LMFDB - Embedded newform 87.2.g.b.49.1

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} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
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			49.1
Root			$1.29273 - 1.62103i$ of defining polynomial
Character	$\chi$	$=$	87.49
Dual form			87.2.g.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86804 + 0.899602i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.43332 - 1.79733i) q^{4} +(-1.70773 + 0.822397i) q^{5} +(1.86804 + 0.899602i) q^{6} +(-2.93833 - 3.68455i) q^{7} +(-0.137887 + 0.604122i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})$	\(q+(-1.86804 + 0.899602i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.43332 - 1.79733i) q^{4} +(-1.70773 + 0.822397i) q^{5} +(1.86804 + 0.899602i) q^{6} +(-2.93833 - 3.68455i) q^{7} +(-0.137887 + 0.604122i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(2.45027 - 3.07255i) q^{10} +(-0.832232 - 3.64624i) q^{11} -2.29887 q^{12} +(0.250393 + 1.09704i) q^{13} +(8.80354 + 4.23956i) q^{14} +(1.70773 + 0.822397i) q^{15} +(0.737200 + 3.22989i) q^{16} -5.60261 q^{17} +(-0.461368 - 2.02139i) q^{18} +(-1.20592 + 1.51218i) q^{19} +(-0.969600 + 4.24810i) q^{20} +(-1.04868 + 4.59455i) q^{21} +(4.83481 + 6.06266i) q^{22} +(3.89751 + 1.87694i) q^{23} +(0.558293 - 0.268860i) q^{24} +(-0.877459 + 1.10030i) q^{25} +(-1.45465 - 1.82407i) q^{26} +(0.900969 - 0.433884i) q^{27} -10.8339 q^{28} +(3.82459 - 3.79111i) q^{29} -3.92993 q^{30} +(-0.874966 + 0.421361i) q^{31} +(-5.05543 - 6.33931i) q^{32} +(-2.33186 + 2.92406i) q^{33} +(10.4659 - 5.04011i) q^{34} +(8.04802 + 3.87572i) q^{35} +(1.43332 + 1.79733i) q^{36} +(2.21633 - 9.71037i) q^{37} +(0.892354 - 3.90966i) q^{38} +(0.701586 - 0.879761i) q^{39} +(-0.261356 - 1.14507i) q^{40} +1.59051 q^{41} +(-2.17430 - 9.52621i) q^{42} +(-4.08593 - 1.96768i) q^{43} +(-7.74634 - 3.73044i) q^{44} +(-0.421773 - 1.84791i) q^{45} -8.96921 q^{46} +(-1.30426 - 5.71432i) q^{47} +(2.06559 - 2.59017i) q^{48} +(-3.38446 + 14.8283i) q^{49} +(0.649300 - 2.84477i) q^{50} +(3.49317 + 4.38029i) q^{51} +(2.33064 + 1.12238i) q^{52} +(-4.64798 + 2.23835i) q^{53} +(-1.29273 + 1.62103i) q^{54} +(4.41989 + 5.54236i) q^{55} +(2.63107 - 1.26706i) q^{56} +1.93415 q^{57} +(-3.73401 + 10.5226i) q^{58} +5.71853 q^{59} +(3.92583 - 1.89058i) q^{60} +(-6.51069 - 8.16415i) q^{61} +(1.25542 - 1.57424i) q^{62} +(4.24601 - 2.04477i) q^{63} +(9.17690 + 4.41936i) q^{64} +(-1.32981 - 1.66753i) q^{65} +(1.72552 - 7.56002i) q^{66} +(0.883099 - 3.86911i) q^{67} +(-8.03032 + 10.0697i) q^{68} +(-0.962605 - 4.21745i) q^{69} -18.5206 q^{70} +(0.0665482 + 0.291567i) q^{71} +(-0.558293 - 0.268860i) q^{72} +(13.6108 + 6.55462i) q^{73} +(4.59527 + 20.1332i) q^{74} +1.40734 q^{75} +(0.989404 + 4.33486i) q^{76} +(-10.9894 + 13.7803i) q^{77} +(-0.519158 + 2.27458i) q^{78} +(3.07354 - 13.4661i) q^{79} +(-3.91519 - 4.90949i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(-2.97115 + 1.43083i) q^{82} +(1.81951 - 2.28159i) q^{83} +(6.75482 + 8.47027i) q^{84} +(9.56772 - 4.60757i) q^{85} +9.40282 q^{86} +(-5.34860 - 0.626466i) q^{87} +2.31753 q^{88} +(-6.56353 + 3.16083i) q^{89} +(2.45027 + 3.07255i) q^{90} +(3.30637 - 4.14606i) q^{91} +(8.95985 - 4.31484i) q^{92} +(0.874966 + 0.421361i) q^{93} +(7.57701 + 9.50127i) q^{94} +(0.815772 - 3.57413i) q^{95} +(-1.80426 + 7.90500i) q^{96} +(-7.99029 + 10.0195i) q^{97} +(-7.01725 - 30.7446i) q^{98} +3.74001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * 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 $

$2$	−1.86804	+	0.899602i	−1.32091	+	0.636115i	−0.955571	−	0.294762i	$-0.904760\pi$
$2$	−1.86804	+	0.899602i	−1.32091	+	0.636115i	−0.365335	+	0.930876i	$0.619045\pi$
$3$	−0.623490	−	0.781831i	−0.359972	−	0.451391i
$3$	−0.623490	−	0.781831i	−0.359972	−	0.451391i
$4$	1.43332	−	1.79733i	0.716660	−	0.898663i
$5$	−1.70773	+	0.822397i	−0.763718	+	0.367787i	−0.774845	−	0.632151i	$-0.782172\pi$
$5$	−1.70773	+	0.822397i	−0.763718	+	0.367787i	0.0111272	+	0.999938i	$0.496458\pi$
$6$	1.86804	+	0.899602i	0.762625	+	0.367261i
$7$	−2.93833	−	3.68455i	−1.11058	−	1.39263i	−0.910830	−	0.412781i	$-0.864558\pi$
$7$	−2.93833	−	3.68455i	−1.11058	−	1.39263i	−0.199753	−	0.979846i	$-0.564014\pi$
$8$	−0.137887	+	0.604122i	−0.0487504	+	0.213590i
$9$	−0.222521	+	0.974928i	−0.0741736	+	0.324976i
$10$	2.45027	−	3.07255i	0.774845	−	0.971624i
$11$	−0.832232	−	3.64624i	−0.250927	−	1.09938i	−0.930649	−	0.365914i	$-0.880757\pi$
$11$	−0.832232	−	3.64624i	−0.250927	−	1.09938i	0.679722	−	0.733470i	$-0.262101\pi$
$12$	−2.29887			−0.663625
$13$	0.250393	+	1.09704i	0.0694465	+	0.304265i	0.997708	−	0.0676624i	$-0.0215541\pi$
$13$	0.250393	+	1.09704i	0.0694465	+	0.304265i	−0.928262	+	0.371928i	$0.878697\pi$
$14$	8.80354	+	4.23956i	2.35285	+	1.13307i
$15$	1.70773	+	0.822397i	0.440933	+	0.212342i
$16$	0.737200	+	3.22989i	0.184300	+	0.807472i
$17$	−5.60261			−1.35883			−0.679416	−	0.733753i	$-0.737767\pi$
$17$	−5.60261			−1.35883			−0.679416	+	0.733753i	$0.737767\pi$
$18$	−0.461368	−	2.02139i	−0.108746	−	0.476445i
$19$	−1.20592	+	1.51218i	−0.276657	+	0.346917i	−0.900675	−	0.434493i	$-0.856928\pi$
$19$	−1.20592	+	1.51218i	−0.276657	+	0.346917i	0.624018	+	0.781410i	$0.285499\pi$
$20$	−0.969600	+	4.24810i	−0.216809	+	0.949903i
$21$	−1.04868	+	4.59455i	−0.228840	+	1.00261i
$22$	4.83481	+	6.06266i	1.03079	+	1.29256i
$23$	3.89751	+	1.87694i	0.812687	+	0.391369i	0.793593	−	0.608448i	$-0.208208\pi$
$23$	3.89751	+	1.87694i	0.812687	+	0.391369i	0.0190933	+	0.999818i	$0.493922\pi$
$24$	0.558293	−	0.268860i	0.113961	−	0.0548808i
$25$	−0.877459	+	1.10030i	−0.175492	+	0.220060i
$26$	−1.45465	−	1.82407i	−0.285280	−	0.357730i
$27$	0.900969	−	0.433884i	0.173392	−	0.0835010i
$28$	−10.8339			−2.04741
$29$	3.82459	−	3.79111i	0.710208	−	0.703991i
$29$	3.82459	−	3.79111i	0.710208	−	0.703991i
$30$	−3.92993			−0.717505
$31$	−0.874966	+	0.421361i	−0.157148	+	0.0756787i	−0.510805	−	0.859697i	$-0.670653\pi$
$31$	−0.874966	+	0.421361i	−0.157148	+	0.0756787i	0.353656	+	0.935375i	$0.384938\pi$
$32$	−5.05543	−	6.33931i	−0.893683	−	1.12064i
$33$	−2.33186	+	2.92406i	−0.405925	+	0.509014i
$34$	10.4659	−	5.04011i	1.79489	−	0.864373i
$35$	8.04802	+	3.87572i	1.36036	+	0.655116i
$36$	1.43332	+	1.79733i	0.238887	+	0.299554i
$37$	2.21633	−	9.71037i	0.364362	−	1.59637i	−0.377624	−	0.925959i	$-0.623259\pi$
$37$	2.21633	−	9.71037i	0.364362	−	1.59637i	0.741986	−	0.670416i	$-0.233884\pi$
$38$	0.892354	−	3.90966i	0.144759	−	0.634230i
$39$	0.701586	−	0.879761i	0.112344	−	0.140874i
$40$	−0.261356	−	1.14507i	−0.0413239	−	0.181052i
$41$	1.59051			0.248397			0.124198	−	0.992257i	$-0.460364\pi$
$41$	1.59051			0.248397			0.124198	+	0.992257i	$0.460364\pi$
$42$	−2.17430	−	9.52621i	−0.335501	−	1.46993i
$43$	−4.08593	−	1.96768i	−0.623098	−	0.300068i	0.0955686	−	0.995423i	$-0.469533\pi$
$43$	−4.08593	−	1.96768i	−0.623098	−	0.300068i	−0.718667	+	0.695355i	$0.755247\pi$
$44$	−7.74634	−	3.73044i	−1.16780	−	0.562385i
$45$	−0.421773	−	1.84791i	−0.0628743	−	0.275470i
$46$	−8.96921			−1.32244
$47$	−1.30426	−	5.71432i	−0.190245	−	0.833519i	−0.976483	−	0.215595i	$-0.930831\pi$
