LMFDB - Embedded newform 87.2.g.a.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.3
Root			$-1.05678 + 1.32516i$ of defining polynomial
Character	$\chi$	$=$	87.49
Dual form			87.2.g.a.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.626118 - 0.301523i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.945872 + 1.18609i) q^{4} +(1.81798 - 0.875492i) q^{5} +(0.626118 + 0.301523i) q^{6} +(-1.49319 - 1.87240i) q^{7} +(-0.543873 + 2.38286i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})$	\(q+(0.626118 - 0.301523i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.945872 + 1.18609i) q^{4} +(1.81798 - 0.875492i) q^{5} +(0.626118 + 0.301523i) q^{6} +(-1.49319 - 1.87240i) q^{7} +(-0.543873 + 2.38286i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(0.874288 - 1.09632i) q^{10} +(0.213150 + 0.933871i) q^{11} -1.51706 q^{12} +(-1.45377 - 6.36940i) q^{13} +(-1.49948 - 0.722111i) q^{14} +(1.81798 + 0.875492i) q^{15} +(-0.297197 - 1.30211i) q^{16} -3.81642 q^{17} +(0.154638 + 0.677515i) q^{18} +(-2.69251 + 3.37631i) q^{19} +(-0.681165 + 2.98438i) q^{20} +(0.532912 - 2.33484i) q^{21} +(0.415040 + 0.520444i) q^{22} +(4.85446 + 2.33778i) q^{23} +(-2.20209 + 1.06047i) q^{24} +(-0.578892 + 0.725907i) q^{25} +(-2.83075 - 3.54965i) q^{26} +(-0.900969 + 0.433884i) q^{27} +3.63318 q^{28} +(5.32202 + 0.822256i) q^{29} +1.40225 q^{30} +(-2.46382 + 1.18651i) q^{31} +(-3.62649 - 4.54747i) q^{32} +(-0.597233 + 0.748906i) q^{33} +(-2.38953 + 1.15074i) q^{34} +(-4.35384 - 2.09670i) q^{35} +(-0.945872 - 1.18609i) q^{36} +(0.414041 - 1.81403i) q^{37} +(-0.667799 + 2.92582i) q^{38} +(4.07339 - 5.10787i) q^{39} +(1.09743 + 4.80814i) q^{40} +11.8282 q^{41} +(-0.370341 - 1.62257i) q^{42} +(3.33752 + 1.60727i) q^{43} +(-1.30926 - 0.630508i) q^{44} +(0.449003 + 1.96721i) q^{45} +3.74436 q^{46} +(0.719344 + 3.15165i) q^{47} +(0.832729 - 1.04421i) q^{48} +(0.281385 - 1.23283i) q^{49} +(-0.143577 + 0.629053i) q^{50} +(-2.37950 - 2.98379i) q^{51} +(8.92974 + 4.30034i) q^{52} +(-2.04315 + 0.983927i) q^{53} +(-0.433287 + 0.543325i) q^{54} +(1.20510 + 1.51115i) q^{55} +(5.27376 - 2.53971i) q^{56} -4.31846 q^{57} +(3.58014 - 1.08988i) q^{58} -9.30726 q^{59} +(-2.75798 + 1.32817i) q^{60} +(1.95684 + 2.45380i) q^{61} +(-1.18488 + 1.48579i) q^{62} +(2.15772 - 1.03910i) q^{63} +(-1.23512 - 0.594802i) q^{64} +(-8.21929 - 10.3067i) q^{65} +(-0.148126 + 0.648983i) q^{66} +(-2.69277 + 11.7978i) q^{67} +(3.60984 - 4.52660i) q^{68} +(1.19895 + 5.25295i) q^{69} -3.35822 q^{70} +(1.02436 + 4.48801i) q^{71} +(-2.20209 - 1.06047i) q^{72} +(-8.19102 - 3.94459i) q^{73} +(-0.287733 - 1.26064i) q^{74} -0.928470 q^{75} +(-1.45781 - 6.38710i) q^{76} +(1.43030 - 1.79354i) q^{77} +(1.01028 - 4.42634i) q^{78} +(-0.954127 + 4.18030i) q^{79} +(-1.68028 - 2.10701i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(7.40582 - 3.56646i) q^{82} +(10.0888 - 12.6510i) q^{83} +(2.26525 + 2.84054i) q^{84} +(-6.93816 + 3.34124i) q^{85} +2.57431 q^{86} +(2.67536 + 4.67359i) q^{87} -2.34121 q^{88} +(-13.9137 + 6.70047i) q^{89} +(0.874288 + 1.09632i) q^{90} +(-9.75529 + 12.2327i) q^{91} +(-7.36451 + 3.54656i) q^{92} +(-2.46382 - 1.18651i) q^{93} +(1.40069 + 1.75641i) q^{94} +(-1.93900 + 8.49532i) q^{95} +(1.29428 - 5.67061i) q^{96} +(9.82817 - 12.3241i) q^{97} +(-0.195546 - 0.856741i) q^{98} -0.957887 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

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 $

$2$	0.626118	−	0.301523i	0.442732	−	0.213209i	−0.199218	−	0.979955i	$-0.563840\pi$
$2$	0.626118	−	0.301523i	0.442732	−	0.213209i	0.641950	+	0.766747i	$0.278126\pi$
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$4$	−0.945872	+	1.18609i	−0.472936	+	0.593043i
$5$	1.81798	−	0.875492i	0.813024	−	0.391532i	0.0193032	−	0.999814i	$-0.493855\pi$
$5$	1.81798	−	0.875492i	0.813024	−	0.391532i	0.793721	+	0.608282i	$0.208141\pi$
$6$	0.626118	+	0.301523i	0.255612	+	0.123096i
$7$	−1.49319	−	1.87240i	−0.564371	−	0.707699i	0.414988	−	0.909827i	$-0.363786\pi$
$7$	−1.49319	−	1.87240i	−0.564371	−	0.707699i	−0.979359	+	0.202128i	$0.935214\pi$
$8$	−0.543873	+	2.38286i	−0.192288	+	0.842469i
$9$	−0.222521	+	0.974928i	−0.0741736	+	0.324976i
$10$	0.874288	−	1.09632i	0.276474	−	0.346688i
$11$	0.213150	+	0.933871i	0.0642671	+	0.281573i	0.996843	−	0.0794022i	$-0.0253012\pi$
$11$	0.213150	+	0.933871i	0.0642671	+	0.281573i	−0.932576	+	0.360975i	$0.882444\pi$
$12$	−1.51706			−0.437938
$13$	−1.45377	−	6.36940i	−0.403205	−	1.76655i	−0.614283	−	0.789086i	$-0.710555\pi$
$13$	−1.45377	−	6.36940i	−0.403205	−	1.76655i	0.211078	−	0.977469i	$-0.432302\pi$
$14$	−1.49948	−	0.722111i	−0.400753	−	0.192992i
$15$	1.81798	+	0.875492i	0.469400	+	0.226051i
$16$	−0.297197	−	1.30211i	−0.0742994	−	0.325527i
$17$	−3.81642			−0.925617			−0.462808	−	0.886458i	$-0.653158\pi$
$17$	−3.81642			−0.925617			−0.462808	+	0.886458i	$0.653158\pi$
$18$	0.154638	+	0.677515i	0.0364486	+	0.159692i
$19$	−2.69251	+	3.37631i	−0.617705	+	0.774578i	−0.988020	−	0.154329i	$-0.950678\pi$
$19$	−2.69251	+	3.37631i	−0.617705	+	0.774578i	0.370315	+	0.928906i	$0.379250\pi$
$20$	−0.681165	+	2.98438i	−0.152313	+	0.667328i
$21$	0.532912	−	2.33484i	0.116291	−	0.509504i
$22$	0.415040	+	0.520444i	0.0884868	+	0.110959i
$23$	4.85446	+	2.33778i	1.01222	+	0.487462i	0.865070	−	0.501652i	$-0.167274\pi$
$23$	4.85446	+	2.33778i	1.01222	+	0.487462i	0.147155	+	0.989113i	$0.452988\pi$
$24$	−2.20209	+	1.06047i	−0.449501	+	0.216468i
$25$	−0.578892	+	0.725907i	−0.115778	+	0.145181i
$26$	−2.83075	−	3.54965i	−0.555156	−	0.696144i
$27$	−0.900969	+	0.433884i	−0.173392	+	0.0835010i
$28$	3.63318			0.686607
$29$	5.32202	+	0.822256i	0.988274	+	0.152689i
$29$	5.32202	+	0.822256i	0.988274	+	0.152689i
$30$	1.40225			0.256015
$31$	−2.46382	+	1.18651i	−0.442515	+	0.213104i	−0.641855	−	0.766826i	$-0.721835\pi$
$31$	−2.46382	+	1.18651i	−0.442515	+	0.213104i	0.199339	+	0.979931i	$0.436120\pi$
$32$	−3.62649	−	4.54747i	−0.641079	−	0.803887i
$33$	−0.597233	+	0.748906i	−0.103965	+	0.130368i
$34$	−2.38953	+	1.15074i	−0.409800	+	0.197349i
$35$	−4.35384	−	2.09670i	−0.735934	−	0.354407i
$36$	−0.945872	−	1.18609i	−0.157645	−	0.197681i
$37$	0.414041	−	1.81403i	0.0680679	−	0.298225i	−0.929423	−	0.369015i	$-0.879695\pi$
$37$	0.414041	−	1.81403i	0.0680679	−	0.298225i	0.997491	+	0.0707903i	$0.0225521\pi$
$38$	−0.667799	+	2.92582i	−0.108331	+	0.474631i
$39$	4.07339	−	5.10787i	0.652264	−	0.817913i
$40$	1.09743	+	4.80814i	0.173519	+	0.760234i
$41$	11.8282			1.84725			0.923624	−	0.383300i	$-0.125212\pi$
$41$	11.8282			1.84725			0.923624	+	0.383300i	$0.125212\pi$
$42$	−0.370341	−	1.62257i	−0.0571448	−	0.250368i
$43$	3.33752	+	1.60727i	0.508967	+	0.245106i	0.670700	−	0.741729i	$-0.265994\pi$
$43$	3.33752	+	1.60727i	0.508967	+	0.245106i	−0.161733	+	0.986835i	$0.551708\pi$
$44$	−1.30926	−	0.630508i	−0.197379	−	0.0950526i
$45$	0.449003	+	1.96721i	0.0669335	+	0.293255i
$46$	3.74436			0.552075
$47$	0.719344	+	3.15165i	0.104927	+	0.459716i	0.999907	+	0.0136100i	$0.00433232\pi$
$47$	0.719344	+	3.15165i	0.104927	+	0.459716i	−0.894980	+	0.446106i	$0.852811\pi$
$48$	0.832729	−	1.04421i	0.120194	−	0.150719i
