{3} +(-0.213011 - 1.20805i) q^{4} +(-0.286989 + 1.62760i) q^{5} +(1.65270 + 0.601535i) q^{6} +(0.0603074 + 0.104455i) q^{7} +(1.41875 - 2.45734i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.673648 + 0.565258i) q^{2} +(1.87939 - 0.684040i) q^{3} +(-0.213011 - 1.20805i) q^{4} +(-0.286989 + 1.62760i) q^{5} +(1.65270 + 0.601535i) q^{6} +(0.0603074 + 0.104455i) q^{7} +(1.41875 - 2.45734i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-1.11334 + 0.934204i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.22668 - 2.12467i) q^{12} +(4.29813 + 1.56439i) q^{13} +(-0.0184183 + 0.104455i) q^{14} +(0.573978 + 3.25519i) q^{15} +(0.0393628 - 0.0143269i) q^{16} +(-5.26991 - 4.42198i) q^{17} +0.879385 q^{18} +(-4.11721 + 1.43128i) q^{19} +2.02734 q^{20} +(0.184793 + 0.155059i) q^{21} +(-0.826352 + 0.300767i) q^{22} +(-0.726682 - 4.12122i) q^{23} +(0.985452 - 5.58878i) q^{24} +(2.13176 + 0.775897i) q^{25} +(2.01114 + 3.48340i) q^{26} +(-2.00000 + 3.46410i) q^{27} +(0.113341 - 0.0951042i) q^{28} +(-5.94356 + 4.98724i) q^{29} +(-1.45336 + 2.51730i) q^{30} +(3.08512 + 5.34359i) q^{31} +(-5.29813 - 1.92836i) q^{32} +(-0.347296 + 1.96962i) q^{33} +(-1.05051 - 5.95772i) q^{34} +(-0.187319 + 0.0681784i) q^{35} +(-0.939693 - 0.788496i) q^{36} -1.46791 q^{37} +(-3.58260 - 1.36310i) q^{38} +9.14796 q^{39} +(3.59240 + 3.01438i) q^{40} +(-2.09240 + 0.761570i) q^{41} +(0.0368366 + 0.208911i) q^{42} +(-1.75490 + 9.95253i) q^{43} +(1.15270 + 0.419550i) q^{44} +(0.826352 + 1.43128i) q^{45} +(1.84002 - 3.18701i) q^{46} +(5.54189 - 4.65020i) q^{47} +(0.0641778 - 0.0538515i) q^{48} +(3.49273 - 6.04958i) q^{49} +(0.997474 + 1.72768i) q^{50} +(-12.9290 - 4.70578i) q^{51} +(0.974308 - 5.52557i) q^{52} +(-2.11721 - 12.0073i) q^{53} +(-3.30541 + 1.20307i) q^{54} +(-1.26604 - 1.06234i) q^{55} +0.342244 q^{56} +(-6.75877 + 5.50627i) q^{57} -6.82295 q^{58} +(3.17752 + 2.66625i) q^{59} +(3.81016 - 1.38678i) q^{60} +(-1.54916 - 8.78574i) q^{61} +(-0.942219 + 5.34359i) q^{62} +(0.113341 + 0.0412527i) q^{63} +(-2.52094 - 4.36640i) q^{64} +(-3.77972 + 6.54666i) q^{65} +(-1.34730 + 1.13052i) q^{66} +(3.63429 - 3.04953i) q^{67} +(-4.21941 + 7.30823i) q^{68} +(-4.18479 - 7.24827i) q^{69} +(-0.164725 - 0.0599551i) q^{70} +(-0.0748553 + 0.424525i) q^{71} +(-0.492726 - 2.79439i) q^{72} +(5.36484 - 1.95264i) q^{73} +(-0.988856 - 0.829748i) q^{74} +4.53714 q^{75} +(2.60607 + 4.66890i) q^{76} -0.120615 q^{77} +(6.16250 + 5.17095i) q^{78} +(2.77972 - 1.01173i) q^{79} +(0.0120217 + 0.0681784i) q^{80} +(-1.91013 + 10.8329i) q^{81} +(-1.84002 - 0.669713i) q^{82} +(-1.54323 - 2.67296i) q^{83} +(0.147956 - 0.256267i) q^{84} +(8.70961 - 7.30823i) q^{85} +(-6.80793 + 5.71253i) q^{86} +(-7.75877 + 13.4386i) q^{87} +(1.41875 + 2.45734i) q^{88} +(9.90420 + 3.60483i) q^{89} +(-0.252374 + 1.43128i) q^{90} +(0.0957998 + 0.543308i) q^{91} +(-4.82383 + 1.75573i) q^{92} +(9.45336 + 7.93231i) q^{93} +6.36184 q^{94} +(-1.14796 - 7.11192i) q^{95} -11.2763 q^{96} +(4.25490 + 3.57029i) q^{97} +(5.77244 - 2.10100i) q^{98} +(0.173648 + 0.984808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8} - 3 q^{11} + 6 q^{12} + 12 q^{13} - 12 q^{14} - 12 q^{15} + 9 q^{16} - 3 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} - 6 q^{21} - 6 q^{22} + 9 q^{23} - 30 q^{24} + 18 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} + 18 q^{30} - 3 q^{31} - 18 q^{32} - 9 q^{34} + 21 q^{35} - 18 q^{37} - 15 q^{38} + 24 q^{39} + 18 q^{40} - 9 q^{41} + 24 q^{42} - 12 q^{43} + 9 q^{44} + 6 q^{45} - 9 q^{46} + 27 q^{47} - 18 q^{48} + 3 q^{49} + 21 q^{50} - 12 q^{51} - 24 q^{52} + 18 q^{53} - 24 q^{54} - 3 q^{55} + 30 q^{56} - 18 q^{57} - 6 q^{59} + 60 q^{60} - 21 q^{61} + 15 q^{62} - 6 q^{63} - 12 q^{64} + 3 q^{65} - 6 q^{66} + 12 q^{67} + 6 q^{68} - 18 q^{69} - 54 q^{70} - 42 q^{71} + 15 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} - 9 q^{76} - 12 q^{77} + 42 q^{78} - 9 q^{79} + 51 q^{80} + 9 q^{82} + 6 q^{83} - 30 q^{84} + 18 q^{85} - 30 q^{86} - 24 q^{87} + 6 q^{88} + 21 q^{89} - 18 q^{90} + 39 q^{91} - 45 q^{92} + 30 q^{93} + 72 q^{94} + 24 q^{95} + 27 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8 - 3 * q^11 + 6 * q^12 + 12 * q^13 - 12 * q^14 - 12 * q^15 + 9 * q^16 - 3 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 - 6 * q^21 - 6 * q^22 + 9 * q^23 - 30 * q^24 + 18 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 + 18 * q^30 - 3 * q^31 - 18 * q^32 - 9 * q^34 + 21 * q^35 - 18 * q^37 - 15 * q^38 + 24 * q^39 + 18 * q^40 - 9 * q^41 + 24 * q^42 - 12 * q^43 + 9 * q^44 + 6 * q^45 - 9 * q^46 + 27 * q^47 - 18 * q^48 + 3 * q^49 + 21 * q^50 - 12 * q^51 - 24 * q^52 + 18 * q^53 - 24 * q^54 - 3 * q^55 + 30 * q^56 - 18 * q^57 - 6 * q^59 + 60 * q^60 - 21 * q^61 + 15 * q^62 - 6 * q^63 - 12 * q^64 + 3 * q^65 - 6 * q^66 + 12 * q^67 + 6 * q^68 - 18 * q^69 - 54 * q^70 - 42 * q^71 + 15 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 - 9 * q^76 - 12 * q^77 + 42 * q^78 - 9 * q^79 + 51 * q^80 + 9 * q^82 + 6 * q^83 - 30 * q^84 + 18 * q^85 - 30 * q^86 - 24 * q^87 + 6 * q^88 + 21 * q^89 - 18 * q^90 + 39 * q^91 - 45 * q^92 + 30 * q^93 + 72 * q^94 + 24 * q^95 + 27 * q^97 - 9 * q^98

Introduction

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