$47$	−1.30426	−	5.71432i	−0.190245	−	0.833519i	0.786238	−	0.617924i	$-0.212026\pi$
$48$	2.06559	−	2.59017i	0.298142	−	0.373859i
$49$	−3.38446	+	14.8283i	−0.483495	+	2.11833i
$50$	0.649300	−	2.84477i	0.0918249	−	0.402311i
$51$	3.49317	+	4.38029i	0.489141	+	0.613364i
$52$	2.33064	+	1.12238i	0.323201	+	0.155646i
$53$	−4.64798	+	2.23835i	−0.638449	+	0.307461i	−0.724961	−	0.688790i	$-0.758142\pi$
$53$	−4.64798	+	2.23835i	−0.638449	+	0.307461i	0.0865120	+	0.996251i	$0.472428\pi$
$54$	−1.29273	+	1.62103i	−0.175918	+	0.220594i
$55$	4.41989	+	5.54236i	0.595977	+	0.747332i
$56$	2.63107	−	1.26706i	0.351592	−	0.169318i
$57$	1.93415			0.256184
$58$	−3.73401	+	10.5226i	−0.490299	+	1.38168i
$59$	5.71853			0.744490			0.372245	−	0.928135i	$-0.378588\pi$
$59$	5.71853			0.744490			0.372245	+	0.928135i	$0.378588\pi$
$60$	3.92583	−	1.89058i	0.506823	−	0.244073i
$61$	−6.51069	−	8.16415i	−0.833608	−	1.04531i	−0.998260	−	0.0589600i	$-0.981222\pi$
$61$	−6.51069	−	8.16415i	−0.833608	−	1.04531i	0.164652	−	0.986352i	$-0.447350\pi$
$62$	1.25542	−	1.57424i	0.159438	−	0.199929i
$63$	4.24601	−	2.04477i	0.534946	−	0.257617i
$64$	9.17690	+	4.41936i	1.14711	+	0.552420i
$65$	−1.32981	−	1.66753i	−0.164942	−	0.206831i
$66$	1.72552	−	7.56002i	0.212397	−	0.930574i
$67$	0.883099	−	3.86911i	0.107888	−	0.472687i	−0.891903	−	0.452227i	$-0.850630\pi$
$67$	0.883099	−	3.86911i	0.107888	−	0.472687i	0.999791	−	0.0204600i	$-0.00651307\pi$
$68$	−8.03032	+	10.0697i	−0.973820	+	1.22113i
$69$	−0.962605	−	4.21745i	−0.115884	−	0.507721i
$70$	−18.5206			−2.21364
$71$	0.0665482	+	0.291567i	0.00789782	+	0.0346026i	0.978723	−	0.205185i	$-0.0657795\pi$
$71$	0.0665482	+	0.291567i	0.00789782	+	0.0346026i	−0.970825	+	0.239787i	$0.922922\pi$
$72$	−0.558293	−	0.268860i	−0.0657955	−	0.0316854i
$73$	13.6108	+	6.55462i	1.59302	+	0.767160i	0.999296	−	0.0375058i	$-0.0119413\pi$
$73$	13.6108	+	6.55462i	1.59302	+	0.767160i	0.593728	+	0.804666i	$0.297656\pi$
$74$	4.59527	+	20.1332i	0.534189	+	2.34044i
$75$	1.40734			0.162505
$76$	0.989404	+	4.33486i	0.113492	+	0.497243i
$77$	−10.9894	+	13.7803i	−1.25236	+	1.57041i
$78$	−0.519158	+	2.27458i	−0.0587830	+	0.257545i
$79$	3.07354	−	13.4661i	0.345801	−	1.51505i	−0.440809	−	0.897601i	$-0.645308\pi$
$79$	3.07354	−	13.4661i	0.345801	−	1.51505i	0.786609	−	0.617451i	$-0.211835\pi$
$80$	−3.91519	−	4.90949i	−0.437731	−	0.548897i
$81$	−0.900969	−	0.433884i	−0.100108	−	0.0482093i
$82$	−2.97115	+	1.43083i	−0.328108	+	0.158009i
$83$	1.81951	−	2.28159i	0.199717	−	0.250437i	−0.671880	−	0.740660i	$-0.734513\pi$
$83$	1.81951	−	2.28159i	0.199717	−	0.250437i	0.871597	+	0.490223i	$0.163085\pi$
$84$	6.75482	+	8.47027i	0.737011	+	0.924183i
$85$	9.56772	−	4.60757i	1.03776	−	0.499761i
$86$	9.40282			1.01393
$87$	−5.34860	−	0.626466i	−0.573430	−	0.0671642i
$88$	2.31753			0.247050
$89$	−6.56353	+	3.16083i	−0.695732	+	0.335047i	−0.748105	−	0.663581i	$-0.769036\pi$
$89$	−6.56353	+	3.16083i	−0.695732	+	0.335047i	0.0523724	+	0.998628i	$0.483322\pi$
$90$	2.45027	+	3.07255i	0.258282	+	0.323875i
$91$	3.30637	−	4.14606i	0.346602	−	0.434625i
$92$	8.95985	−	4.31484i	0.934129	−	0.449853i
$93$	0.874966	+	0.421361i	0.0907297	+	0.0436931i
$94$	7.57701	+	9.50127i	0.781509	+	0.979981i
$95$	0.815772	−	3.57413i	0.0836964	−	0.366698i
$96$	−1.80426	+	7.90500i	−0.184147	+	0.806800i
$97$	−7.99029	+	10.0195i	−0.811291	+	1.01733i	0.188090	+	0.982152i	$0.439770\pi$
$97$	−7.99029	+	10.0195i	−0.811291	+	1.01733i	−0.999381	+	0.0351751i	$0.988801\pi$
$98$	−7.01725	−	30.7446i	−0.708849	−	3.10567i
$99$	3.74001			0.375886
$100$	0.719916	+	3.15416i	0.0719916	+	0.315416i
$101$	8.51665	+	4.10140i	0.847438	+	0.408105i	0.806626	−	0.591062i	$-0.201291\pi$
$101$	8.51665	+	4.10140i	0.847438	+	0.408105i	0.0408123	+	0.999167i	$0.487005\pi$
$102$	−10.4659	−	5.04011i	−1.03628	−	0.499046i
$103$	−1.23571	−	5.41401i	−0.121758	−	0.533458i	−0.998611	−	0.0526978i	$-0.983218\pi$
$103$	−1.23571	−	5.41401i	−0.121758	−	0.533458i	0.876852	−	0.480760i	$-0.159639\pi$
$104$	−0.697275			−0.0683734
$105$	−1.98770	−	8.70867i	−0.193979	−	0.849879i
$106$	6.66900	−	8.36266i	0.647750	−	0.812253i
$107$	−1.40124	+	6.13923i	−0.135463	+	0.593502i	0.860936	+	0.508713i	$0.169879\pi$
$107$	−1.40124	+	6.13923i	−0.135463	+	0.593502i	−0.996399	+	0.0847887i	$0.972978\pi$
$108$	0.511546	−	2.24123i	0.0492235	−	0.215662i
$109$	−10.2240	−	12.8205i	−0.979284	−	1.22798i	−0.973661	−	0.227999i	$-0.926782\pi$
$109$	−10.2240	−	12.8205i	−0.979284	−	1.22798i	−0.00562210	−	0.999984i	$-0.501790\pi$
$110$	−13.2424	−	6.37723i	−1.26262	−	0.608045i
$111$	−8.97373	+	4.32152i	−0.851749	+	0.410181i
$112$	9.73453	−	12.2067i	0.919826	−	1.15343i
$113$	1.71259	+	2.14752i	0.161107	+	0.202022i	0.855832	−	0.517253i	$-0.173046\pi$
$113$	1.71259	+	2.14752i	0.161107	+	0.202022i	−0.694725	+	0.719275i	$0.744474\pi$
$114$	−3.61307	+	1.73996i	−0.338395	+	0.162962i
$115$	−8.19947			−0.764604
$116$	−1.33200	−	12.3079i	−0.123673	−	1.14276i
$117$	−1.12526			−0.104030
$118$	−10.6825	+	5.14440i	−0.983400	+	0.473581i
$119$	16.4623	+	20.6431i	1.50910	+	1.89235i
$120$	−0.732302	+	0.918278i	−0.0668497	+	0.0838269i
$121$	−2.69183	+	1.29632i	−0.244712	+	0.117847i
$122$	19.5067	+	9.39394i	1.76606	+	0.850488i
$123$	−0.991669	−	1.24351i	−0.0894158	−	0.112124i
$124$	−0.496782	+	2.17654i	−0.0446123	+	0.195459i
$125$	2.70244	−	11.8402i	0.241714	−	1.05902i
$126$	−6.09224	+	7.63943i	−0.542740	+	0.680574i
$127$	2.76187	+	12.1005i	0.245076	+	1.07375i	0.936326	+	0.351132i	$0.114203\pi$
$127$	2.76187	+	12.1005i	0.245076	+	1.07375i	−0.691250	+	0.722616i	$0.742940\pi$
$128$	−4.90192			−0.433273
$129$	1.00914	+	4.42134i	0.0888499	+	0.389277i
$130$	3.98425	+	1.91871i	0.349442	+	0.168282i
$131$	−17.0367	−	8.20444i	−1.48850	−	0.716825i	−0.499720	−	0.866187i	$-0.666564\pi$
$131$	−17.0367	−	8.20444i	−1.48850	−	0.716825i	−0.988783	+	0.149362i	$0.952278\pi$
$132$	1.91319	+	8.38222i	0.166522	+	0.729579i
$133$	9.11507			0.790377
$134$	1.83099	+	8.02209i	0.158173	+	0.693003i
$135$	−1.18178	+	1.48191i	−0.101712	+	0.127542i
$136$	0.772527	−	3.38466i	0.0662436	−	0.290232i
$137$	−1.96363	+	8.60324i	−0.167764	+	0.735024i	0.819123	+	0.573617i	$0.194460\pi$
$137$	−1.96363	+	8.60324i	−0.167764	+	0.735024i	−0.986888	+	0.161407i	$0.948397\pi$
$138$	5.59221	+	7.01241i	0.476041	+	0.596936i
$139$	−9.32088	−	4.48870i	−0.790587	−	0.380727i	−0.00539998	−	0.999985i	$-0.501719\pi$
$139$	−9.32088	−	4.48870i	−0.790587	−	0.380727i	−0.785187	+	0.619259i	$0.787433\pi$
$140$	18.5013	−	8.90976i	1.56365	−	0.753012i
$141$	−3.65444	+	4.58253i	−0.307760	+	0.385918i
$142$	−0.386609	−	0.484792i	−0.0324435	−	0.0406829i
$143$	3.79170	−	1.82599i	0.317078	−	0.152697i
$144$	−3.31295			−0.276079
$145$	−3.41355	+	9.61951i	−0.283480	+	0.798857i
$146$	−31.3221			−2.59224
$147$	13.7034	−	6.59921i	1.13024	−	0.544294i
$148$	−14.2760	−	17.9015i	−1.17348	−	1.47150i
$149$	7.54443	−	9.46042i	0.618064	−	0.775028i	−0.370007	−	0.929029i	$-0.620645\pi$
$149$	7.54443	−	9.46042i	0.618064	−	0.775028i	0.988071	+	0.154001i	$0.0492160\pi$
$150$	−2.62896	+	1.26604i	−0.214654	+	0.103372i
$151$	−8.59578	−	4.13951i	−0.699514	−	0.336868i	0.0500991	−	0.998744i	$-0.484046\pi$