$49$	0.281385	−	1.23283i	0.0401979	−	0.176119i
$50$	−0.143577	+	0.629053i	−0.0203049	+	0.0889615i
$51$	−2.37950	−	2.98379i	−0.333196	−	0.417815i
$52$	8.92974	+	4.30034i	1.23833	+	0.596350i
$53$	−2.04315	+	0.983927i	−0.280648	+	0.135153i	−0.568913	−	0.822398i	$-0.692636\pi$
$53$	−2.04315	+	0.983927i	−0.280648	+	0.135153i	0.288265	+	0.957551i	$0.406922\pi$
$54$	−0.433287	+	0.543325i	−0.0589629	+	0.0739371i
$55$	1.20510	+	1.51115i	0.162495	+	0.203763i
$56$	5.27376	−	2.53971i	0.704736	−	0.339383i
$57$	−4.31846			−0.571994
$58$	3.58014	−	1.08988i	0.470096	−	0.143108i
$59$	−9.30726			−1.21170			−0.605851	−	0.795578i	$-0.707167\pi$
$59$	−9.30726			−1.21170			−0.605851	+	0.795578i	$0.707167\pi$
$60$	−2.75798	+	1.32817i	−0.356054	+	0.171467i
$61$	1.95684	+	2.45380i	0.250547	+	0.314176i	0.891161	−	0.453687i	$-0.149891\pi$
$61$	1.95684	+	2.45380i	0.250547	+	0.314176i	−0.640614	+	0.767863i	$0.721320\pi$
$62$	−1.18488	+	1.48579i	−0.150480	+	0.188696i
$63$	2.15772	−	1.03910i	0.271847	−	0.130914i
$64$	−1.23512	−	0.594802i	−0.154390	−	0.0743503i
$65$	−8.21929	−	10.3067i	−1.01948	−	1.27838i
$66$	−0.148126	+	0.648983i	−0.0182331	+	0.0798843i
$67$	−2.69277	+	11.7978i	−0.328975	+	1.44133i	0.492113	+	0.870531i	$0.336225\pi$
$67$	−2.69277	+	11.7978i	−0.328975	+	1.44133i	−0.821088	+	0.570801i	$0.806633\pi$
$68$	3.60984	−	4.52660i	0.437757	−	0.548930i
$69$	1.19895	+	5.25295i	0.144337	+	0.632381i
$70$	−3.35822			−0.401384
$71$	1.02436	+	4.48801i	0.121569	+	0.532629i	0.998634	+	0.0522567i	$0.0166414\pi$
$71$	1.02436	+	4.48801i	0.121569	+	0.532629i	−0.877065	+	0.480373i	$0.840501\pi$
$72$	−2.20209	−	1.06047i	−0.259519	−	0.124978i
$73$	−8.19102	−	3.94459i	−0.958687	−	0.461679i	−0.111963	−	0.993712i	$-0.535714\pi$
$73$	−8.19102	−	3.94459i	−0.958687	−	0.461679i	−0.846723	+	0.532033i	$0.821428\pi$
$74$	−0.287733	−	1.26064i	−0.0334483	−	0.146547i
$75$	−0.928470			−0.107211
$76$	−1.45781	−	6.38710i	−0.167223	−	0.732651i
$77$	1.43030	−	1.79354i	0.162998	−	0.204393i
$78$	1.01028	−	4.42634i	0.114392	−	0.501185i
$79$	−0.954127	+	4.18030i	−0.107348	+	0.470321i	0.892468	+	0.451111i	$0.148972\pi$
$79$	−0.954127	+	4.18030i	−0.107348	+	0.470321i	−0.999815	+	0.0192099i	$0.993885\pi$
$80$	−1.68028	−	2.10701i	−0.187861	−	0.235571i
$81$	−0.900969	−	0.433884i	−0.100108	−	0.0482093i
$82$	7.40582	−	3.56646i	0.817836	−	0.393849i
$83$	10.0888	−	12.6510i	1.10739	−	1.38863i	0.194270	−	0.980948i	$-0.437766\pi$
$83$	10.0888	−	12.6510i	1.10739	−	1.38863i	0.913124	−	0.407681i	$-0.133662\pi$
$84$	2.26525	+	2.84054i	0.247159	+	0.309928i
$85$	−6.93816	+	3.34124i	−0.752549	+	0.362408i
$86$	2.57431			0.277595
$87$	2.67536	+	4.67359i	0.286829	+	0.501062i
$88$	−2.34121			−0.249574
$89$	−13.9137	+	6.70047i	−1.47485	+	0.710248i	−0.986706	−	0.162517i	$-0.948039\pi$
$89$	−13.9137	+	6.70047i	−1.47485	+	0.710248i	−0.488140	+	0.872765i	$0.662325\pi$
$90$	0.874288	+	1.09632i	0.0921581	+	0.115563i
$91$	−9.75529	+	12.2327i	−1.02263	+	1.28234i
$92$	−7.36451	+	3.54656i	−0.767803	+	0.369754i
$93$	−2.46382	−	1.18651i	−0.255486	−	0.123036i
$94$	1.40069	+	1.75641i	0.144470	+	0.181160i
$95$	−1.93900	+	8.49532i	−0.198937	+	0.871602i
$96$	1.29428	−	5.67061i	0.132097	−	0.578754i
$97$	9.82817	−	12.3241i	0.997899	−	1.25133i	0.0301150	−	0.999546i	$-0.490413\pi$
$97$	9.82817	−	12.3241i	0.997899	−	1.25133i	0.967785	−	0.251780i	$-0.0810159\pi$
$98$	−0.195546	−	0.856741i	−0.0197531	−	0.0865439i
$99$	−0.957887			−0.0962713
$100$	−0.313431	−	1.37323i	−0.0313431	−	0.137323i
$101$	−8.33981	−	4.01624i	−0.829842	−	0.399631i	−0.0297862	−	0.999556i	$-0.509483\pi$
$101$	−8.33981	−	4.01624i	−0.829842	−	0.399631i	−0.800056	+	0.599925i	$0.795197\pi$
$102$	−2.38953	−	1.15074i	−0.236598	−	0.113940i
$103$	−2.35751	−	10.3289i	−0.232292	−	1.01774i	−0.947733	−	0.319065i	$-0.896631\pi$
$103$	−2.35751	−	10.3289i	−0.232292	−	1.01774i	0.715440	−	0.698674i	$-0.246226\pi$
$104$	15.9681			1.56580
$105$	−1.07531	−	4.71124i	−0.104940	−	0.459770i
$106$	−0.982574	+	1.23211i	−0.0954360	+	0.119673i
$107$	0.0279718	−	0.122553i	0.00270414	−	0.0118476i	−0.973558	−	0.228441i	$-0.926637\pi$
$107$	0.0279718	−	0.122553i	0.00270414	−	0.0118476i	0.976262	+	0.216593i	$0.0694945\pi$
$108$	0.337578	−	1.47902i	0.0324834	−	0.142319i
$109$	−6.01455	−	7.54201i	−0.576089	−	0.722393i	0.405351	−	0.914161i	$-0.367149\pi$
$109$	−6.01455	−	7.54201i	−0.576089	−	0.722393i	−0.981440	+	0.191768i	$0.938578\pi$
$110$	1.21018	+	0.582791i	0.115386	+	0.0555669i
$111$	1.67642	−	0.807320i	0.159119	−	0.0766274i
$112$	−1.99429	+	2.50076i	−0.188442	+	0.236299i
$113$	1.93810	+	2.43030i	0.182321	+	0.228623i	0.864590	−	0.502478i	$-0.167578\pi$
$113$	1.93810	+	2.43030i	0.182321	+	0.228623i	−0.682269	+	0.731101i	$0.739007\pi$
$114$	−2.70386	+	1.30211i	−0.253240	+	0.121954i
$115$	10.8720			1.01382
$116$	−6.00921	+	5.53462i	−0.557941	+	0.513877i
$117$	6.53321			0.603995
$118$	−5.82744	+	2.80635i	−0.536460	+	0.258345i
$119$	5.69862	+	7.14584i	0.522391	+	0.655058i
$120$	−3.07492	+	3.85583i	−0.280701	+	0.351988i
$121$	9.08398	−	4.37461i	0.825816	−	0.397692i
$122$	1.96509	+	0.946336i	0.177911	+	0.0856772i
$123$	7.37474	+	9.24763i	0.664958	+	0.833830i
$124$	0.923152	−	4.04459i	0.0829015	−	0.363215i
$125$	−2.66190	+	11.6626i	−0.238088	+	1.04313i
$126$	1.03767	−	1.30120i	0.0924432	−	0.115920i
$127$	0.872287	+	3.82174i	0.0774029	+	0.339124i	0.998771	−	0.0495674i	$-0.0157843\pi$
$127$	0.872287	+	3.82174i	0.0774029	+	0.339124i	−0.921368	+	0.388692i	$0.872927\pi$
$128$	10.6802			0.944005
$129$	0.824300	+	3.61149i	0.0725755	+	0.317974i
$130$	−8.25394	−	3.97489i	−0.723918	−	0.348621i
$131$	14.8614	+	7.15689i	1.29845	+	0.625300i	0.950065	−	0.312052i	$-0.101016\pi$
$131$	14.8614	+	7.15689i	1.29845	+	0.625300i	0.348384	+	0.937352i	$0.386730\pi$
$132$	−0.323361	−	1.41674i	−0.0281450	−	0.123311i
$133$	10.3422			0.896782
$134$	1.87131	+	8.19876i	0.161657	+	0.708265i
$135$	−1.25808	+	1.57758i	−0.108278	+	0.135777i
$136$	2.07564	−	9.09399i	0.177985	−	0.779803i
$137$	0.677588	−	2.96871i	0.0578902	−	0.253634i	−0.937700	−	0.347447i	$-0.887049\pi$
$137$	0.677588	−	2.96871i	0.0578902	−	0.253634i	0.995590	+	0.0938135i	$0.0299057\pi$
$138$	2.33457	+	2.92746i	0.198732	+	0.249202i
$139$	−10.1634	−	4.89444i	−0.862050	−	0.415141i	−0.0500136	−	0.998749i	$-0.515926\pi$
$139$	−10.1634	−	4.89444i	−0.862050	−	0.415141i	−0.812036	+	0.583607i	$0.801641\pi$
$140$	6.60505	−	3.18082i	0.558228	−	0.268829i
$141$	−2.01556	+	2.52743i	−0.169741	+	0.212848i
$142$	1.99461	+	2.50116i	0.167384	+	0.209893i
$143$	5.63833	−	2.71528i	0.471501	−	0.227063i
$144$	1.33559			0.111299
$145$	10.3952	−	3.16454i	0.863274	−	0.262801i
$146$	−6.31793			−0.522875
$147$	1.13931	−	0.548661i	0.0939684	−	0.0452528i
$148$	1.75997	+	2.20693i	0.144668	+	0.181408i
$149$	3.05371	−	3.82923i	0.250170	−	0.313703i	−0.640851	−	0.767665i	$-0.721418\pi$
$149$	3.05371	−	3.82923i	0.250170	−	0.313703i	0.891021	+	0.453962i	$0.149990\pi$
$150$	−0.581332	+	0.279955i	−0.0474656	+	0.0228582i
$151$	−15.3405	−	7.38759i	−1.24839	−	0.601194i	−0.311312	−	0.950308i	$-0.600768\pi$
$151$	−15.3405	−	7.38759i	−1.24839	−	0.601194i	−0.937080	+	0.349114i	$0.886483\pi$