$151$	−8.59578	−	4.13951i	−0.699514	−	0.336868i	−0.749613	+	0.661876i	$0.769761\pi$
$152$	−0.747259	−	0.937033i	−0.0606107	−	0.0760034i
$153$	1.24670	−	5.46214i	0.100790	−	0.441588i
$154$	8.13190	−	35.6282i	0.655287	−	2.87100i
$155$	1.14767	−	1.43914i	0.0921835	−	0.115594i
$156$	−0.575620	−	2.52196i	−0.0460865	−	0.201918i
$157$	0.889508			0.0709905			0.0354952	−	0.999370i	$-0.488699\pi$
$157$	0.889508			0.0709905			0.0354952	+	0.999370i	$0.488699\pi$
$158$	6.37260	+	27.9202i	0.506977	+	2.22121i
$159$	4.64798	+	2.23835i	0.368609	+	0.177513i
$160$	13.8467	+	6.66823i	1.09468	+	0.527170i
$161$	−4.53648	−	19.8756i	−0.357525	−	1.56642i
$162$	2.07337			0.162899
$163$	−1.71620	−	7.51914i	−0.134423	−	0.588945i	−0.996604	−	0.0823446i	$-0.973759\pi$
$163$	−1.71620	−	7.51914i	−0.134423	−	0.588945i	0.862181	−	0.506600i	$-0.169098\pi$
$164$	2.27971	−	2.85867i	0.178016	−	0.223225i
$165$	1.57744	−	6.91121i	0.122803	−	0.538037i
$166$	−1.34639	+	5.89894i	−0.104500	+	0.457846i
$167$	5.23031	+	6.55860i	0.404734	+	0.507520i	0.941871	−	0.335975i	$-0.109066\pi$
$167$	5.23031	+	6.55860i	0.404734	+	0.507520i	−0.537137	+	0.843495i	$0.680494\pi$
$168$	−2.63107	−	1.26706i	−0.202992	−	0.0977557i
$169$	10.5718	−	5.09110i	0.813214	−	0.391623i
$170$	−13.7279	+	17.2143i	−1.05288	+	1.32027i
$171$	−1.20592	−	1.51218i	−0.0922191	−	0.115639i
$172$	−9.39300	+	4.52343i	−0.716210	+	0.344908i
$173$	−3.52185			−0.267761			−0.133881	−	0.990997i	$-0.542744\pi$
$173$	−3.52185			−0.267761			−0.133881	+	0.990997i	$0.542744\pi$
$174$	10.5550	−	3.64135i	0.800171	−	0.276050i
$175$	6.63236			0.501360
$176$	11.1634	−	5.37603i	0.841475	−	0.405233i
$177$	−3.56545	−	4.47093i	−0.267995	−	0.336056i
$178$	9.41746	−	11.8091i	0.705868	−	0.885131i
$179$	−6.42875	+	3.09592i	−0.480507	+	0.231400i	−0.658427	−	0.752645i	$-0.728778\pi$
$179$	−6.42875	+	3.09592i	−0.480507	+	0.231400i	0.177919	+	0.984045i	$0.443063\pi$
$180$	−3.92583	−	1.89058i	−0.292614	−	0.140916i
$181$	13.1435	+	16.4814i	0.976949	+	1.22505i	0.974345	+	0.225058i	$0.0722573\pi$
$181$	13.1435	+	16.4814i	0.976949	+	1.22505i	0.00260345	+	0.999997i	$0.499171\pi$
$182$	−2.44664	+	10.7194i	−0.181357	+	0.794577i
$183$	−2.32364	+	10.1805i	−0.171768	+	0.752566i
$184$	−1.67132	+	2.09577i	−0.123211	+	0.154502i
$185$	4.20090	+	18.4053i	0.308856	+	1.35319i
$186$	−2.01353			−0.147639
$187$	4.66267	+	20.4285i	0.340968	+	1.49388i
$188$	−12.1399	−	5.84627i	−0.885393	−	0.426383i
$189$	−4.24601	−	2.04477i	−0.308851	−	0.148735i
$190$	1.69140	+	7.41049i	0.122707	+	0.537614i
$191$	−13.8150			−0.999620			−0.499810	−	0.866135i	$-0.666597\pi$
$191$	−13.8150			−0.999620			−0.499810	+	0.866135i	$0.666597\pi$
$192$	−2.26651	−	9.93021i	−0.163571	−	0.716651i
$193$	2.63922	−	3.30948i	0.189975	−	0.238222i	−0.677717	−	0.735322i	$-0.737031\pi$
$193$	2.63922	−	3.30948i	0.189975	−	0.238222i	0.867693	+	0.497101i	$0.165602\pi$
$194$	5.91263	−	25.9049i	0.424502	−	1.85987i
$195$	−0.474603	+	2.07937i	−0.0339870	+	0.148907i
$196$	21.8003	+	27.3367i	1.55716	+	1.95262i
$197$	−4.15777	−	2.00228i	−0.296229	−	0.142656i	0.279866	−	0.960039i	$-0.409710\pi$
$197$	−4.15777	−	2.00228i	−0.296229	−	0.142656i	−0.576095	+	0.817383i	$0.695424\pi$
$198$	−6.98651	+	3.36452i	−0.496509	+	0.239106i
$199$	−2.38547	+	2.99128i	−0.169101	+	0.212046i	−0.859160	−	0.511707i	$-0.829013\pi$
$199$	−2.38547	+	2.99128i	−0.169101	+	0.212046i	0.690059	+	0.723753i	$0.257585\pi$
$200$	−0.543725	−	0.681810i	−0.0384472	−	0.0482112i
$201$	−3.57559	+	1.72191i	−0.252203	+	0.121455i
$202$	−19.5991			−1.37899
$203$	−25.2064	−	2.95235i	−1.76914	−	0.207214i
$204$	12.8796			0.901755
$205$	−2.71616	+	1.30803i	−0.189705	+	0.0913571i
$206$	7.17881	+	9.00194i	0.500171	+	0.627195i
$207$	−2.69716	+	3.38213i	−0.187466	+	0.235074i
$208$	−3.35874	+	1.61748i	−0.232886	+	0.112152i
$209$	6.51737	+	3.13860i	0.450816	+	0.217102i
$210$	11.5474	+	14.4800i	0.796848	+	0.999216i
$211$	2.22081	−	9.73000i	0.152887	−	0.669841i	−0.839151	−	0.543899i	$-0.816948\pi$
$211$	2.22081	−	9.73000i	0.152887	−	0.669841i	0.992038	−	0.125942i	$-0.0401953\pi$
$212$	−2.63900	+	11.5622i	−0.181247	+	0.794095i
$213$	0.186464	−	0.233818i	0.0127763	−	0.0160210i
$214$	−2.90529	−	12.7289i	−0.198601	−	0.870130i
$215$	8.59586			0.586233
$216$	0.137887	+	0.604122i	0.00938202	+	0.0411053i
$217$	4.12346	+	1.98575i	0.279919	+	0.134802i
$218$	30.6323	+	14.7517i	2.07468	+	0.999113i
$219$	−3.36159	−	14.7281i	−0.227155	−	0.995232i
$220$	16.2965			1.09871
$221$	−1.40285	−	6.14630i	−0.0943662	−	0.413445i
$222$	12.8757	−	16.1456i	0.864158	−	1.08362i
$223$	−1.71179	+	7.49983i	−0.114630	+	0.502226i	0.884718	+	0.466126i	$0.154351\pi$
$223$	−1.71179	+	7.49983i	−0.114630	+	0.502226i	−0.999348	+	0.0360999i	$0.988507\pi$
$224$	−8.50297	+	37.2540i	−0.568129	+	2.48913i
$225$	−0.877459	−	1.10030i	−0.0584973	−	0.0733533i
$226$	−5.13110	−	2.47101i	−0.341316	−	0.164369i
$227$	−5.94778	+	2.86430i	−0.394768	+	0.190110i	−0.620727	−	0.784027i	$-0.713163\pi$
$227$	−5.94778	+	2.86430i	−0.394768	+	0.190110i	0.225959	+	0.974137i	$0.427448\pi$
$228$	2.77225	−	3.47629i	0.183597	−	0.230223i
$229$	−1.45190	−	1.82062i	−0.0959441	−	0.120310i	0.731542	−	0.681797i	$-0.238801\pi$
$229$	−1.45190	−	1.82062i	−0.0959441	−	0.120310i	−0.827486	+	0.561487i	$0.810230\pi$
$230$	15.3170	−	7.37626i	1.00997	−	0.486376i
$231$	17.6256			1.15968
$232$	1.76293	+	2.83327i	0.115742	+	0.186013i
$233$	1.74843			0.114544			0.0572719	−	0.998359i	$-0.481760\pi$
$233$	1.74843			0.114544			0.0572719	+	0.998359i	$0.481760\pi$
$234$	2.10203	−	1.01228i	0.137414	−	0.0661750i
$235$	6.92675	+	8.68587i	0.451851	+	0.566604i
$236$	8.19648	−	10.2781i	0.533546	−	0.669045i
$237$	−12.4445	+	5.99297i	−0.808359	+	0.389285i
$238$	−49.3228	−	23.7526i	−3.19712	−	1.53965i
$239$	−14.2277	−	17.8409i	−0.920312	−	1.15403i	−0.987708	−	0.156308i	$-0.950041\pi$
$239$	−14.2277	−	17.8409i	−0.920312	−	1.15403i	0.0673967	−	0.997726i	$-0.478531\pi$
$240$	−1.39731	+	6.12203i	−0.0901962	+	0.395175i
$241$	−2.48695	+	10.8960i	−0.160199	+	0.701876i	0.829476	+	0.558542i	$0.188639\pi$
$241$	−2.48695	+	10.8960i	−0.160199	+	0.701876i	−0.989674	+	0.143333i	$0.954218\pi$
$242$	3.86229	−	4.84315i	0.248277	−	0.311330i
$243$	0.222521	+	0.974928i	0.0142747	+	0.0625417i
$244$	−24.0055			−1.53680
$245$	−6.41502	−	28.1060i	−0.409841	−	1.79563i
$246$	2.97115	+	1.43083i	0.189433	+	0.0912263i
$247$	−1.96088	−	0.944309i	−0.124768	−	0.0600850i
$248$	−0.133907	−	0.586687i	−0.00850313	−	0.0372546i
$249$	−2.91826			−0.184937
$250$	5.60317	+	24.5491i	0.354375	+	1.55262i
$251$	12.9264	−	16.2091i	0.815904	−	1.02311i	−0.183293	−	0.983058i	$-0.558676\pi$
$251$	12.9264	−	16.2091i	0.815904	−	1.02311i	0.999198	−	0.0400532i	$-0.0127527\pi$
$252$	2.41077	−	10.5623i	0.151864	−	0.665360i
$253$	3.60016	−	15.7733i	0.226340	−	0.991660i
$254$	−16.0449	−	20.1197i	−1.00675	−	1.26242i
$255$	−9.56772	−	4.60757i	−0.599154	−	0.288537i
$256$	−9.19680	+	4.42894i	−0.574800	+	0.276809i
$257$	1.47517	−	1.84981i	0.0920186	−	0.115388i	−0.733691	−	0.679484i	$-0.762204\pi$
$257$	1.47517	−	1.84981i	0.0920186	−	0.115388i	0.825709	+	0.564096i	$0.190775\pi$