$152$	−6.58088	−	8.25217i	−0.533780	−	0.669339i
$153$	0.849232	−	3.72073i	0.0686564	−	0.300803i
$154$	0.354745	−	1.55424i	0.0285861	−	0.125244i
$155$	−3.44039	+	4.31411i	−0.276339	+	0.346518i
$156$	2.20546	+	9.66277i	0.176578	+	0.773641i
$157$	20.3897			1.62728			0.813639	−	0.581371i	$-0.197483\pi$
$157$	20.3897			1.62728			0.813639	+	0.581371i	$0.197483\pi$
$158$	0.663060	+	2.90505i	0.0527502	+	0.231114i
$159$	−2.04315	−	0.983927i	−0.162032	−	0.0780305i
$160$	−10.5742	−	5.09224i	−0.835960	−	0.402577i
$161$	−2.87135	−	12.5802i	−0.226294	−	0.991459i
$162$	−0.694939			−0.0545995
$163$	−1.69789	−	7.43895i	−0.132989	−	0.582664i	−0.996876	−	0.0789783i	$-0.974834\pi$
$163$	−1.69789	−	7.43895i	−0.132989	−	0.582664i	0.863887	−	0.503685i	$-0.168023\pi$
$164$	−11.1879	+	14.0292i	−0.873630	+	1.09550i
$165$	−0.430095	+	1.88437i	−0.0334828	+	0.146698i
$166$	2.50224	−	10.9630i	0.194212	−	0.850897i
$167$	−13.5489	−	16.9898i	−1.04845	−	1.31471i	−0.947477	−	0.319824i	$-0.896376\pi$
$167$	−13.5489	−	16.9898i	−1.04845	−	1.31471i	−0.100972	−	0.994889i	$-0.532195\pi$
$168$	5.27376	+	2.53971i	0.406879	+	0.195943i
$169$	−26.7433	+	12.8789i	−2.05717	+	0.990682i
$170$	−3.33665	+	4.18402i	−0.255909	+	0.320900i
$171$	−2.69251	−	3.37631i	−0.205902	−	0.258193i
$172$	−5.06322	+	2.43832i	−0.386067	+	0.185920i
$173$	4.01358			0.305147			0.152573	−	0.988292i	$-0.451244\pi$
$173$	4.01358			0.305147			0.152573	+	0.988292i	$0.451244\pi$
$174$	3.08428	+	2.11954i	0.233819	+	0.160682i
$175$	2.22358			0.168087
$176$	1.15265	−	0.555088i	0.0868844	−	0.0418413i
$177$	−5.80298	−	7.27671i	−0.436179	−	0.546951i
$178$	−6.69126	+	8.39057i	−0.501531	+	0.628900i
$179$	3.48470	−	1.67814i	0.260459	−	0.125430i	−0.299098	−	0.954222i	$-0.596686\pi$
$179$	3.48470	−	1.67814i	0.260459	−	0.125430i	0.559557	+	0.828792i	$0.310971\pi$
$180$	−2.75798	−	1.32817i	−0.205568	−	0.0989963i
$181$	10.3685	+	13.0017i	0.770686	+	0.966410i	0.999976	−	0.00694853i	$-0.00221180\pi$
$181$	10.3685	+	13.0017i	0.770686	+	0.966410i	−0.229290	+	0.973358i	$0.573640\pi$
$182$	−2.41951	+	10.6006i	−0.179346	+	0.785767i
$183$	−0.698387	+	3.05983i	−0.0516263	+	0.226189i
$184$	−8.21082	+	10.2960i	−0.605310	+	0.759034i
$185$	−0.835453	−	3.66036i	−0.0614237	−	0.269115i
$186$	−1.90040			−0.139344
$187$	−0.813469	−	3.56404i	−0.0594867	−	0.260628i
$188$	−4.41854	−	2.12785i	−0.322255	−	0.155190i
$189$	2.15772	+	1.03910i	0.156951	+	0.0755835i
$190$	1.34749	+	5.90373i	0.0977570	+	0.428301i
$191$	−2.64112			−0.191105			−0.0955525	−	0.995424i	$-0.530462\pi$
$191$	−2.64112			−0.191105			−0.0955525	+	0.995424i	$0.530462\pi$
$192$	−0.305049	−	1.33651i	−0.0220150	−	0.0964542i
$193$	4.07831	−	5.11404i	0.293563	−	0.368117i	−0.613075	−	0.790024i	$-0.710068\pi$
$193$	4.07831	−	5.11404i	0.293563	−	0.368117i	0.906639	+	0.421907i	$0.138639\pi$
$194$	2.43759	−	10.6798i	0.175009	−	0.766763i
$195$	2.93343	−	12.8522i	0.210067	−	0.920365i
$196$	1.19609	+	1.49985i	0.0854348	+	0.107132i
$197$	8.85143	+	4.26262i	0.630638	+	0.303699i	0.721763	−	0.692140i	$-0.243332\pi$
$197$	8.85143	+	4.26262i	0.630638	+	0.303699i	−0.0911250	+	0.995839i	$0.529046\pi$
$198$	−0.599750	+	0.288825i	−0.0426224	+	0.0205259i
$199$	0.327153	−	0.410236i	0.0231912	−	0.0290809i	−0.770101	−	0.637922i	$-0.779794\pi$
$199$	0.327153	−	0.410236i	0.0231912	−	0.0290809i	0.793292	+	0.608842i	$0.208365\pi$
$200$	−1.41489	−	1.77422i	−0.100048	−	0.125456i
$201$	−10.9028	+	5.25052i	−0.769026	+	0.370343i
$202$	−6.43269			−0.452603
$203$	−6.40717	−	11.1927i	−0.449695	−	0.785574i
$204$	5.78973			0.405362
$205$	21.5033	−	10.3555i	1.50186	−	0.723257i
$206$	−4.59048	−	5.75628i	−0.319834	−	0.401059i
$207$	−3.35939	+	4.21254i	−0.233494	+	0.292792i
$208$	−7.86159	+	3.78594i	−0.545103	+	0.262508i
$209$	−3.72694	−	1.79480i	−0.257798	−	0.124149i
$210$	−2.09382	−	2.62556i	−0.144487	−	0.181181i
$211$	−3.68219	+	16.1327i	−0.253493	+	1.11062i	0.674573	+	0.738208i	$0.264328\pi$
$211$	−3.68219	+	16.1327i	−0.253493	+	1.11062i	−0.928066	+	0.372416i	$0.878529\pi$
$212$	0.765532	−	3.35401i	0.0525770	−	0.230355i
$213$	−2.87019	+	3.59911i	−0.196662	+	0.246607i
$214$	−0.0194387	−	0.0851665i	−0.00132880	−	0.00582186i
$215$	7.47469			0.509769
$216$	−0.543873	−	2.38286i	−0.0370058	−	0.162133i
$217$	5.90056	+	2.84156i	0.400556	+	0.192898i
$218$	−6.03990	−	2.90866i	−0.409074	−	0.197000i
$219$	−2.02302	−	8.86341i	−0.136703	−	0.598934i
$220$	−2.93222			−0.197690
$221$	5.54821	+	24.3083i	0.373213	+	1.63515i
$222$	0.806210	−	1.01096i	0.0541093	−	0.0678509i
$223$	2.61351	−	11.4505i	0.175014	−	0.766785i	−0.808872	−	0.587985i	$-0.799921\pi$
$223$	2.61351	−	11.4505i	0.175014	−	0.766785i	0.983885	−	0.178800i	$-0.0572215\pi$
$224$	−3.09965	+	13.5804i	−0.207104	+	0.907381i
$225$	−0.578892	−	0.725907i	−0.0385928	−	0.0483938i
$226$	1.94627	+	0.937273i	0.129464	+	0.0623465i
$227$	19.1970	−	9.24479i	1.27415	−	0.613598i	0.330270	−	0.943887i	$-0.392860\pi$
$227$	19.1970	−	9.24479i	1.27415	−	0.613598i	0.943880	+	0.330288i	$0.107146\pi$
$228$	4.08471	−	5.12206i	0.270516	−	0.339217i
$229$	0.114294	+	0.143320i	0.00755275	+	0.00947084i	0.785594	−	0.618743i	$-0.212358\pi$
$229$	0.114294	+	0.143320i	0.00755275	+	0.00947084i	−0.778041	+	0.628214i	$0.783786\pi$
$230$	6.80716	−	3.27816i	0.448851	−	0.216155i
$231$	2.29403			0.150936
$232$	−4.85382	+	12.2344i	−0.318669	+	0.803230i
$233$	−23.8810			−1.56449			−0.782247	−	0.622969i	$-0.785926\pi$
$233$	−23.8810			−1.56449			−0.782247	+	0.622969i	$0.785926\pi$
$234$	4.09056	−	1.96991i	0.267408	−	0.128777i
$235$	4.06700	+	5.09985i	0.265302	+	0.332678i
$236$	8.80347	−	11.0392i	0.573057	−	0.718591i
$237$	−3.86318	+	1.86041i	−0.250941	+	0.120847i
$238$	5.72264	+	2.75588i	0.370943	+	0.178637i
$239$	−5.24316	−	6.57471i	−0.339152	−	0.425283i	0.582783	−	0.812628i	$-0.301964\pi$
$239$	−5.24316	−	6.57471i	−0.339152	−	0.425283i	−0.921935	+	0.387345i	$0.873392\pi$
$240$	0.599686	−	2.62740i	0.0387096	−	0.169598i
$241$	0.119797	−	0.524865i	0.00771681	−	0.0338095i	−0.970923	−	0.239392i	$-0.923052\pi$
$241$	0.119797	−	0.524865i	0.00771681	−	0.0338095i	0.978640	+	0.205583i	$0.0659090\pi$
$242$	4.36860	−	5.47805i	0.280824	−	0.352142i
$243$	−0.222521	−	0.974928i	−0.0142747	−	0.0625417i
$244$	−4.76133			−0.304813
$245$	−0.567780	−	2.48761i	−0.0362742	−	0.158927i
$246$	7.40582	+	3.56646i	0.472178	+	0.227389i
$247$	25.4194	+	12.2413i	1.61740	+	0.778896i
$248$	−1.48729	−	6.51625i	−0.0944432	−	0.413783i
$249$	16.1813			1.02545
$250$	1.84986	+	8.10476i	0.116995	+	0.512590i
$251$	−1.06622	+	1.33699i	−0.0672989	+	0.0843902i	−0.814341	−	0.580386i	$-0.802902\pi$
$251$	−1.06622	+	1.33699i	−0.0672989	+	0.0843902i	0.747043	+	0.664776i	$0.231473\pi$
$252$	−0.808459	+	3.54209i	−0.0509281	+	0.223131i
$253$	−1.14846	+	5.03173i	−0.0722031	+	0.316342i
$254$	1.69849	+	2.12984i	0.106573	+	0.133638i
$255$	−6.93816	−	3.34124i	−0.434484	−	0.209237i
$256$	9.15730	−	4.40992i	0.572331	−	0.275620i
$257$	−11.2754	+	14.1389i	−0.703339	+	0.881959i	−0.997268	−	0.0738684i	$-0.976466\pi$
$257$	−11.2754	+	14.1389i	−0.703339	+	0.881959i	0.293929	+	0.955827i	$0.405037\pi$
$258$	1.60506	+	2.01268i	0.0999264	+	0.125304i
$259$	−4.01482	+	1.93344i	−0.249469	+	0.120138i
$260$	19.9990			1.24028
$261$	−1.98590	+	5.00562i	−0.122924	+	0.309840i
$262$	11.4630			0.708185
$263$	−0.869873	+	0.418909i	−0.0536387	+	0.0258310i	−0.460511	−	0.887654i	$-0.652334\pi$
$263$	−0.869873	+	0.418909i	−0.0536387	+	0.0258310i	0.406872	+	0.913485i	$0.366619\pi$
$264$	−1.45972	−	1.83043i	−0.0898396	−	0.112655i
$265$	−2.85297	+	3.57752i	−0.175257	+	0.219765i
$266$	6.47544	−	3.11841i	0.397035	−	0.191202i
$267$	−13.9137	−	6.70047i	−0.851503	−	0.410062i
$268$	−11.4462	−	14.3531i	−0.699188	−	0.876754i
$269$	−2.16024	+	9.46463i	−0.131712	+	0.577069i	0.865397	+	0.501087i	$0.167066\pi$
$269$	−2.16024	+	9.46463i	−0.131712	+	0.577069i	−0.997109	+	0.0759819i	$0.975791\pi$
$270$	−0.312030	+	1.36709i	−0.0189895	+	0.0831986i
$271$	10.5687	−	13.2527i	0.642002	−	0.805045i	−0.349250	−	0.937030i	$-0.613564\pi$
$271$	10.5687	−	13.2527i	0.642002	−	0.805045i	0.991252	+	0.131985i	$0.0421350\pi$
$272$	1.13423	+	4.96938i	0.0687727	+	0.301313i
$273$	−15.6463			−0.946955
$274$	−0.470882	−	2.06307i	−0.0284470	−	0.124635i
$275$	−0.801294	−	0.385883i	−0.0483199	−	0.0232696i
$276$	−7.36451	−	3.54656i	−0.443291	−	0.213478i
$277$	4.90011	+	21.4688i	0.294419	+	1.28994i	0.878306	+	0.478100i	$0.158674\pi$
$277$	4.90011	+	21.4688i	0.294419	+	1.28994i	−0.583886	+	0.811835i	$0.698469\pi$
$278$	−7.83928			−0.470169
$279$	−0.608513	−	2.66607i	−0.0364307	−	0.159614i
$280$	7.36408	−	9.23427i	0.440088	−	0.551853i
$281$	−2.38729	+	10.4594i	−0.142414	+	0.623957i	0.852456	+	0.522798i	$0.175112\pi$
$281$	−2.38729	+	10.4594i	−0.142414	+	0.623957i	−0.994870	+	0.101158i	$0.967745\pi$
$282$	−0.499900	+	2.19020i	−0.0297686	+	0.130425i
$283$	9.48869	+	11.8984i	0.564044	+	0.707289i	0.979300	−	0.202416i	$-0.0648793\pi$
$283$	9.48869	+	11.8984i	0.564044	+	0.707289i	−0.415256	+	0.909705i	$0.636308\pi$
$284$	−6.29208	−	3.03011i	−0.373366	−	0.179804i
$285$	−7.85086	+	3.78077i	−0.465045	+	0.223954i
$286$	2.71154	−	3.40017i	0.160337	−	0.201056i
$287$	−17.6616	−	22.1470i	−1.04253	−	1.30730i
$288$	5.24043	−	2.52366i	0.308795	−	0.148708i
$289$	−2.43497			−0.143234
$290$	5.55444	−	5.11576i	0.326168	−	0.300408i
$291$	15.7632			0.924053
$292$	12.4263	−	5.98418i	0.727193	−	0.350198i
$293$	14.4563	+	18.1276i	0.844547	+	1.05903i	0.997491	+	0.0707934i	$0.0225531\pi$
$293$	14.4563	+	18.1276i	0.844547	+	1.05903i	−0.152944	+	0.988235i	$0.548875\pi$
$294$	0.547907	−	0.687053i	0.0319546	−	0.0400697i
$295$	−16.9204	+	8.14843i	−0.985143	+	0.474420i
$296$	4.09740	+	1.97320i	0.238157	+	0.114690i
$297$	−0.597233	−	0.748906i	−0.0346550	−	0.0434559i
$298$	0.757384	−	3.31832i	0.0438741	−	0.192225i
$299$	7.83300	−	34.3186i	0.452994	−	1.98470i
$300$	0.878214	−	1.10125i	0.0507037	−	0.0635804i
$301$	−1.97410	−	8.64910i	−0.113785	−	0.498526i
$302$	−11.8325			−0.680883
$303$	−2.05976	−	9.02441i	−0.118330	−	0.518439i
$304$	5.19652	+	2.50251i	0.298041	+	0.143529i
$305$	5.70577	+	2.74775i	0.326711	+	0.157336i
$306$	−0.590164	−	2.58568i	−0.0337374	−	0.147813i
$307$	−18.8555			−1.07614			−0.538070	−	0.842900i	$-0.680846\pi$
$307$	−18.8555			−1.07614			−0.538070	+	0.842900i	$0.680846\pi$
$308$	0.774413	+	3.39292i	0.0441262	+	0.193330i
$309$	6.60560	−	8.28316i	0.375779	−	0.471212i
$310$	−0.853287	+	3.73850i	−0.0484635	+	0.212332i
$311$	−6.04072	+	26.4661i	−0.342538	+	1.50076i	0.451160	+	0.892443i	$0.351010\pi$
$311$	−6.04072	+	26.4661i	−0.342538	+	1.50076i	−0.793698	+	0.608312i	$0.791847\pi$
$312$	9.95593	+	12.4843i	0.563644	+	0.706787i
$313$	−6.67788	−	3.21590i	−0.377456	−	0.181773i	0.235530	−	0.971867i	$-0.424317\pi$
$313$	−6.67788	−	3.21590i	−0.377456	−	0.181773i	−0.612986	+	0.790094i	$0.710032\pi$
$314$	12.7664	−	6.14796i	0.720448	−	0.346950i
$315$	3.01295	−	3.77812i	0.169761	−	0.212873i
$316$	−4.05572	−	5.08571i	−0.228152	−	0.286093i
$317$	−2.01091	+	0.968401i	−0.112944	+	0.0543908i	−0.489502	−	0.872002i	$-0.662822\pi$
$317$	−2.01091	+	0.968401i	−0.112944	+	0.0543908i	0.376559	+	0.926393i	$0.377107\pi$
$318$	−1.57593			−0.0883736
$319$	0.366507	+	5.14534i	0.0205205	+	0.288084i
$320$	−2.76617			−0.154633
$321$	0.113256	−	0.0545410i	0.00632131	−	0.00304418i
$322$	−5.59102	−	7.01092i	−0.311575	−	0.390703i
$323$	10.2758	−	12.8854i	0.571758	−	0.716962i
$324$	1.36682	−	0.658228i	0.0759347	−	0.0365682i
$325$	5.46518	+	2.63189i	0.303153	+	0.145991i
$326$	−3.30609	−	4.14571i	−0.183108	−	0.229610i
$327$	2.14657	−	9.40473i	0.118705	−	0.520083i
$328$	−6.43301	+	28.1849i	−0.355204	+	1.55625i
$329$	4.82702	−	6.05290i	0.266122	−	0.333707i
$330$	0.298889	+	1.30952i	0.0164533	+	0.0720867i
$331$	−23.2235			−1.27648			−0.638241	−	0.769837i	$-0.720337\pi$
$331$	−23.2235			−1.27648			−0.638241	+	0.769837i	$0.720337\pi$
$332$	5.46243	+	23.9325i	0.299790	+	1.31346i
$333$	1.67642	+	0.807320i	0.0918671	+	0.0442409i
$334$	−13.6061	−	6.55233i	−0.744491	−	0.358528i
$335$	5.43349	+	23.8057i	0.296863	+	1.30064i
$336$	−3.19859			−0.174497
$337$	−6.02416	−	26.3936i	−0.328157	−	1.43775i	−0.822641	−	0.568562i	$-0.807500\pi$
$337$	−6.02416	−	26.3936i	−0.328157	−	1.43775i	0.494484	−	0.869187i	$-0.335357\pi$
$338$	−12.8612	+	16.1274i	−0.699555	+	0.877214i
$339$	−0.691699	+	3.03053i	−0.0375679	+	0.164596i
$340$	2.59961	−	11.3896i	0.140984	−	0.617690i
$341$	−1.63321	−	2.04798i	−0.0884435	−	0.110905i
$342$	−2.70386	−	1.30211i	−0.146208	−	0.0704102i
$343$	−17.8325	+	8.58769i	−0.962865	+	0.463691i
$344$	−5.64508	+	7.07870i	−0.304362	+	0.381658i
$345$	6.77859	+	8.50008i	0.364947	+	0.457629i
$346$	2.51297	−	1.21018i	0.135098	−	0.0650599i
$347$	−33.0378			−1.77356			−0.886780	−	0.462191i	$-0.847063\pi$
$347$	−33.0378			−1.77356			−0.886780	+	0.462191i	$0.847063\pi$
$348$	−8.07383	−	1.24741i	−0.432802	−	0.0668683i
$349$	6.36434			0.340675			0.170338	−	0.985386i	$-0.445514\pi$
$349$	6.36434			0.340675			0.170338	+	0.985386i	$0.445514\pi$
$350$	1.39222	−	0.670459i	0.0744174	−	0.0358375i
$351$	4.07339	+	5.10787i	0.217421	+	0.272638i
$352$	3.47377	−	4.35597i	0.185152	−	0.232174i
$353$	−15.8323	+	7.62444i	−0.842669	+	0.405808i	−0.804851	−	0.593477i	$-0.797755\pi$
$353$	−15.8323	+	7.62444i	−0.842669	+	0.405808i	−0.0378175	+	0.999285i	$0.512041\pi$
$354$	−5.82744	−	2.80635i	−0.309725	−	0.149156i
$355$	5.79148	+	7.26229i	0.307380	+	0.385442i
$356$	5.21322	−	22.8406i	0.276300	−	1.21055i
$357$	−2.03381	+	8.91071i	−0.107641	+	0.471605i
$358$	1.67584	−	2.10143i	0.0885707	−	0.111064i
$359$	−1.74009	−	7.62384i	−0.0918385	−	0.402371i	0.908025	−	0.418917i	$-0.137590\pi$
$359$	−1.74009	−	7.62384i	−0.0918385	−	0.402371i	−0.999863	+	0.0165460i	$0.994733\pi$
$360$	−4.93180			−0.259928
$361$	0.0780901	+	0.342135i	0.00411000	+	0.0180071i
$362$	10.4122	+	5.01426i	0.547254	+	0.263544i
$363$	9.08398	+	4.37461i	0.476785	+	0.229608i
$364$	−5.28183	−	23.1412i	−0.276843	−	1.21293i
$365$	−18.3446			−0.960198
$366$	0.485336	+	2.12640i	0.0253689	+	0.111149i
$367$	18.1847	−	22.8028i	0.949231	−	1.19030i	−0.0323932	−	0.999475i	$-0.510313\pi$
$367$	18.1847	−	22.8028i	0.949231	−	1.19030i	0.981624	−	0.190823i	$-0.0611157\pi$
$368$	1.60131	−	7.01581i	0.0834742	−	0.365724i
$369$	−2.63201	+	11.5316i	−0.137017	+	0.600311i
$370$	−1.62677	−	2.03991i	−0.0845719	−	0.106050i