$258$	−5.86256	−	7.35142i	−0.364987	−	0.457679i
$259$	−42.2906	+	20.3661i	−2.62781	+	1.26549i
$260$	−4.90313			−0.304079
$261$	2.84501	+	4.57230i	0.176102	+	0.283018i
$262$	39.2060			2.42215
$263$	22.0382	−	10.6131i	1.35894	−	0.654429i	0.394537	−	0.918880i	$-0.370905\pi$
$263$	22.0382	−	10.6131i	1.35894	−	0.654429i	0.964399	+	0.264451i	$0.0851908\pi$
$264$	−1.44496	−	1.81192i	−0.0889310	−	0.111516i
$265$	6.09666	−	7.64497i	0.374515	−	0.469627i
$266$	−17.0273	+	8.19994i	−1.04401	+	0.502770i
$267$	6.56353	+	3.16083i	0.401681	+	0.193440i
$268$	−5.68828	−	7.13288i	−0.347467	−	0.435710i
$269$	−1.44384	+	6.32587i	−0.0880324	+	0.385695i	−0.999680	−	0.0252765i	$-0.991953\pi$
$269$	−1.44384	+	6.32587i	−0.0880324	+	0.385695i	0.911648	+	0.410972i	$0.134811\pi$
$270$	0.874493	−	3.83140i	0.0532199	−	0.233172i
$271$	−0.298700	+	0.374558i	−0.0181447	+	0.0227528i	−0.790821	−	0.612047i	$-0.790346\pi$
$271$	−0.298700	+	0.374558i	−0.0181447	+	0.0227528i	0.772676	+	0.634800i	$0.218918\pi$
$272$	−4.13024	−	18.0958i	−0.250433	−	1.09722i
$273$	−5.30301			−0.320953
$274$	−4.07134	−	17.8377i	−0.245959	−	1.07761i
$275$	4.74221	+	2.28373i	0.285966	+	0.137714i
$276$	−8.95985	−	4.31484i	−0.539319	−	0.259723i
$277$	−0.926181	−	4.05787i	−0.0556488	−	0.243813i	0.939452	−	0.342681i	$-0.111335\pi$
$277$	−0.926181	−	4.05787i	−0.0556488	−	0.243813i	−0.995101	+	0.0988677i	$0.968478\pi$
$278$	21.4498			1.28648
$279$	−0.216099	−	0.946790i	−0.0129375	−	0.0566828i
$280$	−3.45113	+	4.32758i	−0.206244	+	0.258622i
$281$	2.07349	−	9.08457i	0.123694	−	0.541940i	−0.874667	−	0.484723i	$-0.838920\pi$
$281$	2.07349	−	9.08457i	0.123694	−	0.541940i	0.998362	−	0.0572168i	$-0.0182226\pi$
$282$	2.70420	−	11.8479i	0.161033	−	0.705532i
$283$	6.10026	+	7.64949i	0.362623	+	0.454715i	0.929355	−	0.369187i	$-0.120364\pi$
$283$	6.10026	+	7.64949i	0.362623	+	0.454715i	−0.566732	+	0.823902i	$0.691793\pi$
$284$	0.619425	+	0.298300i	0.0367561	+	0.0177008i
$285$	−3.30299	+	1.59064i	−0.195652	+	0.0942212i
$286$	−5.44040	+	6.82205i	−0.321698	+	0.403396i
$287$	−4.67345	−	5.86032i	−0.275865	−	0.345924i
$288$	7.30531	−	3.51805i	0.430470	−	0.207303i
$289$	14.3892			0.846424
$290$	−2.27707	−	21.0405i	−0.133714	−	1.23554i
$291$	12.8154			0.751254
$292$	31.2894	−	15.0682i	1.83107	−	0.881799i
$293$	−7.13649	−	8.94887i	−0.416918	−	0.522799i	0.528379	−	0.849008i	$-0.322800\pi$
$293$	−7.13649	−	8.94887i	−0.416918	−	0.522799i	−0.945297	+	0.326210i	$0.894228\pi$
$294$	−19.6619	+	24.6552i	−1.14670	+	1.43792i
$295$	−9.76569	+	4.70291i	−0.568580	+	0.273814i
$296$	5.56065	+	2.67787i	0.323206	+	0.155648i
$297$	−2.33186	−	2.92406i	−0.135308	−	0.169671i
$298$	−5.58271	+	24.4594i	−0.323398	+	1.41690i
$299$	−1.08318	+	4.74571i	−0.0626418	+	0.274452i
$300$	2.01716	−	2.52944i	0.116461	−	0.146037i
$301$	4.75579	+	20.8365i	0.274119	+	1.20099i
$302$	19.7812			1.13828
$303$	−2.10344	−	9.21577i	−0.120839	−	0.529432i
$304$	−5.77316	−	2.78021i	−0.331114	−	0.159456i
$305$	17.8326	+	8.58775i	1.02109	+	0.491733i
$306$	2.58487	+	11.3250i	0.147767	+	0.647409i
$307$	−20.1309			−1.14893			−0.574465	−	0.818529i	$-0.694790\pi$
$307$	−20.1309			−1.14893			−0.574465	+	0.818529i	$0.694790\pi$
$308$	9.01630	+	39.5030i	0.513751	+	2.25089i
$309$	−3.46239	+	4.34170i	−0.196968	+	0.246990i
$310$	−0.849253	+	3.72082i	−0.0482344	+	0.211329i
$311$	−0.395288	+	1.73187i	−0.0224147	+	0.0982054i	−0.984898	−	0.173136i	$-0.944610\pi$
$311$	−0.395288	+	1.73187i	−0.0224147	+	0.0982054i	0.962483	+	0.271341i	$0.0874672\pi$
$312$	0.434744	+	0.545151i	0.0246125	+	0.0308631i
$313$	13.4354	+	6.47017i	0.759416	+	0.365716i	0.773177	−	0.634190i	$-0.218666\pi$
$313$	13.4354	+	6.47017i	0.759416	+	0.365716i	−0.0137612	+	0.999905i	$0.504380\pi$
$314$	−1.66164	+	0.800203i	−0.0937717	+	0.0451581i
$315$	−5.56940	+	6.98381i	−0.313800	+	0.393493i
$316$	−19.7976	−	24.8253i	−1.11370	−	1.39653i
$317$	10.2900	−	4.95542i	0.577946	−	0.278324i	−0.121988	−	0.992532i	$-0.538927\pi$
$317$	10.2900	−	4.95542i	0.577946	−	0.278324i	0.699934	+	0.714208i	$0.253213\pi$
$318$	−10.6962			−0.599815
$319$	−17.0063	−	10.7903i	−0.952168	−	0.604141i
$320$	−19.3061			−1.07924
$321$	5.67350	−	2.73221i	0.316664	−	0.152497i
$322$	26.3545	+	33.0475i	1.46868	+	1.84166i
$323$	6.75630	−	8.47213i	0.375931	−	0.471402i
$324$	−2.07121	+	0.997440i	−0.115067	+	0.0554133i
$325$	−1.42679	−	0.687104i	−0.0791438	−	0.0381137i
$326$	9.97016	+	12.5022i	0.552196	+	0.692432i
$327$	−3.64891	+	15.9869i	−0.201785	+	0.884079i
$328$	−0.219311	+	0.960865i	−0.0121094	+	0.0530549i
$329$	−17.2223	+	21.5961i	−0.949498	+	1.19063i
$330$	3.27061	+	14.3295i	0.180041	+	0.788813i
$331$	9.83216			0.540424			0.270212	−	0.962801i	$-0.412906\pi$
$331$	9.83216			0.540424			0.270212	+	0.962801i	$0.412906\pi$
$332$	−1.49282	−	6.54049i	−0.0819294	−	0.358956i
$333$	8.97373	+	4.32152i	0.491757	+	0.236818i
$334$	−15.6706	−	7.54655i	−0.857456	−	0.412929i
$335$	1.67385	+	7.33363i	0.0914524	+	0.400679i
$336$	−15.6130			−0.851757
$337$	3.33880	+	14.6283i	0.181876	+	0.796852i	0.980737	+	0.195335i	$0.0625795\pi$
$337$	3.33880	+	14.6283i	0.181876	+	0.796852i	−0.798860	+	0.601517i	$0.794563\pi$
$338$	−15.1686	+	19.0208i	−0.825062	+	1.03459i
$339$	0.611216	−	2.67791i	0.0331967	−	0.145444i
$340$	5.43229	−	23.8004i	0.294607	−	1.29076i
$341$	2.26456	+	2.83967i	0.122633	+	0.153777i
$342$	3.61307	+	1.73996i	0.195372	+	0.0940864i
$343$	34.8582	−	16.7868i	1.88216	−	0.906403i
$344$	1.75212	−	2.19708i	0.0944678	−	0.118459i
$345$	5.11228	+	6.41060i	0.275236	+	0.345135i
$346$	6.57897	−	3.16826i	0.353687	−	0.170327i
$347$	33.4677			1.79664			0.898320	−	0.439341i	$-0.144788\pi$
$347$	33.4677			1.79664			0.898320	+	0.439341i	$0.144788\pi$
$348$	−8.79222	+	8.71525i	−0.471312	+	0.467187i
$349$	27.7844			1.48727			0.743633	−	0.668588i	$-0.233101\pi$
$349$	27.7844			1.48727			0.743633	+	0.668588i	$0.233101\pi$
$350$	−12.3895	+	5.96649i	−0.662249	+	0.318922i
$351$	0.701586	+	0.879761i	0.0374479	+	0.0469582i
$352$	−18.9074	+	23.7091i	−1.00777	+	1.26370i
$353$	−12.3781	+	5.96096i	−0.658817	+	0.317270i	−0.733253	−	0.679956i	$-0.761999\pi$
$353$	−12.3781	+	5.96096i	−0.658817	+	0.317270i	0.0744354	+	0.997226i	$0.476285\pi$
$354$	10.6825	+	5.14440i	0.567766	+	0.273422i
$355$	−0.353430	−	0.443187i	−0.0187581	−	0.0235219i
$356$	−3.72659	+	16.3273i	−0.197509	+	0.865343i
$357$	5.87532	−	25.7415i	0.310955	−	1.36238i
$358$	9.22408	−	11.5666i	0.487508	−	0.611315i
$359$	5.47410	+	23.9836i	0.288912	+	1.26581i	0.886021	+	0.463646i	$0.153459\pi$
$359$	5.47410	+	23.9836i	0.288912	+	1.26581i	−0.597109	+	0.802160i	$0.703684\pi$
$360$	1.17452			0.0619027
$361$	3.39546	+	14.8765i	0.178709	+	0.782974i
$362$	−39.3793	−	18.9641i	−2.06973	−	0.996730i
$363$	2.69183	+	1.29632i	0.141285	+	0.0680390i
$364$	−2.71273	−	11.8852i	−0.142186	−	0.622956i
$365$	−28.6340			−1.49877
$366$	−4.81776	−	21.1080i	−0.251828	−	1.10333i
$367$	−2.76423	+	3.46624i	−0.144292	+	0.180936i	−0.848726	−	0.528834i	$-0.822630\pi$
$367$	−2.76423	+	3.46624i	−0.144292	+	0.180936i	0.704434	+	0.709770i	$0.251201\pi$
$368$	−3.18906	+	13.9722i	−0.166241	+	0.728351i
$369$	−0.353923	+	1.55064i	−0.0184245	+	0.0807229i
$370$	−24.4049	−	30.6028i	−1.26875	−	1.59097i
$371$	21.9046	+	10.5487i	1.13723	+	0.547661i
$372$	2.01143	−	0.968653i	0.104288	−	0.0502223i
$373$	15.1984	−	19.0582i	0.786944	−	0.986797i	−0.213008	−	0.977050i	$-0.568326\pi$
$373$	15.1984	−	19.0582i	0.786944	−	0.986797i	0.999953	−	0.00974631i	$-0.00310239\pi$
$374$	−27.0875	−	33.9667i	−1.40066	−	1.75638i
$375$	−10.9420	+	5.26938i	−0.565041	+	0.272109i
$376$	3.63199			0.187305
$377$	5.11666	+	3.24647i	0.263522	+	0.167202i
$378$	9.77119			0.502576
$379$	−12.1680	+	5.85978i	−0.625027	+	0.300997i	−0.719460	−	0.694534i	$-0.755610\pi$
$379$	−12.1680	+	5.85978i	−0.625027	+	0.300997i	0.0944331	+	0.995531i	$0.469896\pi$
$380$	−5.25461	−	6.58908i	−0.269556	−	0.338012i
$381$	7.73857	−	9.70387i	0.396459	−	0.497144i
$382$	25.8070	−	12.4280i	1.32040	−	0.635873i
$383$	−22.2743	−	10.7267i	−1.13816	−	0.548111i	−0.232707	−	0.972547i	$-0.574758\pi$
$383$	−22.2743	−	10.7267i	−1.13816	−	0.548111i	−0.905458	+	0.424436i	$0.860472\pi$
$384$	3.05630	+	3.83248i	0.155966	+	0.195575i
$385$	7.43401	−	32.5705i	0.378872	−	1.65995i
$386$	−1.95296	+	8.55650i	−0.0994033	+	0.435514i
$387$	2.82755	−	3.54564i	0.143732	−	0.180235i
$388$	6.55568	+	28.7223i	0.332814	+	1.45815i
$389$	30.2883			1.53568			0.767839	−	0.640643i	$-0.221332\pi$
$389$	30.2883			1.53568			0.767839	+	0.640643i	$0.221332\pi$
$390$	−0.984028	−	4.31131i	−0.0498282	−	0.218312i
$391$	−21.8362	−	10.5158i	−1.10430	−	0.531805i
$392$	−8.49144	−	4.08926i	−0.428882	−	0.206539i
$393$	4.20771	+	18.4352i	0.212251	+	0.929933i
$394$	9.56814			0.482036
$395$	5.82570	+	25.5240i	0.293123	+	1.28425i
$396$	5.36063	−	6.72202i	0.269382	−	0.337794i
$397$	3.02597	−	13.2577i	0.151869	−	0.665383i	−0.840472	−	0.541855i	$-0.817722\pi$
$397$	3.02597	−	13.2577i	0.151869	−	0.665383i	0.992341	−	0.123528i	$-0.0394208\pi$
$398$	1.76519	−	7.73381i	0.0884810	−	0.387661i
$399$	−5.68316	−	7.12645i	−0.284514	−	0.356769i
$400$	−4.20070	−	2.02295i	−0.210035	−	0.101148i
$401$	13.4305	−	6.46779i	0.670687	−	0.322986i	−0.0673661	−	0.997728i	$-0.521460\pi$
$401$	13.4305	−	6.46779i	0.670687	−	0.322986i	0.738053	+	0.674742i	$0.235745\pi$
$402$	5.13032	−	6.43322i	0.255877	−	0.320860i
$403$	−0.681337	−	0.854370i	−0.0339398	−	0.0425592i
$404$	19.5786	−	9.42857i	0.974073	−	0.469089i
$405$	1.89543			0.0941848
$406$	49.7426	−	17.1606i	2.46868	−	0.851667i
$407$	−37.2509			−1.84646
$408$	−3.12790	+	1.50632i	−0.154854	+	0.0745737i
$409$	−12.8458	−	16.1081i	−0.635182	−	0.796494i	0.355209	−	0.934787i	$-0.384410\pi$
$409$	−12.8458	−	16.1081i	−0.635182	−	0.796494i	−0.990391	+	0.138293i	$0.955838\pi$
$410$	3.89720	−	4.88693i	0.192469	−	0.241348i
$411$	7.95059	−	3.82880i	0.392174	−	0.188861i
$412$	−11.5019	−	5.53902i	−0.566658	−	0.272888i
$413$	−16.8029	−	21.0702i	−0.826818	−	1.03680i
$414$	1.99584	−	8.74433i	0.0980900	−	0.429761i
$415$	−1.23085	+	5.39269i	−0.0604198	+	0.264717i
$416$	5.68866	−	7.13335i	0.278909	−	0.349741i
$417$	2.30207	+	10.0860i	0.112733	+	0.493914i
$418$	−14.9982			−0.733587
$419$	1.19222	+	5.22348i	0.0582440	+	0.255184i	0.995665	−	0.0930153i	$-0.0296505\pi$
$419$	1.19222	+	5.22348i	0.0582440	+	0.255184i	−0.937421	+	0.348199i	$0.886793\pi$
$420$	−18.5013	−	8.90976i	−0.902771	−	0.434752i
$421$	−1.72756	−	0.831947i	−0.0841959	−	0.0405466i	0.391312	−	0.920258i	$-0.372021\pi$
$421$	−1.72756	−	0.831947i	−0.0841959	−	0.0405466i	−0.475508	+	0.879712i	$0.657736\pi$
$422$	4.60456	+	20.1739i	0.224146	+	0.982049i
$423$	5.86127			0.284985
$424$	−0.711341	−	3.11659i	−0.0345458	−	0.151355i
$425$	4.91606	−	6.16454i	0.238464	−	0.299024i
$426$	−0.137979	+	0.604526i	−0.00668511	+	0.0292894i
$427$	−10.9506	+	47.9779i	−0.529938	+	2.32181i
$428$	9.02577	+	11.3180i	0.436277	+	0.547074i
$429$	−3.79170	−	1.82599i	−0.183065	−	0.0881596i
$430$	−16.0574	+	7.73285i	−0.774358	+	0.372911i
$431$	−12.6219	+	15.8273i	−0.607975	+	0.762377i	−0.986597	−	0.163175i	$-0.947827\pi$
$431$	−12.6219	+	15.8273i	−0.607975	+	0.762377i	0.378622	+	0.925551i	$0.376398\pi$
$432$	2.06559	+	2.59017i	0.0993807	+	0.124620i
$433$	16.3972	−	7.89648i	0.788000	−	0.379481i	0.00380279	−	0.999993i	$-0.498790\pi$
$433$	16.3972	−	7.89648i	0.788000	−	0.379481i	0.784197	+	0.620512i	$0.213075\pi$
$434$	−9.48918			−0.455495
$435$	9.64915	−	3.32884i	0.462641	−	0.159606i
$436$	−37.6969			−1.80536
$437$	−7.53835	+	3.63028i	−0.360608	+	0.173660i
$438$	19.5290	+	24.4886i	0.933132	+	1.17011i
$439$	−0.244431	+	0.306507i	−0.0116661	+	0.0146288i	−0.787630	−	0.616148i	$-0.788692\pi$
$439$	−0.244431	+	0.306507i	−0.0116661	+	0.0146288i	0.775964	+	0.630777i	$0.217264\pi$
$440$	−3.95771	+	1.90593i	−0.188676	+	0.0908618i
$441$	−13.7034	−	6.59921i	−0.652543	−	0.314248i
$442$	8.14982	+	10.2195i	0.387647	+	0.486094i
$443$	−1.21378	+	5.31793i	−0.0576685	+	0.252662i	−0.995543	−	0.0943137i	$-0.969934\pi$
$443$	−1.21378	+	5.31793i	−0.0576685	+	0.252662i	0.937874	+	0.346976i	$0.112791\pi$
$444$	−5.09504	+	22.3228i	−0.241800	+	1.05939i
$445$	8.60925	−	10.7957i	0.408117	−	0.511763i
$446$	−3.54917	−	15.5499i	−0.168058	−	0.736310i
$447$	−12.1003			−0.572326
$448$	−10.6814	−	46.7982i	−0.504648	−	2.21101i
$449$	−2.50192	−	1.20486i	−0.118073	−	0.0568608i	0.373915	−	0.927463i	$-0.378015\pi$
$449$	−2.50192	−	1.20486i	−0.118073	−	0.0568608i	−0.491988	+	0.870602i	$0.663729\pi$
$450$	2.62896	+	1.26604i	0.123930	+	0.0596818i
$451$	−1.32368	−	5.79940i	−0.0623295	−	0.273083i
$452$	6.31448			0.297008
$453$	2.12298	+	9.30139i	0.0997464	+	0.437017i
$454$	8.53397	−	10.7013i	0.400519	−	0.502235i
$455$	−2.23667	+	9.79948i	−0.104857	+	0.459407i
$456$	−0.266694	+	1.16846i	−0.0124891	+	0.0547182i
$457$	−22.7119	−	28.4798i	−1.06242	−	1.33223i	−0.940539	−	0.339686i	$-0.889679\pi$
$457$	−22.7119	−	28.4798i	−1.06242	−	1.33223i	−0.121880	−	0.992545i	$-0.538892\pi$
$458$	4.35004	+	2.09487i	0.203264	+	0.0978868i
$459$	−5.04777	+	2.43088i	−0.235610	+	0.113464i
$460$	−11.7525	+	14.7371i	−0.547961	+	0.687121i
$461$	15.8091	+	19.8240i	0.736304	+	0.923296i	0.999137	−	0.0415457i	$-0.0132282\pi$
$461$	15.8091	+	19.8240i	0.736304	+	0.923296i	−0.262833	+	0.964841i	$0.584657\pi$
$462$	−32.9254	+	15.8560i	−1.53183	+	0.737689i
$463$	28.4073			1.32020			0.660099	−	0.751179i	$-0.270514\pi$
$463$	28.4073			1.32020			0.660099	+	0.751179i	$0.270514\pi$
$464$	15.0643	+	9.55818i	0.699345	+	0.443727i
$465$	−1.84073			−0.0853617
$466$	−3.26615	+	1.57289i	−0.151301	+	0.0728629i
$467$	−8.27602	−	10.3778i	−0.382968	−	0.480227i	0.552563	−	0.833471i	$-0.313650\pi$
$467$	−8.27602	−	10.3778i	−0.382968	−	0.480227i	−0.935531	+	0.353244i	$0.885079\pi$
$468$	−1.61285	+	2.02245i	−0.0745541	+	0.0934879i
$469$	−16.8507	+	8.11489i	−0.778095	+	0.374711i
$470$	−20.7533	−	9.99425i	−0.957277	−	0.461001i
$471$	−0.554599	−	0.695445i	−0.0255546	−	0.0320444i
$472$	−0.788511	+	3.45469i	−0.0362942	+	0.159015i
$473$	−3.77420	+	16.5359i	−0.173538	+	0.760320i
$474$	17.8556	−	22.3902i	0.820136	−	1.02842i
$475$	−0.605700	−	2.65375i	−0.0277914	−	0.121762i
$476$	60.6980			2.78209
$477$	−1.14796	−	5.02952i	−0.0525613	−	0.230286i
$478$	42.6276	+	20.5284i	1.94974	+	0.938947i