$371$	4.89310	+	2.35639i	0.254037	+	0.122338i
$372$	3.73776	−	1.80001i	0.193794	−	0.0933263i
$373$	−3.65125	+	4.57852i	−0.189054	+	0.237067i	−0.867321	−	0.497749i	$-0.834160\pi$
$373$	−3.65125	+	4.57852i	−0.189054	+	0.237067i	0.678267	+	0.734816i	$0.262731\pi$
$374$	−1.58397	−	1.98623i	−0.0819049	−	0.102705i
$375$	−10.7778	+	5.19033i	−0.556565	+	0.268027i
$376$	−7.90118			−0.407472
$377$	−2.49974	−	35.0935i	−0.128743	−	1.80741i
$378$	1.66430			0.0856022
$379$	2.08807	−	1.00556i	0.107257	−	0.0516523i	−0.379486	−	0.925198i	$-0.623899\pi$
$379$	2.08807	−	1.00556i	0.107257	−	0.0516523i	0.486743	+	0.873545i	$0.338185\pi$
$380$	−8.24213	−	10.3353i	−0.422812	−	0.530190i
$381$	−2.44409	+	3.06480i	−0.125215	+	0.157014i
$382$	−1.65366	+	0.796358i	−0.0846084	+	0.0407452i
$383$	16.4369	+	7.91562i	0.839889	+	0.404469i	0.803815	−	0.594880i	$-0.202800\pi$
$383$	16.4369	+	7.91562i	0.839889	+	0.404469i	0.0360743	+	0.999349i	$0.488515\pi$
$384$	6.65899	+	8.35011i	0.339815	+	0.426115i
$385$	1.03003	−	4.51284i	0.0524950	−	0.229996i
$386$	1.01151	−	4.43170i	0.0514843	−	0.225568i
$387$	−2.30964	+	2.89619i	−0.117405	+	0.147222i
$388$	5.32129	+	23.3141i	0.270148	+	1.18359i
$389$	29.6576			1.50370			0.751850	−	0.659335i	$-0.229162\pi$
$389$	29.6576			1.50370			0.751850	+	0.659335i	$0.229162\pi$
$390$	−2.03855	−	8.93149i	−0.103226	−	0.452264i
$391$	−18.5266	−	8.92195i	−0.936932	−	0.451203i
$392$	2.78463	+	1.34100i	0.140645	+	0.0677310i
$393$	3.67047	+	16.0814i	0.185151	+	0.811198i
$394$	6.82732			0.343955
$395$	1.92524	+	8.43503i	0.0968694	+	0.424413i
$396$	0.906038	−	1.13614i	0.0455301	−	0.0570930i
$397$	−0.452224	+	1.98132i	−0.0226965	+	0.0994398i	−0.985008	−	0.172511i	$-0.944812\pi$
$397$	−0.452224	+	1.98132i	−0.0226965	+	0.0994398i	0.962311	+	0.271951i	$0.0876690\pi$
$398$	0.0811406	−	0.355500i	0.00406721	−	0.0178196i
$399$	6.44826	+	8.08586i	0.322817	+	0.404799i
$400$	1.11725	+	0.538041i	0.0558627	+	0.0269021i
$401$	0.128477	−	0.0618714i	0.00641585	−	0.00308971i	−0.430673	−	0.902508i	$-0.641724\pi$
$401$	0.128477	−	0.0618714i	0.00641585	−	0.00308971i	0.437089	+	0.899418i	$0.356010\pi$
$402$	−5.24330	+	6.57489i	−0.261512	+	0.327926i
$403$	11.1392	+	13.9681i	0.554884	+	0.695803i
$404$	12.6520	−	6.09288i	0.629460	−	0.303132i
$405$	−2.01780			−0.100265
$406$	−7.38650	−	5.07605i	−0.366586	−	0.251920i
$407$	1.78232			0.0883465
$408$	8.40411	−	4.04721i	0.416065	−	0.200367i
$409$	−12.9332	−	16.2178i	−0.639507	−	0.801917i	0.351434	−	0.936213i	$-0.385694\pi$
$409$	−12.9332	−	16.2178i	−0.639507	−	0.801917i	−0.990941	+	0.134296i	$0.957123\pi$
$410$	10.3412	−	12.9675i	0.510716	−	0.640418i
$411$	2.74350	−	1.32120i	0.135327	−	0.0651699i
$412$	14.4809	+	6.97363i	0.713422	+	0.343566i
$413$	13.8975	+	17.4269i	0.683849	+	0.857520i
$414$	−0.833198	+	3.65048i	−0.0409494	+	0.179411i
$415$	7.26544	−	31.8320i	0.356646	−	1.56257i
$416$	−23.6926	+	29.7096i	−1.16163	+	1.45663i
$417$	−2.51016	−	10.9977i	−0.122923	−	0.538560i
$418$	−2.87468			−0.140605
$419$	−1.45786	−	6.38728i	−0.0712209	−	0.312039i	0.926752	−	0.375673i	$-0.122588\pi$
$419$	−1.45786	−	6.38728i	−0.0712209	−	0.312039i	−0.997973	+	0.0636334i	$0.979731\pi$
$420$	6.60505	+	3.18082i	0.322293	+	0.155208i
$421$	−7.77401	−	3.74377i	−0.378882	−	0.182460i	0.234743	−	0.972057i	$-0.424575\pi$
$421$	−7.77401	−	3.74377i	−0.378882	−	0.182460i	−0.613625	+	0.789597i	$0.710289\pi$
$422$	2.55890	+	11.2113i	0.124565	+	0.545756i
$423$	−3.23270			−0.157179
$424$	−1.23335	−	5.40366i	−0.0598968	−	0.262425i
$425$	2.20929	−	2.77036i	0.107166	−	0.134382i
$426$	−0.711867	+	3.11889i	−0.0344901	+	0.151111i
$427$	1.67256	−	7.32795i	0.0809406	−	0.354624i
$428$	0.118900	+	0.149096i	0.00574725	+	0.00720683i
$429$	5.63833	+	2.71528i	0.272221	+	0.131095i
$430$	4.68004	−	2.25379i	0.225691	−	0.108687i
$431$	19.6857	−	24.6850i	0.948225	−	1.18904i	−0.0336362	−	0.999434i	$-0.510709\pi$
$431$	19.6857	−	24.6850i	0.948225	−	1.18904i	0.981861	−	0.189602i	$-0.0607198\pi$
$432$	0.832729	+	1.04421i	0.0400647	+	0.0502395i
$433$	2.83832	−	1.36686i	0.136401	−	0.0656873i	−0.364438	−	0.931228i	$-0.618739\pi$
$433$	2.83832	−	1.36686i	0.136401	−	0.0656873i	0.500839	+	0.865540i	$0.333025\pi$
$434$	4.55124			0.218467
$435$	8.95544	+	6.15423i	0.429380	+	0.295073i
$436$	14.6345			0.700863
$437$	−20.9638	+	10.0956i	−1.00283	+	0.482939i
$438$	−3.93916	−	4.93956i	−0.188221	−	0.236021i
$439$	14.2209	−	17.8324i	0.678727	−	0.851096i	−0.316510	−	0.948589i	$-0.602511\pi$
$439$	14.2209	−	17.8324i	0.678727	−	0.851096i	0.995236	+	0.0974931i	$0.0310824\pi$
$440$	−4.25627	+	2.04971i	−0.202910	+	0.0977161i
$441$	1.13931	+	0.548661i	0.0542527	+	0.0261267i
$442$	10.8033	+	13.5469i	0.513862	+	0.644363i
$443$	−4.25594	+	18.6465i	−0.202206	+	0.885922i	0.767384	+	0.641188i	$0.221558\pi$
$443$	−4.25594	+	18.6465i	−0.202206	+	0.885922i	−0.969590	+	0.244735i	$0.921299\pi$
$444$	−0.628125	+	2.75200i	−0.0298095	+	0.130604i
$445$	−19.4285	+	24.3626i	−0.921001	+	1.15490i
$446$	−1.81623	−	7.95742i	−0.0860010	−	0.376795i
$447$	4.89777			0.231657
$448$	0.730558	+	3.20078i	0.0345156	+	0.151223i
$449$	35.8493	+	17.2641i	1.69184	+	0.814745i	0.995259	+	0.0972626i	$0.0310087\pi$
$449$	35.8493	+	17.2641i	1.69184	+	0.814745i	0.696577	+	0.717482i	$0.254706\pi$
$450$	−0.581332	−	0.279955i	−0.0274043	−	0.0131972i
$451$	2.52117	+	11.0460i	0.118717	+	0.520134i
$452$	−4.71573			−0.221809
$453$	−3.78879	−	16.5998i	−0.178013	−	0.779925i
$454$	9.23208	−	11.5767i	0.433283	−	0.543320i
$455$	−7.02523	+	30.7795i	−0.329348	+	1.44297i
$456$	2.34869	−	10.2903i	0.109987	−	0.481887i
$457$	18.2165	+	22.8427i	0.852130	+	1.06854i	0.996869	+	0.0790675i	$0.0251943\pi$
$457$	18.2165	+	22.8427i	0.852130	+	1.06854i	−0.144739	+	0.989470i	$0.546234\pi$
$458$	0.114776	+	0.0552730i	0.00536311	+	0.00258274i
$459$	3.43847	−	1.65588i	0.160494	−	0.0772899i
$460$	−10.2835	+	12.8951i	−0.479472	+	0.601239i
$461$	0.612669	+	0.768263i	0.0285348	+	0.0357816i	0.795894	−	0.605436i	$-0.207001\pi$
$461$	0.612669	+	0.768263i	0.0285348	+	0.0357816i	−0.767359	+	0.641217i	$0.778430\pi$
$462$	1.43633	−	0.691701i	0.0668242	−	0.0321808i
$463$	−10.1420			−0.471340			−0.235670	−	0.971833i	$-0.575728\pi$
$463$	−10.1420			−0.471340			−0.235670	+	0.971833i	$0.575728\pi$
$464$	−0.511025	−	7.17421i	−0.0237238	−	0.333054i
$465$	−5.51795			−0.255889
$466$	−14.9523	+	7.20065i	−0.692652	+	0.333563i
$467$	11.2090	+	14.0557i	0.518692	+	0.650419i	0.970331	−	0.241782i	$-0.0777319\pi$
$467$	11.2090	+	14.0557i	0.518692	+	0.650419i	−0.451639	+	0.892201i	$0.649160\pi$
$468$	−6.17957	+	7.74894i	−0.285651	+	0.358195i
$469$	26.1110	−	12.5744i	1.20569	−	0.580631i
$470$	4.08414	+	1.96682i	0.188387	+	0.0907226i
$471$	12.7128	+	15.9413i	0.585774	+	0.734538i
$472$	5.06196	−	22.1779i	0.232996	−	1.02082i
$473$	−0.789586	+	3.45940i	−0.0363052	+	0.159063i
$474$	−1.85785	+	2.32967i	−0.0853340	+	0.107005i
$475$	−0.892211	−	3.90903i	−0.0409374	−	0.179359i
$476$	−13.8657			−0.635535
$477$	−0.504615	−	2.21086i	−0.0231048	−	0.101229i
$478$	−5.26526	−	2.53562i	−0.240827	−	0.115976i
$479$	−18.5533	−	8.93481i	−0.847723	−	0.408242i	−0.0409911	−	0.999160i	$-0.513052\pi$
$479$	−18.5533	−	8.93481i	−0.847723	−	0.408242i	−0.806732	+	0.590918i	$0.798766\pi$
$480$	−2.61160	−	11.4422i	−0.119203	−	0.522261i
$481$	−12.1562			−0.554276
$482$	−0.0832516	−	0.364749i	−0.00379201	−	0.0166139i
$483$	8.04534	−	10.0885i	0.366076	−	0.459045i
$484$	−3.40361	+	14.9122i	−0.154710	+	0.677827i
$485$	7.07771	−	31.0095i	0.321382	−	1.40807i
$486$	−0.433287	−	0.543325i	−0.0196543	−	0.0246457i
$487$	−14.4078	−	6.93844i	−0.652880	−	0.314411i	0.0779626	−	0.996956i	$-0.475159\pi$
$487$	−14.4078	−	6.93844i	−0.652880	−	0.314411i	−0.730843	+	0.682546i	$0.760873\pi$
$488$	−6.91133	+	3.32832i	−0.312861	+	0.150666i
$489$	4.75739	−	5.96558i	0.215137	−	0.269773i
$490$	−1.10557	−	1.38634i	−0.0499444	−	0.0626284i
$491$	9.19032	−	4.42582i	0.414753	−	0.199735i	−0.214858	−	0.976645i	$-0.568929\pi$
$491$	9.19032	−	4.42582i	0.414753	−	0.199735i	0.629611	+	0.776911i	$0.283214\pi$
$492$	−17.9440			−0.808979
$493$	−20.3110	−	3.13807i	−0.914763	−	0.141332i
$494$	19.6066			0.882141
$495$	−1.74142	+	0.838622i	−0.0782709	+	0.0376933i
$496$	2.27721	+	2.85553i	0.102250	+	0.128217i
$497$	6.87378	−	8.61944i	0.308331	−	0.386635i
$498$	10.1314	−	4.87901i	0.453998	−	0.218634i
$499$	5.54276	+	2.66925i	0.248128	+	0.119492i	0.553815	−	0.832640i	$-0.313172\pi$
$499$	5.54276	+	2.66925i	0.248128	+	0.119492i	−0.305687	+	0.952132i	$0.598886\pi$
$500$	−11.3150	−	14.1885i	−0.506021	−	0.634530i
$501$	4.83556	−	21.1860i	0.216037	−	0.946520i
$502$	−0.264443	+	1.15860i	−0.0118027	+	0.0517110i
$503$	−12.6166	+	15.8207i	−0.562545	+	0.705410i	−0.979026	−	0.203735i	$-0.934692\pi$
$503$	−12.6166	+	15.8207i	−0.562545	+	0.705410i	0.416481	+	0.909145i	$0.363263\pi$
$504$	1.30251	+	5.70667i	0.0580185	+	0.254195i
$505$	−18.6778			−0.831150
$506$	0.798110	+	3.49675i	0.0354803	+	0.155449i
$507$	−26.7433	−	12.8789i	−1.18771	−	0.571971i
$508$	−5.35798	−	2.58027i	−0.237722	−	0.114481i
$509$	0.903261	+	3.95744i	0.0400363	+	0.175411i	0.990993	−	0.133913i	$-0.0427544\pi$
$509$	0.903261	+	3.95744i	0.0400363	+	0.175411i	−0.950957	+	0.309324i	$0.899897\pi$
$510$	−5.35157			−0.236971
$511$	4.84489	+	21.2268i	0.214325	+	0.939020i
$512$	−8.91413	+	11.1780i	−0.393952	+	0.494001i
$513$	0.960947	−	4.21018i	0.0424268	−	0.185884i
$514$	−2.79653	+	12.2524i	−0.123350	+	0.540429i
$515$	−13.3288	−	16.7138i	−0.587337	−	0.736497i
$516$	−5.06322	−	2.43832i	−0.222896	−	0.107341i
$517$	−2.78991	+	1.34355i	−0.122700	+	0.0590892i
$518$	−1.93078	+	2.42112i	−0.0848335	+	0.106378i
$519$	2.50243	+	3.13794i	0.109844	+	0.137740i
$520$	29.0296	−	13.9799i	1.27303	−	0.613060i
$521$	10.9066			0.477828			0.238914	−	0.971041i	$-0.423209\pi$
$521$	10.9066			0.477828			0.238914	+	0.971041i	$0.423209\pi$
$522$	0.265898	+	3.73290i	0.0116380	+	0.163385i
$523$	3.65147			0.159668			0.0798339	−	0.996808i	$-0.474561\pi$
$523$	3.65147			0.159668			0.0798339	+	0.996808i	$0.474561\pi$
$524$	−22.5457	+	10.8574i	−0.984913	+	0.474309i
$525$	1.38638	+	1.73846i	0.0605065	+	0.0758728i
$526$	−0.418333	+	0.524573i	−0.0182402	+	0.0228725i
$527$	9.40296	−	4.52823i	0.409600	−	0.197253i
$528$	1.15265	+	0.555088i	0.0501627	+	0.0241571i
$529$	3.76026	+	4.71522i	0.163490	+	0.205010i
$530$	−0.707596	+	3.10018i	−0.0307360	+	0.134663i
$531$	2.07106	−	9.07391i	0.0898764	−	0.393774i
$532$	−9.78239	+	12.2667i	−0.424121	+	0.531830i
$533$	−17.1955	−	75.3383i	−0.744819	−	3.26326i
$534$	−10.7319			−0.464417
$535$	−0.0564416	−	0.247287i	−0.00244018	−	0.0106911i
$536$	−26.6480	−	12.8330i	−1.15102	−	0.554302i
$537$	3.48470	+	1.67814i	0.150376	+	0.0724173i
$538$	1.50123	+	6.57734i	0.0647228	+	0.283569i
$539$	1.21128			0.0521736
$540$	−0.681165	−	2.98438i	−0.0293127	−	0.128427i
$541$	−21.1554	+	26.5281i	−0.909543	+	1.14053i	0.0800725	+	0.996789i	$0.474485\pi$
$541$	−21.1554	+	26.5281i	−0.909543	+	1.14053i	−0.989615	+	0.143741i	$0.954087\pi$
$542$	2.62125	−	11.4845i	0.112592	−	0.493300i
$543$	−3.70048	+	16.2129i	−0.158803	+	0.695761i
$544$	13.8402	+	17.3550i	0.593393	+	0.744092i
$545$	−17.5373	−	8.44551i	−0.751215	−	0.361766i
$546$	−9.79641	+	4.71770i	−0.419248	+	0.201899i
$547$	12.2604	−	15.3741i	0.524217	−	0.657347i	−0.447281	−	0.894393i	$-0.647608\pi$
$547$	12.2604	−	15.3741i	0.524217	−	0.657347i	0.971498	+	0.237046i	$0.0761792\pi$
$548$	2.88023	+	3.61169i	0.123037	+	0.154284i
$549$	−2.82771	+	1.36175i	−0.120684	+	0.0581183i
$550$	−0.618057			−0.0263541
$551$	−17.1058	+	15.7548i	−0.728731	+	0.671178i
$552$	−13.1691			−0.560516
$553$	9.25187	−	4.45547i	0.393430	−	0.189466i
$554$	9.54138	+	11.9645i	0.405374	+	0.508323i
$555$	2.34089	−	2.93538i	0.0993651	−	0.124600i
$556$	15.4185	−	7.42517i	0.653891	−	0.314897i
$557$	34.4588	+	16.5945i	1.46006	+	0.703130i	0.984310	−	0.176448i	$-0.0564606\pi$
$557$	34.4588	+	16.5945i	1.46006	+	0.703130i	0.475755	+	0.879578i	$0.342175\pi$
$558$	−1.18488	−	1.48579i	−0.0501600	−	0.0628987i
$559$	5.38532	−	23.5946i	0.227775	−	0.997946i
$560$	−1.43618	+	6.29231i	−0.0606896	+	0.265898i
$561$	2.27929	−	2.85814i	0.0962316	−	0.120671i
$562$	1.65902	+	7.26865i	0.0699817	+	0.306610i
$563$	−23.4745			−0.989330			−0.494665	−	0.869084i	$-0.664709\pi$
$563$	−23.4745			−0.989330			−0.494665	+	0.869084i	$0.664709\pi$
$564$	−1.09129	−	4.78125i	−0.0459515	−	0.201327i
$565$	5.65113	+	2.72144i	0.237745	+	0.114492i
$566$	9.52868	+	4.58877i	0.400520	+	0.192880i
$567$	0.532912	+	2.33484i	0.0223802	+	0.0980540i
$568$	−11.2514			−0.472100
$569$	0.758682	+	3.32400i	0.0318056	+	0.139349i	0.988338	−	0.152277i	$-0.0486607\pi$
$569$	0.758682	+	3.32400i	0.0318056	+	0.139349i	−0.956532	+	0.291627i	$0.905804\pi$
$570$	−3.77558	+	4.73442i	−0.158141	+	0.198303i
$571$	−5.16346	+	22.6226i	−0.216084	+	0.946726i	0.744256	+	0.667894i	$0.232804\pi$
$571$	−5.16346	+	22.6226i	−0.216084	+	0.946726i	−0.960340	+	0.278832i	$0.910053\pi$
$572$	−2.11259	+	9.25584i	−0.0883316	+	0.387006i
$573$	−1.64671	−	2.06491i	−0.0687925	−	0.0862630i
$574$	−17.7361	−	8.54125i	−0.740290	−	0.356505i
$575$	−4.50722	+	2.17056i	−0.187964	+	0.0905187i
$576$	0.854730	−	1.07180i	0.0356137	−	0.0446582i
$577$	−0.183171	−	0.229689i	−0.00762551	−	0.00956209i	0.778004	−	0.628259i	$-0.216232\pi$
$577$	−0.183171	−	0.229689i	−0.00762551	−	0.00956209i	−0.785630	+	0.618697i	$0.787661\pi$
$578$	−1.52458	+	0.734199i	−0.0634142	+	0.0305387i
$579$	6.54111			0.271839
$580$	−6.07910	+	15.3228i	−0.252421	+	0.636246i
$581$	−38.7522			−1.60771
$582$	9.86960	−	4.75295i	0.409108	−	0.197016i
$583$	−1.35436	−	1.69831i	−0.0560917	−	0.0703368i
$584$	13.8543	−	17.3727i	0.573294	−	0.718888i
$585$	11.8772	−	5.71977i	0.491063	−	0.236483i
$586$	14.5173	+	6.99114i	0.599702	+	0.288801i
$587$	−1.71744	−	2.15360i	−0.0708864	−	0.0888888i	0.745124	−	0.666926i	$-0.232390\pi$
$587$	−1.71744	−	2.15360i	−0.0708864	−	0.0888888i	−0.816010	+	0.578037i	$0.803819\pi$
$588$	−0.426879	+	1.87028i	−0.0176042	+	0.0771290i
$589$	2.62784	−	11.5133i	0.108278	−	0.474398i
$590$	−8.13723	+	10.2038i	−0.335004	+	0.420082i
$591$	2.18612	+	9.57803i	0.0899251	+	0.393987i
$592$	−2.48512			−0.102138
$593$	4.62823	+	20.2776i	0.190059	+	0.832701i	0.976583	+	0.215142i	$0.0690214\pi$
$593$	4.62823	+	20.2776i	0.190059	+	0.832701i	−0.786524	+	0.617559i	$0.788121\pi$