$479$	−23.6592	−	11.3937i	−1.08101	−	0.520589i	−0.193374	−	0.981125i	$-0.561943\pi$
$479$	−23.6592	−	11.3937i	−1.08101	−	0.520589i	−0.887641	+	0.460536i	$0.847657\pi$
$480$	−3.41986	−	14.9834i	−0.156095	−	0.683895i
$481$	11.2077			0.511025
$482$	−5.15637	−	22.5915i	−0.234866	−	1.02902i
$483$	−12.7109	+	15.9390i	−0.578367	+	0.725250i
$484$	−1.52835	+	6.69613i	−0.0694704	+	0.304370i
$485$	5.40521	−	23.6818i	0.245438	−	1.07533i
$486$	−1.29273	−	1.62103i	−0.0586392	−	0.0735312i
$487$	−8.31764	−	4.00556i	−0.376908	−	0.181509i	0.235832	−	0.971794i	$-0.424219\pi$
$487$	−8.31764	−	4.00556i	−0.376908	−	0.181509i	−0.612740	+	0.790284i	$0.709933\pi$
$488$	5.82988	−	2.80752i	0.263906	−	0.127091i
$489$	−4.80867	+	6.02988i	−0.217456	+	0.272681i
$490$	37.2678	+	46.7323i	1.68359	+	2.11115i
$491$	10.9181	−	5.25786i	0.492725	−	0.237284i	−0.170985	−	0.985274i	$-0.554695\pi$
$491$	10.9181	−	5.25786i	0.492725	−	0.237284i	0.663710	+	0.747990i	$0.268981\pi$
$492$	−3.65638			−0.164842
$493$	−21.4277	+	21.2401i	−0.965054	+	0.956606i
$494$	4.51251			0.203027
$495$	−6.38692	+	3.07578i	−0.287071	+	0.138246i
$496$	−2.00597	−	2.51541i	−0.0900709	−	0.112945i
$497$	0.878751	−	1.10192i	0.0394174	−	0.0494278i
$498$	5.45144	−	2.62527i	0.244285	−	0.117641i
$499$	26.6604	+	12.8390i	1.19348	+	0.574750i	0.921811	−	0.387640i	$-0.126710\pi$
$499$	26.6604	+	12.8390i	1.19348	+	0.574750i	0.271671	+	0.962390i	$0.412424\pi$
$500$	−17.4072	−	21.8279i	−0.778473	−	0.976175i
$501$	1.86668	−	8.17845i	0.0833970	−	0.365386i
$502$	−9.56521	+	41.9079i	−0.426916	+	1.87044i
$503$	−5.59719	+	7.01866i	−0.249567	+	0.312947i	−0.890797	−	0.454402i	$-0.849853\pi$
$503$	−5.59719	+	7.01866i	−0.249567	+	0.312947i	0.641230	+	0.767349i	$0.278424\pi$
$504$	0.649822	+	2.84705i	0.0289454	+	0.126818i
$505$	−17.9171			−0.797300
$506$	7.46446	+	32.7039i	0.331836	+	1.45387i
$507$	−10.5718	−	5.09110i	−0.469510	−	0.226104i
$508$	25.7072	+	12.3799i	1.14057	+	0.549271i
$509$	−6.60071	−	28.9196i	−0.292572	−	1.28184i	−0.880933	−	0.473241i	$-0.843084\pi$
$509$	−6.60071	−	28.9196i	−0.292572	−	1.28184i	0.588361	−	0.808598i	$-0.299773\pi$
$510$	22.0179			0.974968
$511$	−15.8422	−	69.4092i	−0.700818	−	3.07048i
$512$	19.3083	−	24.2119i	0.853315	−	1.07002i
$513$	−0.430388	+	1.88565i	−0.0190021	+	0.0832536i
$514$	−1.09159	+	4.78258i	−0.0481481	+	0.210951i
$515$	6.56272	+	8.22939i	0.289188	+	0.362630i
$516$	9.39300	+	4.52343i	0.413504	+	0.199133i
$517$	−19.7503	+	9.51127i	−0.868619	+	0.418305i
$518$	60.6793	−	76.0894i	2.66609	−	3.34318i
$519$	2.19584	+	2.75349i	0.0963866	+	0.120865i
$520$	1.19075	−	0.573437i	0.0522180	−	0.0251469i
$521$	−23.8067			−1.04299			−0.521496	−	0.853254i	$-0.674626\pi$
$521$	−23.8067			−1.04299			−0.521496	+	0.853254i	$0.674626\pi$
$522$	−9.42784	−	5.98188i	−0.412646	−	0.261820i
$523$	9.45221			0.413316			0.206658	−	0.978413i	$-0.433741\pi$
$523$	9.45221			0.413316			0.206658	+	0.978413i	$0.433741\pi$
$524$	−39.1651	+	18.8609i	−1.71093	+	0.823942i
$525$	−4.13521	−	5.18539i	−0.180475	−	0.226309i
$526$	−31.6208	+	39.6513i	−1.37873	+	1.72888i
$527$	4.90209	−	2.36072i	0.213538	−	0.102835i
$528$	−11.1634	−	5.37603i	−0.485826	−	0.233962i
$529$	−2.67260	−	3.35133i	−0.116200	−	0.145710i
$530$	−4.51139	+	19.7657i	−0.195962	+	0.858567i
$531$	−1.27249	+	5.57516i	−0.0552215	+	0.241941i
$532$	13.0648	−	16.3828i	0.566431	−	0.710282i
$533$	0.398254	+	1.74486i	0.0172503	+	0.0755784i
$534$	−15.1044			−0.653633
$535$	−2.65596	−	11.6365i	−0.114827	−	0.503090i
$536$	2.21565	+	1.06700i	0.0957014	+	0.0460874i
$537$	6.42875	+	3.09592i	0.277421	+	0.133599i
$538$	−2.99361	−	13.1159i	−0.129064	−	0.565466i
$539$	56.8843			2.45018
$540$	0.969600	+	4.24810i	0.0417250	+	0.182809i
$541$	−14.3377	+	17.9789i	−0.616426	+	0.772973i	−0.987837	−	0.155495i	$-0.950303\pi$
$541$	−14.3377	+	17.9789i	−0.616426	+	0.772973i	0.371411	+	0.928469i	$0.378874\pi$
$542$	0.221031	−	0.968400i	0.00949410	−	0.0415964i
$543$	4.69086	−	20.5520i	0.201304	−	0.881971i
$544$	28.3236	+	35.5167i	1.21436	+	1.52277i
$545$	28.0034	+	13.4857i	1.19953	+	0.577665i
$546$	9.90624	−	4.77059i	0.423948	−	0.204163i
$547$	2.80622	−	3.51888i	0.119985	−	0.150457i	−0.718211	−	0.695825i	$-0.755039\pi$
$547$	2.80622	−	3.51888i	0.119985	−	0.150457i	0.838196	+	0.545369i	$0.183610\pi$
$548$	12.6483	+	15.8605i	0.540309	+	0.677526i
$549$	9.40822	−	4.53076i	0.401533	−	0.193368i
$550$	−10.9131			−0.465336
$551$	1.12068	+	10.3552i	0.0477425	+	0.441148i
$552$	2.68059			0.114093
$553$	−58.6474	+	28.2431i	−2.49394	+	1.20102i
$554$	5.38061	+	6.74707i	0.228600	+	0.286656i
$555$	11.7707	−	14.7599i	0.499637	−	0.626525i
$556$	−21.4275	+	10.3189i	−0.908726	+	0.437620i
$557$	12.4667	+	6.00364i	0.528231	+	0.254382i	0.678938	−	0.734196i	$-0.262441\pi$
$557$	12.4667	+	6.00364i	0.528231	+	0.254382i	−0.150707	+	0.988578i	$0.548155\pi$
$558$	1.25542	+	1.57424i	0.0531460	+	0.0666429i
$559$	1.13554	−	4.97514i	0.0480283	−	0.210426i
$560$	−6.58514	+	28.8514i	−0.278273	+	1.21919i
$561$	13.0645	−	16.3824i	0.551584	−	0.691664i
$562$	4.29912	+	18.8357i	0.181348	+	0.794536i
$563$	−29.6777			−1.25077			−0.625384	−	0.780317i	$-0.715058\pi$
$563$	−29.6777			−1.25077			−0.625384	+	0.780317i	$0.715058\pi$
$564$	2.99831	+	13.1364i	0.126252	+	0.553144i
$565$	−4.69075	−	2.25895i	−0.197341	−	0.0950346i
$566$	−18.2770	−	8.80176i	−0.768241	−	0.369966i
$567$	1.04868	+	4.59455i	0.0440403	+	0.192953i
$568$	−0.185318			−0.00777578
$569$	−2.34470	−	10.2728i	−0.0982950	−	0.430658i	0.901704	−	0.432355i	$-0.142317\pi$
$569$	−2.34470	−	10.2728i	−0.0982950	−	0.430658i	−0.999999	+	0.00169638i	$0.999460\pi$
$570$	4.73919	−	5.94276i	0.198503	−	0.248915i
$571$	7.76939	−	34.0399i	0.325139	−	1.42453i	−0.503137	−	0.864207i	$-0.667821\pi$
$571$	7.76939	−	34.0399i	0.325139	−	1.42453i	0.828276	−	0.560320i	$-0.189322\pi$
$572$	2.15283	−	9.43215i	0.0900142	−	0.394378i
$573$	8.61352	+	10.8010i	0.359835	+	0.451219i
$574$	14.0022	+	6.74308i	0.584439	+	0.281451i
$575$	−5.48510	+	2.64149i	−0.228745	+	0.110158i
$576$	−6.35061	+	7.96341i	−0.264609	+	0.331809i
$577$	−5.20425	−	6.52592i	−0.216656	−	0.271678i	0.661613	−	0.749846i	$-0.269872\pi$
$577$	−5.20425	−	6.52592i	−0.216656	−	0.271678i	−0.878268	+	0.478168i	$0.841301\pi$
$578$	−26.8796	+	12.9446i	−1.11805	+	0.538422i
$579$	−4.23298			−0.175917
$580$	12.3967	+	19.9231i	0.514744	+	0.827261i
$581$	−13.7529			−0.570568
$582$	−23.9398	+	11.5288i	−0.992335	+	0.477883i
$583$	12.0298	+	15.0848i	0.498222	+	0.624750i
$584$	−5.83655	+	7.31880i	−0.241518	+	0.302854i
$585$	1.92163	−	0.925408i	0.0794496	−	0.0382609i
$586$	21.3817	+	10.2969i	0.883269	+	0.425360i
$587$	−10.5208	−	13.1927i	−0.434240	−	0.544520i	0.515775	−	0.856724i	$-0.327504\pi$
$587$	−10.5208	−	13.1927i	−0.434240	−	0.544520i	−0.950015	+	0.312204i	$0.898933\pi$
$588$	7.78042	−	34.0883i	0.320859	−	1.40578i
$589$	0.417967	−	1.83123i	0.0172220	−	0.0754546i
$590$	14.0120	−	17.5705i	0.576864	−	0.723364i
$591$	1.02688	+	4.49907i	0.0422404	+	0.185067i
$592$	32.9973			1.35618
$593$	6.25458	+	27.4031i	0.256845	+	1.12531i	0.924603	+	0.380932i	$0.124397\pi$
$593$	6.25458	+	27.4031i	0.256845	+	1.12531i	−0.667758	+	0.744378i	$0.732746\pi$
$594$	6.98651	+	3.36452i	0.286660	+	0.138048i
$595$	−45.0899	−	21.7141i	−1.84850	−	0.890193i
$596$	−6.18987	−	27.1196i	−0.253547	−	1.11086i
$597$	3.82599			0.156587
$598$	−2.24583	−	9.83962i	−0.0918387	−	0.402372i
$599$	−11.2525	+	14.1101i	−0.459763	+	0.576525i	−0.956631	−	0.291301i	$-0.905912\pi$
$599$	−11.2525	+	14.1101i	−0.459763	+	0.576525i	0.496868	+	0.867826i	$0.334483\pi$
$600$	−0.194053	+	0.850203i	−0.00792219	+	0.0347094i
$601$	3.54163	−	15.5169i	0.144466	−	0.632947i	−0.849900	−	0.526944i	$-0.823338\pi$
$601$	3.54163	−	15.5169i	0.144466	−	0.632947i	0.994366	−	0.106003i	$-0.0338053\pi$
$602$	−27.6285	−	34.6451i	−1.12606	−	1.41203i
$603$	3.57559	+	1.72191i	0.145609	+	0.0701218i
$604$	−19.7605	+	9.51617i	−0.804045	+	0.387208i
$605$	3.53082	−	4.42751i	0.143548	−	0.180004i
$606$	12.2198	+	15.3232i	0.496397	+	0.622462i
$607$	31.9807	−	15.4011i	1.29806	−	0.625112i	0.348091	−	0.937461i	$-0.386830\pi$
$607$	31.9807	−	15.4011i	1.29806	−	0.625112i	0.949967	+	0.312349i	$0.101116\pi$
$608$	15.6826			0.636014
$609$	13.4077	+	21.5479i	0.543307	+	0.873166i
$610$	−41.0377			−1.66157
$611$	5.94228	−	2.86165i	0.240399	−	0.115770i
$612$	−8.03032	−	10.0697i	−0.324607	−	0.407044i
$613$	−17.6983	+	22.1929i	−0.714826	+	0.896364i	−0.998033	−	0.0626951i	$-0.980030\pi$
$613$	−17.6983	+	22.1929i	−0.714826	+	0.896364i	0.283206	+	0.959059i	$0.408602\pi$
$614$	37.6053	−	18.1098i	1.51763	−	0.730851i
$615$	2.71616	+	1.30803i	0.109526	+	0.0527450i
$616$	−6.80967	−	8.53905i	−0.274369	−	0.344048i
$617$	−6.85060	+	30.0144i	−0.275795	+	1.20833i	0.627260	+	0.778810i	$0.284176\pi$
$617$	−6.85060	+	30.0144i	−0.275795	+	1.20833i	−0.903055	+	0.429525i	$0.858681\pi$
$618$	2.56209	−	11.2252i	0.103062	−	0.451545i
$619$	1.19253	−	1.49539i	0.0479319	−	0.0601047i	−0.757288	−	0.653081i	$-0.773476\pi$
$619$	1.19253	−	1.49539i	0.0479319	−	0.0601047i	0.805220	+	0.592977i	$0.202047\pi$
$620$	−0.941616	−	4.12549i	−0.0378162	−	0.165684i
$621$	4.32591			0.173593
$622$	−0.819579	−	3.59081i	−0.0328621	−	0.143978i
$623$	30.9320	+	14.8961i	1.23926	+	0.596798i
$624$	3.35874	+	1.61748i	0.134457	+	0.0647511i
$625$	3.55649	+	15.5820i	0.142260	+	0.623280i
$626$	−30.9186			−1.23575
$627$	−1.60966	−	7.05237i	−0.0642835	−	0.281645i
$628$	1.27495	−	1.59874i	0.0508760	−	0.0637965i
$629$	−12.4172	+	54.4034i	−0.495107	+	2.16920i
$630$	4.12123	−	18.0563i	0.164194	−	0.719380i
$631$	3.99885	+	5.01440i	0.159192	+	0.199620i	0.855030	−	0.518578i	$-0.173539\pi$
$631$	3.99885	+	5.01440i	0.159192	+	0.199620i	−0.695839	+	0.718198i	$0.744967\pi$
$632$	7.71136	+	3.71359i	0.306741	+	0.147719i
$633$	−8.99187	+	4.33026i	−0.357395	+	0.172112i
$634$	−14.7643	+	18.5139i	−0.586366	+	0.735279i
$635$	−14.6679	−	18.3930i	−0.582080	−	0.729905i
$636$	10.6851	−	5.14566i	0.423691	−	0.204039i
$637$	−17.1147			−0.678111
$638$	41.4754	+	4.85789i	1.64203	+	0.192326i
$639$	−0.299065			−0.0118308
$640$	8.37114	−	4.03133i	0.330898	−	0.159352i
$641$	−17.9604	−	22.5217i	−0.709395	−	0.889553i	0.288291	−	0.957543i	$-0.406913\pi$
$641$	−17.9604	−	22.5217i	−0.709395	−	0.889553i	−0.997686	+	0.0679897i	$0.978341\pi$
$642$	−8.14044	+	10.2078i	−0.321277	+	0.402869i
$643$	−2.76235	+	1.33028i	−0.108936	+	0.0524610i	−0.487558	−	0.873090i	$-0.662112\pi$
$643$	−2.76235	+	1.33028i	−0.108936	+	0.0524610i	0.378622	+	0.925551i	$0.376398\pi$
$644$	−42.2252	−	20.3346i	−1.66390	−	0.801294i
$645$	−5.35943	−	6.72051i	−0.211027	−	0.264620i
$646$	−4.99951	+	21.9043i	−0.196703	+	0.861812i
$647$	10.1603	−	44.5151i	0.399442	−	1.75007i	−0.230162	−	0.973152i	$-0.573926\pi$
$647$	10.1603	−	44.5151i	0.399442	−	1.75007i	0.629604	−	0.776917i	$-0.283217\pi$
$648$	0.386351	−	0.484469i	0.0151773	−	0.0190317i
$649$	−4.75914	−	20.8512i	−0.186813	−	0.818480i
$650$	3.28342			0.128786
$651$	−1.01841	−	4.46195i	−0.0399146	−	0.174877i
$652$	−15.9742	−	7.69277i	−0.625598	−	0.301272i
$653$	11.5433	+	5.55897i	0.451725	+	0.217539i	0.645891	−	0.763429i	$-0.276486\pi$
$653$	11.5433	+	5.55897i	0.451725	+	0.217539i	−0.194166	+	0.980969i	$0.562200\pi$
$654$	−7.56554	−	33.1468i	−0.295836	−	1.29614i
$655$	35.8413			1.40044
$656$	1.17253	+	5.13718i	0.0457795	+	0.200573i
$657$	−9.41897	+	11.8110i	−0.367469	+	0.460792i
$658$	12.7441	−	55.8357i	0.496818	−	2.17670i
$659$	−5.61559	+	24.6035i	−0.218752	+	0.958416i	0.739649	+	0.672993i	$0.234991\pi$
$659$	−5.61559	+	24.6035i	−0.218752	+	0.958416i	−0.958401	+	0.285424i	$0.907866\pi$
$660$	−10.1607	−	12.7411i	−0.395506	−	0.495948i
$661$	14.6652	+	7.06237i	0.570409	+	0.274694i	0.696776	−	0.717289i	$-0.254617\pi$
$661$	14.6652	+	7.06237i	0.570409	+	0.274694i	−0.126367	+	0.991984i	$0.540332\pi$
$662$	−18.3669	+	8.84503i	−0.713849	+	0.343772i
$663$	−3.93071	+	4.92895i	−0.152656	+	0.191425i
$664$	1.12747	+	1.41381i	0.0437544	+	0.0548663i
$665$	−15.5660	+	7.49621i	−0.603625	+	0.290691i
$666$	−20.6510			−0.800208
$667$	22.0221	−	7.59736i	0.852698	−	0.294171i
$668$	19.2847			0.746146
$669$	6.93088	−	3.33774i	0.267963	−	0.129044i
$670$	−9.72418	−	12.1937i	−0.375678	−	0.471085i
$671$	−24.3501	+	30.5340i	−0.940024	+	1.17875i
$672$	34.4278	−	16.5796i	1.32808	−	0.639571i
$673$	38.3263	+	18.4570i	1.47737	+	0.711465i	0.987100	−	0.160105i	$-0.0511833\pi$
$673$	38.3263	+	18.4570i	1.47737	+	0.711465i	0.490272	+	0.871570i	$0.336898\pi$
$674$	−19.3966	−	24.3226i	−0.747130	−	0.936872i
$675$	−0.313162	+	1.37205i	−0.0120536	+	0.0528102i
$676$	6.00237	−	26.2981i	0.230861	−	1.01147i
$677$	12.9894	−	16.2882i	0.499224	−	0.626007i	−0.466830	−	0.884347i	$-0.654604\pi$
$677$	12.9894	−	16.2882i	0.499224	−	0.626007i	0.966054	+	0.258340i	$0.0831755\pi$
$678$	1.26728	+	5.55231i	0.0486695	+	0.213235i
$679$	60.3954			2.31776
$680$	1.46427	+	6.41540i	0.0561523	+	0.246019i
$681$	5.94778	+	2.86430i	0.227919	+	0.109760i
$682$	−6.78486	−	3.26742i	−0.259806	−	0.125116i
$683$	−7.62083	−	33.3891i	−0.291603	−	1.27760i	−0.882294	−	0.470699i	$-0.844002\pi$
$683$	−7.62083	−	33.3891i	−0.291603	−	1.27760i	0.590691	−	0.806898i	$-0.298855\pi$
$684$	−4.44634			−0.170010
$685$	−3.72193	−	16.3069i	−0.142208	−	0.623053i
$686$	−50.0151	+	62.7169i	−1.90959	+	2.39454i
$687$	−0.518176	+	2.27028i	−0.0197697	+	0.0866165i
$688$	3.34323	−	14.6477i	0.127460	−	0.558437i
$689$	−3.61939	−	4.53857i	−0.137888	−	0.172906i
$690$	−15.3170	−	7.37626i	−0.583106	−	0.280809i
$691$	8.21851	−	3.95783i	0.312647	−	0.150563i	−0.270979	−	0.962585i	$-0.587348\pi$
$691$	8.21851	−	3.95783i	0.312647	−	0.150563i	0.583626	+	0.812022i	$0.301633\pi$
$692$	−5.04794	+	6.32991i	−0.191894	+	0.240627i
$693$	−10.9894	−	13.7803i	−0.417452	−	0.523469i
$694$	−62.5191	+	30.1076i	−2.37319	+	1.14287i
$695$	19.6090			0.743812
$696$	1.11596	−	3.14483i	0.0423005	−	0.119204i
$697$	−8.91103			−0.337529
$698$	−51.9025	+	24.9949i	−1.96454	+	0.946072i
$699$	−1.09013	−	1.36698i	−0.0412325	−	0.0517040i
$700$	9.50629	−	11.9205i	0.359304	−	0.450553i
$701$	38.5938	−	18.5858i	1.45767	−	0.701976i	0.473760	−	0.880654i	$-0.342897\pi$
$701$	38.5938	−	18.5858i	1.45767	−	0.701976i	0.983907	+	0.178679i	$0.0571822\pi$
$702$	−2.10203	−	1.01228i	−0.0793359	−	0.0382061i
$703$	12.0111	+	15.0614i	0.453006	+	0.568052i
$704$	8.47677	−	37.1391i	0.319480	−	1.39973i