$594$	−0.599750	−	0.288825i	−0.0246081	−	0.0118506i
$595$	16.6161	+	8.00188i	0.681193	+	0.328045i
$596$	1.65338	+	7.24393i	0.0677251	+	0.296723i
$597$	0.524712			0.0214750
$598$	−5.44345	−	23.8493i	−0.222599	−	0.975272i
$599$	21.7810	−	27.3125i	0.889946	−	1.11596i	−0.102677	−	0.994715i	$-0.532741\pi$
$599$	21.7810	−	27.3125i	0.889946	−	1.11596i	0.992623	−	0.121242i	$-0.0386877\pi$
$600$	0.504969	−	2.21242i	0.0206153	−	0.0903215i
$601$	−0.641141	+	2.80902i	−0.0261527	+	0.114582i	−0.986319	−	0.164845i	$-0.947288\pi$
$601$	−0.641141	+	2.80902i	−0.0261527	+	0.114582i	0.960167	+	0.279428i	$0.0901447\pi$
$602$	−3.84392	−	4.82012i	−0.156666	−	0.196454i
$603$	−10.9028	−	5.25052i	−0.443997	−	0.213818i
$604$	23.2725	−	11.2074i	0.946943	−	0.456024i
$605$	12.6845	−	15.9059i	0.515699	−	0.646667i
$606$	−4.01072	−	5.02928i	−0.162924	−	0.204301i
$607$	−20.0682	+	9.66435i	−0.814544	+	0.392264i	−0.794296	−	0.607531i	$-0.792160\pi$
$607$	−20.0682	+	9.66435i	−0.814544	+	0.392264i	−0.0202484	+	0.999795i	$0.506446\pi$
$608$	25.1180			1.01867
$609$	4.75600	−	11.9879i	0.192723	−	0.485773i
$610$	4.40099			0.178191
$611$	19.0284	−	9.16359i	0.769806	−	0.370719i
$612$	3.60984	+	4.52660i	0.145919	+	0.182977i
$613$	1.04225	−	1.30693i	0.0420959	−	0.0527866i	−0.760338	−	0.649528i	$-0.774967\pi$
$613$	1.04225	−	1.30693i	0.0420959	−	0.0527866i	0.802434	+	0.596741i	$0.203538\pi$
$614$	−11.8058	+	5.68536i	−0.476442	+	0.229442i
$615$	21.5033	+	10.3555i	0.867098	+	0.417572i
$616$	3.49586	+	4.38367i	0.140852	+	0.176623i
$617$	−3.20447	+	14.0397i	−0.129007	+	0.565216i	0.868565	+	0.495575i	$0.165043\pi$
$617$	−3.20447	+	14.0397i	−0.129007	+	0.565216i	−0.997572	+	0.0696414i	$0.977814\pi$
$618$	1.63832	−	7.17797i	0.0659031	−	0.288740i
$619$	−1.71356	+	2.14873i	−0.0688737	+	0.0863649i	−0.815075	−	0.579356i	$-0.803304\pi$
$619$	−1.71356	+	2.14873i	−0.0688737	+	0.0863649i	0.746201	+	0.665720i	$0.231876\pi$
$620$	−1.86274	−	8.16119i	−0.0748094	−	0.327761i
$621$	−5.38804			−0.216215
$622$	4.19793	+	18.3923i	0.168322	+	0.737465i
$623$	33.3216	+	16.0468i	1.33500	+	0.642903i
$624$	−7.86159	−	3.78594i	−0.314715	−	0.151559i
$625$	4.33818	+	19.0068i	0.173527	+	0.760272i
$626$	−5.15081			−0.205868
$627$	−0.920479	−	4.03288i	−0.0367604	−	0.161058i
$628$	−19.2861	+	24.1840i	−0.769598	+	0.965045i
$629$	−1.58015	+	6.92310i	−0.0630048	+	0.276042i
$630$	0.747275	−	3.27403i	0.0297721	−	0.130440i
$631$	−5.65612	−	7.09255i	−0.225167	−	0.282350i	0.656397	−	0.754416i	$-0.272080\pi$
$631$	−5.65612	−	7.09255i	−0.225167	−	0.282350i	−0.881563	+	0.472066i	$0.843508\pi$
$632$	−9.44216	−	4.54711i	−0.375589	−	0.180874i
$633$	−14.9089	+	7.17975i	−0.592576	+	0.285369i
$634$	−0.967070	+	1.21267i	−0.0384072	+	0.0481612i
$635$	4.93170	+	6.18415i	0.195708	+	0.245411i
$636$	3.09958	−	1.49268i	0.122906	−	0.0591885i
$637$	−8.26146			−0.327331
$638$	1.78091	+	3.11108i	0.0705070	+	0.123169i
$639$	−4.60343			−0.182109
$640$	19.4164	−	9.35043i	0.767499	−	0.369608i
$641$	−7.09852	−	8.90126i	−0.280375	−	0.351579i	0.621625	−	0.783315i	$-0.286473\pi$
$641$	−7.09852	−	8.90126i	−0.280375	−	0.351579i	−0.902000	+	0.431736i	$0.857901\pi$
$642$	0.0544660	−	0.0682982i	0.00214960	−	0.00269552i
$643$	9.74947	−	4.69510i	0.384482	−	0.185157i	−0.231651	−	0.972799i	$-0.574413\pi$
$643$	9.74947	−	4.69510i	0.384482	−	0.185157i	0.616133	+	0.787642i	$0.288699\pi$
$644$	17.6371	+	8.49360i	0.695000	+	0.334695i
$645$	4.66039	+	5.84395i	0.183503	+	0.230105i
$646$	2.54860	−	11.1661i	0.100273	−	0.439326i
$647$	4.91549	−	21.5362i	0.193248	−	0.846674i	−0.781596	−	0.623785i	$-0.785594\pi$
$647$	4.91549	−	21.5362i	0.193248	−	0.846674i	0.974844	−	0.222889i	$-0.0715488\pi$
$648$	1.52390	−	1.91091i	0.0598643	−	0.0750675i
$649$	−1.98384	−	8.69178i	−0.0778726	−	0.341182i
$650$	4.21542			0.165342
$651$	1.45732	+	6.38493i	0.0571168	+	0.250245i
$652$	10.4292	+	5.02245i	0.408440	+	0.196694i
$653$	−17.4603	−	8.40844i	−0.683274	−	0.329048i	0.0598439	−	0.998208i	$-0.480940\pi$
$653$	−17.4603	−	8.40844i	−0.683274	−	0.329048i	−0.743118	+	0.669160i	$0.766654\pi$
$654$	−1.49173	−	6.53571i	−0.0583314	−	0.255566i
$655$	33.2836			1.30050
$656$	−3.51530	−	15.4015i	−0.137249	−	0.601329i
$657$	5.66836	−	7.10790i	0.221144	−	0.277306i
$658$	1.19720	−	5.24528i	0.0466718	−	0.204482i
$659$	−1.48867	+	6.52230i	−0.0579904	+	0.254073i	−0.995611	−	0.0935875i	$-0.970167\pi$
$659$	−1.48867	+	6.52230i	−0.0579904	+	0.254073i	0.937621	+	0.347660i	$0.113024\pi$
$660$	−1.82821	−	2.29250i	−0.0711629	−	0.0892354i
$661$	40.0727	+	19.2980i	1.55865	+	0.750606i	0.997046	−	0.0768020i	$-0.0244709\pi$
$661$	40.0727	+	19.2980i	1.55865	+	0.750606i	0.561602	+	0.827407i	$0.310185\pi$
$662$	−14.5407	+	7.00242i	−0.565139	+	0.272157i
$663$	−15.5457	+	19.4937i	−0.603746	+	0.757074i
$664$	24.6586	+	30.9209i	0.956938	+	1.19996i
$665$	18.8019	−	9.05451i	0.729106	−	0.351119i
$666$	1.29306			0.0501051
$667$	23.9133	+	16.4333i	0.925925	+	0.636301i
$668$	32.9670			1.27553
$669$	10.5819	−	5.09597i	0.409120	−	0.197022i
$670$	10.5800	+	13.2668i	0.408739	+	0.512543i
$671$	−1.87443	+	2.35046i	−0.0723615	+	0.0907385i
$672$	−12.5502	+	6.04386i	−0.484135	+	0.233147i
$673$	−18.9884	−	9.14433i	−0.731949	−	0.352488i	0.0305016	−	0.999535i	$-0.490290\pi$
$673$	−18.9884	−	9.14433i	−0.731949	−	0.352488i	−0.762450	+	0.647047i	$0.776004\pi$
$674$	−11.7301	−	14.7091i	−0.451826	−	0.566572i
$675$	0.206604	−	0.905192i	0.00795220	−	0.0348408i
$676$	10.0202	−	43.9015i	0.385394	−	1.68852i
$677$	2.23420	−	2.80160i	0.0858673	−	0.107674i	−0.737042	−	0.675847i	$-0.763778\pi$
$677$	2.23420	−	2.80160i	0.0858673	−	0.107674i	0.822909	+	0.568173i	$0.192349\pi$
$678$	0.480688	+	2.10603i	0.0184607	+	0.0808817i
$679$	−37.7509			−1.44875
$680$	−4.18824	−	18.3499i	−0.160612	−	0.703686i
$681$	19.1970	+	9.24479i	0.735631	+	0.354261i
$682$	−1.64010	−	0.789829i	−0.0628026	−	0.0302441i
$683$	2.99758	+	13.1333i	0.114699	+	0.502530i	0.999342	+	0.0362615i	$0.0115449\pi$
$683$	2.99758	+	13.1333i	0.114699	+	0.502530i	−0.884643	+	0.466269i	$0.845598\pi$
$684$	6.55136			0.250497
$685$	−1.36724	−	5.99027i	−0.0522395	−	0.228876i
$686$	−8.57588	+	10.7538i	−0.327428	+	0.410582i
$687$	−0.0407910	+	0.178717i	−0.00155627	+	0.00681848i
$688$	1.10093	−	4.82348i	0.0419725	−	0.183894i
$689$	9.23730	+	11.5832i	0.351913	+	0.441285i
$690$	6.80716	+	3.27816i	0.259144	+	0.124797i
$691$	−15.7501	+	7.58486i	−0.599163	+	0.288542i	−0.708777	−	0.705432i	$-0.750753\pi$
$691$	−15.7501	+	7.58486i	−0.599163	+	0.288542i	0.109614	+	0.993974i	$0.465039\pi$
$692$	−3.79633	+	4.76045i	−0.144315	+	0.180965i
$693$	1.43030	+	1.79354i	0.0543327	+	0.0681311i
$694$	−20.6855	+	9.96163i	−0.785213	+	0.378138i
$695$	−22.7619			−0.863408
$696$	−12.5916	+	3.83317i	−0.477282	+	0.145296i
$697$	−45.1412			−1.70984
$698$	3.98483	−	1.91899i	0.150828	−	0.0726349i
$699$	−14.8895	−	18.6709i	−0.563174	−	0.706198i
$700$	−2.10322	+	2.63735i	−0.0794942	+	0.0996826i
$701$	26.5799	−	12.8002i	1.00391	−	0.483458i	0.141646	−	0.989917i	$-0.454760\pi$
$701$	26.5799	−	12.8002i	1.00391	−	0.483458i	0.862264	+	0.506460i	$0.169046\pi$
$702$	4.09056	+	1.96991i	0.154388	+	0.0743494i
$703$	5.00991	+	6.28223i	0.188953	+	0.236939i