$705$	2.47213	−	10.8311i	0.0931057	−	0.407923i
$706$	17.7602	−	22.2706i	0.668416	−	0.838167i
$707$	−9.91290	−	43.4312i	−0.372813	−	1.63340i
$708$	−13.1461			−0.494062
$709$	−2.44899	−	10.7297i	−0.0919738	−	0.402964i	0.907894	−	0.419199i	$-0.137689\pi$
$709$	−2.44899	−	10.7297i	−0.0919738	−	0.402964i	−0.999868	+	0.0162353i	$0.994832\pi$
$710$	1.05891	+	0.509946i	0.0397403	+	0.0191379i
$711$	12.4445	+	5.99297i	0.466706	+	0.224754i
$712$	−1.00450	−	4.40101i	−0.0376453	−	0.164935i
$713$	−4.20106			−0.157331
$714$	12.1817	+	53.3716i	0.455889	+	1.99738i
$715$	−4.97350	+	6.23658i	−0.185998	+	0.233235i
$716$	−3.65007	+	15.9920i	−0.136409	+	0.597649i
$717$	−5.07780	+	22.2473i	−0.189634	+	0.830840i
$718$	−31.8015	−	39.8779i	−1.18682	−	1.48823i
$719$	−16.3737	−	7.88517i	−0.610637	−	0.294067i	0.102892	−	0.994692i	$-0.467190\pi$
$719$	−16.3737	−	7.88517i	−0.610637	−	0.294067i	−0.713530	+	0.700625i	$0.752905\pi$
$720$	5.65761	−	2.72456i	0.210847	−	0.101538i
$721$	−16.3172	+	20.4612i	−0.607685	+	0.762013i
$722$	−19.7258	−	24.7354i	−0.734118	−	0.920555i
$723$	10.0695	−	4.84919i	0.374487	−	0.180343i
$724$	48.4613			1.80105
$725$	0.815434	+	7.53474i	0.0302845	+	0.279833i
$726$	−6.19463			−0.229904
$727$	37.1991	−	17.9141i	1.37964	−	0.664399i	0.410716	−	0.911763i	$-0.365279\pi$
$727$	37.1991	−	17.9141i	1.37964	−	0.664399i	0.968922	+	0.247365i	$0.0795645\pi$
$728$	2.04882	+	2.56914i	0.0759344	+	0.0952187i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	53.4896	−	25.7592i	1.97974	−	0.953391i
$731$	22.8919	+	11.0241i	0.846686	+	0.407742i
$732$	14.9672	+	18.7683i	0.553204	+	0.693695i
$733$	−1.01201	+	4.43390i	−0.0373794	+	0.163770i	−0.990173	−	0.139850i	$-0.955338\pi$
$733$	−1.01201	+	4.43390i	−0.0373794	+	0.163770i	0.952793	+	0.303619i	$0.0981952\pi$
$734$	2.04547	−	8.96178i	0.0754996	−	0.330785i
$735$	−17.9745	+	22.5393i	−0.662999	+	0.831375i
$736$	−7.80508	−	34.1963i	−0.287699	−	1.26049i
$737$	−14.8427			−0.546736
$738$	−0.733813	−	3.21504i	−0.0270120	−	0.118347i
$739$	−42.6604	−	20.5442i	−1.56929	−	0.755729i	−0.571399	−	0.820672i	$-0.693599\pi$
$739$	−42.6604	−	20.5442i	−1.56929	−	0.755729i	−0.997889	+	0.0649431i	$0.979313\pi$
$740$	39.1016	+	18.8304i	1.43740	+	0.692218i
$741$	0.484297	+	2.12184i	0.0177911	+	0.0779479i
$742$	−50.4083			−1.85055
$743$	3.01788	+	13.2222i	0.110715	+	0.485076i	0.999635	+	0.0270128i	$0.00859948\pi$
$743$	3.01788	+	13.2222i	0.110715	+	0.485076i	−0.888920	+	0.458063i	$0.848543\pi$
$744$	−0.375200	+	0.470486i	−0.0137555	+	0.0172489i
$745$	−5.10360	+	22.3603i	−0.186981	+	0.819219i
$746$	−11.2465	+	49.2741i	−0.411763	+	1.80405i
$747$	1.81951	+	2.28159i	0.0665723	+	0.0834790i
$748$	43.3997	+	20.9002i	1.58685	+	0.764187i
$749$	26.7376	−	12.8761i	0.976970	−	0.470484i
$750$	15.6997	−	19.6868i	0.573273	−	0.718862i
$751$	17.8218	+	22.3478i	0.650326	+	0.815483i	0.992252	−	0.124244i	$-0.0396506\pi$
$751$	17.8218	+	22.3478i	0.650326	+	0.815483i	−0.341926	+	0.939727i	$0.611079\pi$
$752$	17.4951	−	8.42519i	0.637980	−	0.307235i
$753$	−20.7323			−0.755526
$754$	−12.4787	−	1.46159i	−0.454447	−	0.0532280i
$755$	18.0835			0.658128
$756$	−9.76099	+	4.70065i	−0.355004	+	0.170961i
$757$	4.64105	+	5.81969i	0.168682	+	0.211520i	0.858986	−	0.511999i	$-0.171095\pi$
$757$	4.64105	+	5.81969i	0.168682	+	0.211520i	−0.690304	+	0.723519i	$0.742523\pi$
$758$	17.4588	−	21.8927i	0.634132	−	0.795177i
$759$	−14.5767	+	7.01979i	−0.529102	+	0.254802i
$760$	2.04673	+	0.985652i	0.0742426	+	0.0357534i
$761$	27.5300	+	34.5215i	0.997960	+	1.25140i	0.967764	+	0.251858i	$0.0810417\pi$
$761$	27.5300	+	34.5215i	0.997960	+	1.25140i	0.0301959	+	0.999544i	$0.490387\pi$
$762$	−5.72637	+	25.0889i	−0.207444	+	0.908874i
$763$	−17.1963	+	75.3417i	−0.622546	+	2.72755i
$764$	−19.8013	+	24.8301i	−0.716387	+	0.898321i
$765$	2.36303	+	10.3531i	0.0854356	+	0.374318i

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)

\(f(q)\)	\(=\)	\(q+(-1.86804 + 0.899602i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.43332 - 1.79733i) q^{4} +(-1.70773 + 0.822397i) q^{5} +(1.86804 + 0.899602i) q^{6} +(-2.93833 - 3.68455i) q^{7} +(-0.137887 + 0.604122i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})\)	\(q+(-1.86804 + 0.899602i) q^{2} +(-0.623490 - 0.781831i) q^{3} +(1.43332 - 1.79733i) q^{4} +(-1.70773 + 0.822397i) q^{5} +(1.86804 + 0.899602i) q^{6} +(-2.93833 - 3.68455i) q^{7} +(-0.137887 + 0.604122i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(2.45027 - 3.07255i) q^{10} +(-0.832232 - 3.64624i) q^{11} -2.29887 q^{12} +(0.250393 + 1.09704i) q^{13} +(8.80354 + 4.23956i) q^{14} +(1.70773 + 0.822397i) q^{15} +(0.737200 + 3.22989i) q^{16} -5.60261 q^{17} +(-0.461368 - 2.02139i) q^{18} +(-1.20592 + 1.51218i) q^{19} +(-0.969600 + 4.24810i) q^{20} +(-1.04868 + 4.59455i) q^{21} +(4.83481 + 6.06266i) q^{22} +(3.89751 + 1.87694i) q^{23} +(0.558293 - 0.268860i) q^{24} +(-0.877459 + 1.10030i) q^{25} +(-1.45465 - 1.82407i) q^{26} +(0.900969 - 0.433884i) q^{27} -10.8339 q^{28} +(3.82459 - 3.79111i) q^{29} -3.92993 q^{30} +(-0.874966 + 0.421361i) q^{31} +(-5.05543 - 6.33931i) q^{32} +(-2.33186 + 2.92406i) q^{33} +(10.4659 - 5.04011i) q^{34} +(8.04802 + 3.87572i) q^{35} +(1.43332 + 1.79733i) q^{36} +(2.21633 - 9.71037i) q^{37} +(0.892354 - 3.90966i) q^{38} +(0.701586 - 0.879761i) q^{39} +(-0.261356 - 1.14507i) q^{40} +1.59051 q^{41} +(-2.17430 - 9.52621i) q^{42} +(-4.08593 - 1.96768i) q^{43} +(-7.74634 - 3.73044i) q^{44} +(-0.421773 - 1.84791i) q^{45} -8.96921 q^{46} +(-1.30426 - 5.71432i) q^{47} +(2.06559 - 2.59017i) q^{48} +(-3.38446 + 14.8283i) q^{49} +(0.649300 - 2.84477i) q^{50} +(3.49317 + 4.38029i) q^{51} +(2.33064 + 1.12238i) q^{52} +(-4.64798 + 2.23835i) q^{53} +(-1.29273 + 1.62103i) q^{54} +(4.41989 + 5.54236i) q^{55} +(2.63107 - 1.26706i) q^{56} +1.93415 q^{57} +(-3.73401 + 10.5226i) q^{58} +5.71853 q^{59} +(3.92583 - 1.89058i) q^{60} +(-6.51069 - 8.16415i) q^{61} +(1.25542 - 1.57424i) q^{62} +(4.24601 - 2.04477i) q^{63} +(9.17690 + 4.41936i) q^{64} +(-1.32981 - 1.66753i) q^{65} +(1.72552 - 7.56002i) q^{66} +(0.883099 - 3.86911i) q^{67} +(-8.03032 + 10.0697i) q^{68} +(-0.962605 - 4.21745i) q^{69} -18.5206 q^{70} +(0.0665482 + 0.291567i) q^{71} +(-0.558293 - 0.268860i) q^{72} +(13.6108 + 6.55462i) q^{73} +(4.59527 + 20.1332i) q^{74} +1.40734 q^{75} +(0.989404 + 4.33486i) q^{76} +(-10.9894 + 13.7803i) q^{77} +(-0.519158 + 2.27458i) q^{78} +(3.07354 - 13.4661i) q^{79} +(-3.91519 - 4.90949i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(-2.97115 + 1.43083i) q^{82} +(1.81951 - 2.28159i) q^{83} +(6.75482 + 8.47027i) q^{84} +(9.56772 - 4.60757i) q^{85} +9.40282 q^{86} +(-5.34860 - 0.626466i) q^{87} +2.31753 q^{88} +(-6.56353 + 3.16083i) q^{89} +(2.45027 + 3.07255i) q^{90} +(3.30637 - 4.14606i) q^{91} +(8.95985 - 4.31484i) q^{92} +(0.874966 + 0.421361i) q^{93} +(7.57701 + 9.50127i) q^{94} +(0.815772 - 3.57413i) q^{95} +(-1.80426 + 7.90500i) q^{96} +(-7.99029 + 10.0195i) q^{97} +(-7.01725 - 30.7446i) q^{98} +3.74001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

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