$704$	0.292203	−	1.28022i	0.0110128	−	0.0482503i
$705$	−1.45149	+	6.35941i	−0.0546664	+	0.239509i
$706$	−7.61395	+	9.54759i	−0.286555	+	0.359328i
$707$	4.93289	+	21.6124i	0.185521	+	0.812818i
$708$	14.1197			0.530650
$709$	−5.48443	−	24.0289i	−0.205972	−	0.902423i	−0.967216	−	0.253957i	$-0.918268\pi$
$709$	−5.48443	−	24.0289i	−0.205972	−	0.902423i	0.761244	−	0.648466i	$-0.224589\pi$
$710$	5.81590	+	2.80079i	0.218267	+	0.105112i
$711$	−3.86318	−	1.86041i	−0.144881	−	0.0697708i
$712$	−8.39903	−	36.7985i	−0.314767	−	1.37908i
$713$	−14.7343			−0.551805
$714$	1.41337	+	6.19240i	0.0528942	+	0.231745i
$715$	7.87315	−	9.87262i	0.294439	−	0.369215i
$716$	−1.30566	+	5.72046i	−0.0487948	+	0.213784i
$717$	1.87126	−	8.19853i	0.0698835	−	0.306180i
$718$	−3.38826	−	4.24875i	−0.126449	−	0.158562i
$719$	1.24578	+	0.599937i	0.0464598	+	0.0223739i	0.456969	−	0.889482i	$-0.348935\pi$
$719$	1.24578	+	0.599937i	0.0464598	+	0.0223739i	−0.410510	+	0.911856i	$0.634649\pi$
$720$	2.42808	−	1.16930i	0.0904892	−	0.0435773i
$721$	−15.8196	+	19.8372i	−0.589154	+	0.738776i
$722$	0.152055	+	0.190671i	0.00565890	+	0.00709604i
$723$	0.485048	−	0.233587i	0.0180391	−	0.00868719i
$724$	−25.2284			−0.937607
$725$	−3.67776	+	3.38730i	−0.136588	+	0.125801i
$726$	7.00668			0.260042
$727$	−34.0179	+	16.3821i	−1.26165	+	0.607580i	−0.940611	−	0.339485i	$-0.889747\pi$
$727$	−34.0179	+	16.3821i	−1.26165	+	0.607580i	−0.321041	+	0.947065i	$0.604033\pi$
$728$	−23.8433	−	29.8985i	−0.883691	−	1.10811i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	−11.4859	+	5.53130i	−0.425111	+	0.204722i
$731$	−12.7374	−	6.13399i	−0.471108	−	0.226874i
$732$	−2.96864	−	3.72256i	−0.109724	−	0.137590i
$733$	7.24828	−	31.7568i	0.267721	−	1.17296i	−0.644936	−	0.764237i	$-0.723116\pi$
$733$	7.24828	−	31.7568i	0.267721	−	1.17296i	0.912657	−	0.408727i	$-0.134027\pi$
$734$	4.51017	−	19.7603i	0.166473	−	0.729368i
$735$	1.59089	−	1.99491i	0.0586807	−	0.0735833i
$736$	−6.97363	−	30.5535i	−0.257051	−	1.12622i
$737$	−11.5916			−0.426982
$738$	1.82909	+	8.01375i	0.0673296	+	0.294990i
$739$	34.2033	+	16.4714i	1.25819	+	0.605911i	0.939695	−	0.342014i	$-0.111109\pi$
$739$	34.2033	+	16.4714i	1.25819	+	0.605911i	0.318493	+	0.947925i	$0.396823\pi$
$740$	5.13173	+	2.47131i	0.188646	+	0.0908472i
$741$	6.27806	+	27.5060i	0.230630	+	1.01046i
$742$	3.77416			0.138554
$743$	2.91935	+	12.7905i	0.107101	+	0.469238i	0.999826	+	0.0186379i	$0.00593297\pi$
$743$	2.91935	+	12.7905i	0.107101	+	0.469238i	−0.892726	+	0.450601i	$0.851210\pi$
$744$	4.16730	−	5.22563i	0.152781	−	0.191581i
$745$	2.19912	−	9.63496i	0.0805694	−	0.352998i
$746$	−0.905585	+	3.96763i	−0.0331558	+	0.145265i
$747$	10.0888	+	12.6510i	0.369132	+	0.462876i
$748$	4.99669	+	2.40628i	0.182697	+	0.0879823i
$749$	−0.271234	+	0.130619i	−0.00991067	+	0.00477273i
$750$	−5.18319	+	6.49952i	−0.189263	+	0.237329i
$751$	−17.5307	−	21.9828i	−0.639704	−	0.802163i	0.351262	−	0.936277i	$-0.385753\pi$
$751$	−17.5307	−	21.9828i	−0.639704	−	0.802163i	−0.990966	+	0.134114i	$0.957181\pi$
$752$	3.89000	−	1.87333i	0.141854	−	0.0683132i
$753$	−1.71008			−0.0623186
$754$	−12.1466	−	21.2189i	−0.442353	−	0.772748i
$755$	−34.3565			−1.25036
$756$	−3.27338	+	1.57638i	−0.119052	+	0.0573323i
$757$	−11.8885	−	14.9078i	−0.432096	−	0.541831i	0.517345	−	0.855777i	$-0.326920\pi$
$757$	−11.8885	−	14.9078i	−0.432096	−	0.541831i	−0.949441	+	0.313946i	$0.898349\pi$
$758$	1.00418	−	1.25920i	0.0364735	−	0.0457363i
$759$	−4.65002	+	2.23933i	−0.168785	+	0.0812826i
$760$	−19.1886	−	9.24074i	−0.696044	−	0.335197i
$761$	5.51450	+	6.91496i	0.199900	+	0.250667i	0.871670	−	0.490093i	$-0.163037\pi$
$761$	5.51450	+	6.91496i	0.199900	+	0.250667i	−0.671770	+	0.740760i	$0.734466\pi$
$762$	−0.606186	+	2.65587i	−0.0219598	+	0.0962121i
$763$	−5.14078	+	22.5232i	−0.186109	+	0.815395i
$764$	2.49816	−	3.13260i	0.0903804	−	0.113333i
$765$	−1.71358	−

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.626118 - 0.301523i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.945872 + 1.18609i) q^{4} +(1.81798 - 0.875492i) q^{5} +(0.626118 + 0.301523i) q^{6} +(-1.49319 - 1.87240i) q^{7} +(-0.543873 + 2.38286i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})\)	\(q+(0.626118 - 0.301523i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.945872 + 1.18609i) q^{4} +(1.81798 - 0.875492i) q^{5} +(0.626118 + 0.301523i) q^{6} +(-1.49319 - 1.87240i) q^{7} +(-0.543873 + 2.38286i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(0.874288 - 1.09632i) q^{10} +(0.213150 + 0.933871i) q^{11} -1.51706 q^{12} +(-1.45377 - 6.36940i) q^{13} +(-1.49948 - 0.722111i) q^{14} +(1.81798 + 0.875492i) q^{15} +(-0.297197 - 1.30211i) q^{16} -3.81642 q^{17} +(0.154638 + 0.677515i) q^{18} +(-2.69251 + 3.37631i) q^{19} +(-0.681165 + 2.98438i) q^{20} +(0.532912 - 2.33484i) q^{21} +(0.415040 + 0.520444i) q^{22} +(4.85446 + 2.33778i) q^{23} +(-2.20209 + 1.06047i) q^{24} +(-0.578892 + 0.725907i) q^{25} +(-2.83075 - 3.54965i) q^{26} +(-0.900969 + 0.433884i) q^{27} +3.63318 q^{28} +(5.32202 + 0.822256i) q^{29} +1.40225 q^{30} +(-2.46382 + 1.18651i) q^{31} +(-3.62649 - 4.54747i) q^{32} +(-0.597233 + 0.748906i) q^{33} +(-2.38953 + 1.15074i) q^{34} +(-4.35384 - 2.09670i) q^{35} +(-0.945872 - 1.18609i) q^{36} +(0.414041 - 1.81403i) q^{37} +(-0.667799 + 2.92582i) q^{38} +(4.07339 - 5.10787i) q^{39} +(1.09743 + 4.80814i) q^{40} +11.8282 q^{41} +(-0.370341 - 1.62257i) q^{42} +(3.33752 + 1.60727i) q^{43} +(-1.30926 - 0.630508i) q^{44} +(0.449003 + 1.96721i) q^{45} +3.74436 q^{46} +(0.719344 + 3.15165i) q^{47} +(0.832729 - 1.04421i) q^{48} +(0.281385 - 1.23283i) q^{49} +(-0.143577 + 0.629053i) q^{50} +(-2.37950 - 2.98379i) q^{51} +(8.92974 + 4.30034i) q^{52} +(-2.04315 + 0.983927i) q^{53} +(-0.433287 + 0.543325i) q^{54} +(1.20510 + 1.51115i) q^{55} +(5.27376 - 2.53971i) q^{56} -4.31846 q^{57} +(3.58014 - 1.08988i) q^{58} -9.30726 q^{59} +(-2.75798 + 1.32817i) q^{60} +(1.95684 + 2.45380i) q^{61} +(-1.18488 + 1.48579i) q^{62} +(2.15772 - 1.03910i) q^{63} +(-1.23512 - 0.594802i) q^{64} +(-8.21929 - 10.3067i) q^{65} +(-0.148126 + 0.648983i) q^{66} +(-2.69277 + 11.7978i) q^{67} +(3.60984 - 4.52660i) q^{68} +(1.19895 + 5.25295i) q^{69} -3.35822 q^{70} +(1.02436 + 4.48801i) q^{71} +(-2.20209 - 1.06047i) q^{72} +(-8.19102 - 3.94459i) q^{73} +(-0.287733 - 1.26064i) q^{74} -0.928470 q^{75} +(-1.45781 - 6.38710i) q^{76} +(1.43030 - 1.79354i) q^{77} +(1.01028 - 4.42634i) q^{78} +(-0.954127 + 4.18030i) q^{79} +(-1.68028 - 2.10701i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(7.40582 - 3.56646i) q^{82} +(10.0888 - 12.6510i) q^{83} +(2.26525 + 2.84054i) q^{84} +(-6.93816 + 3.34124i) q^{85} +2.57431 q^{86} +(2.67536 + 4.67359i) q^{87} -2.34121 q^{88} +(-13.9137 + 6.70047i) q^{89} +(0.874288 + 1.09632i) q^{90} +(-9.75529 + 12.2327i) q^{91} +(-7.36451 + 3.54656i) q^{92} +(-2.46382 - 1.18651i) q^{93} +(1.40069 + 1.75641i) q^{94} +(-1.93900 + 8.49532i) q^{95} +(1.29428 - 5.67061i) q^{96} +(9.82817 - 12.3241i) q^{97} +(-0.195546 - 0.856741i) q^{98} -0.957887 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

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