LMFDB - Embedded newform 87.2.g.b.52.3

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} - 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			52.3
Root			$-0.408260 - 1.78870i$ of defining polynomial
Character	$\chi$	$=$	87.52
Dual form			87.2.g.b.82.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14392 - 1.43443i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.303995 - 1.33189i) q^{4} +(-1.40816 + 1.76577i) q^{5} +(-1.14392 - 1.43443i) q^{6} +(0.165617 - 0.725615i) q^{7} +(1.04778 + 0.504584i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(1.14392 - 1.43443i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.303995 - 1.33189i) q^{4} +(-1.40816 + 1.76577i) q^{5} +(-1.14392 - 1.43443i) q^{6} +(0.165617 - 0.725615i) q^{7} +(1.04778 + 0.504584i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.922058 + 4.03980i) q^{10} +(-5.68404 + 2.73729i) q^{11} -1.36614 q^{12} +(1.48289 - 0.714123i) q^{13} +(-0.851391 - 1.06761i) q^{14} +(1.40816 + 1.76577i) q^{15} +(4.38406 - 2.11125i) q^{16} +4.16595 q^{17} +(-1.65301 + 0.796048i) q^{18} +(-0.231613 - 1.01476i) q^{19} +(2.77988 + 1.33872i) q^{20} +(-0.670569 - 0.322929i) q^{21} +(-2.57563 + 11.2846i) q^{22} +(-2.85155 - 3.57573i) q^{23} +(0.725086 - 0.909229i) q^{24} +(-0.0224408 - 0.0983195i) q^{25} +(0.671949 - 2.94400i) q^{26} +(-0.623490 + 0.781831i) q^{27} -1.01678 q^{28} +(-4.68636 - 2.65293i) q^{29} +4.14369 q^{30} +(-2.20186 + 2.76105i) q^{31} +(1.46901 - 6.43615i) q^{32} +(1.40384 + 6.15063i) q^{33} +(4.76551 - 5.97577i) q^{34} +(1.04806 + 1.31422i) q^{35} +(-0.303995 + 1.33189i) q^{36} +(0.969034 + 0.466662i) q^{37} +(-1.72055 - 0.828574i) q^{38} +(-0.366244 - 1.60462i) q^{39} +(-2.36642 + 1.13961i) q^{40} -1.20065 q^{41} +(-1.23030 + 0.592479i) q^{42} +(-7.99734 - 10.0283i) q^{43} +(5.37367 + 6.73837i) q^{44} +(2.03484 - 0.979929i) q^{45} -8.39108 q^{46} +(7.10498 - 3.42158i) q^{47} +(-1.08277 - 4.74394i) q^{48} +(5.80769 + 2.79684i) q^{49} +(-0.166703 - 0.0802799i) q^{50} +(0.927012 - 4.06150i) q^{51} +(-1.40192 - 1.75795i) q^{52} +(-8.22494 + 10.3138i) q^{53} +(0.408260 + 1.78870i) q^{54} +(3.17058 - 13.8912i) q^{55} +(0.539663 - 0.676716i) q^{56} -1.04086 q^{57} +(-9.16625 + 3.68752i) q^{58} +11.0585 q^{59} +(1.92374 - 2.41229i) q^{60} +(1.43496 - 6.28696i) q^{61} +(1.44178 + 6.31683i) q^{62} +(-0.464048 + 0.581898i) q^{63} +(-1.48405 - 1.86094i) q^{64} +(-0.827164 + 3.62404i) q^{65} +(10.4285 + 5.02211i) q^{66} +(6.19652 + 2.98409i) q^{67} +(-1.26643 - 5.54858i) q^{68} +(-4.12061 + 1.98438i) q^{69} +3.08405 q^{70} +(2.95303 - 1.42211i) q^{71} +(-0.725086 - 0.909229i) q^{72} +(4.42081 + 5.54352i) q^{73} +(1.77789 - 0.856187i) q^{74} -0.100848 q^{75} +(-1.28114 + 0.616965i) q^{76} +(1.04484 + 4.57776i) q^{77} +(-2.72067 - 1.31020i) q^{78} +(-5.75663 - 2.77225i) q^{79} +(-2.44545 + 10.7142i) q^{80} +(0.623490 + 0.781831i) q^{81} +(-1.37344 + 1.72224i) q^{82} +(1.14686 + 5.02472i) q^{83} +(-0.226256 + 0.991291i) q^{84} +(-5.86631 + 7.35612i) q^{85} -23.5333 q^{86} +(-3.62923 + 3.97853i) q^{87} -7.33681 q^{88} +(5.80998 - 7.28549i) q^{89} +(0.922058 - 4.03980i) q^{90} +(-0.272586 - 1.19428i) q^{91} +(-3.89562 + 4.88495i) q^{92} +(2.20186 + 2.76105i) q^{93} +(3.21951 - 14.1056i) q^{94} +(2.11798 + 1.01997i) q^{95} +(-5.94790 - 2.86436i) q^{96} +(3.37522 + 14.7878i) q^{97} +(10.6554 - 5.13137i) q^{98} +6.30880 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 $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	1.14392	−	1.43443i	0.808873	−	1.01429i	−0.190595	−	0.981669i	$-0.561042\pi$
$2$	1.14392	−	1.43443i	0.808873	−	1.01429i	0.999468	−	0.0326259i	$-0.0103870\pi$
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$4$	−0.303995	−	1.33189i	−0.151997	−	0.665944i
$5$	−1.40816	+	1.76577i	−0.629746	+	0.789677i	−0.989679	−	0.143301i	$-0.954228\pi$
$5$	−1.40816	+	1.76577i	−0.629746	+	0.789677i	0.359933	+	0.932978i	$0.382800\pi$
$6$	−1.14392	−	1.43443i	−0.467003	−	0.585603i
$7$	0.165617	−	0.725615i	0.0625973	−	0.274257i	−0.933937	−	0.357437i	$-0.883651\pi$
$7$	0.165617	−	0.725615i	0.0625973	−	0.274257i	0.996534	+	0.0831805i	$0.0265078\pi$
$8$	1.04778	+	0.504584i	0.370446	+	0.178397i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	0.922058	+	4.03980i	0.291580	+	1.27750i
$11$	−5.68404	+	2.73729i	−1.71380	+	0.825323i	−0.722865	+	0.690989i	$0.757175\pi$
$11$	−5.68404	+	2.73729i	−1.71380	+	0.825323i	−0.990936	+	0.134334i	$0.957111\pi$
$12$	−1.36614			−0.394370
$13$	1.48289	−	0.714123i	0.411280	−	0.198062i	−0.216791	−	0.976218i	$-0.569559\pi$
$13$	1.48289	−	0.714123i	0.411280	−	0.198062i	0.628071	+	0.778156i	$0.283845\pi$
$14$	−0.851391	−	1.06761i	−0.227544	−	0.285331i
$15$	1.40816	+	1.76577i	0.363584	+	0.455920i
$16$	4.38406	−	2.11125i	1.09602	−	0.527813i
$17$	4.16595			1.01039			0.505196	−	0.863005i	$-0.331420\pi$
$17$	4.16595			1.01039			0.505196	+	0.863005i	$0.331420\pi$
$18$	−1.65301	+	0.796048i	−0.389618	+	0.187630i
$19$	−0.231613	−	1.01476i	−0.0531356	−	0.232802i	0.941386	−	0.337330i	$-0.109524\pi$
$19$	−0.231613	−	1.01476i	−0.0531356	−	0.232802i	−0.994522	+	0.104528i	$0.966667\pi$
$20$	2.77988	+	1.33872i	0.621600	+	0.299347i
$21$	−0.670569	−	0.322929i	−0.146330	−	0.0704689i
$22$	−2.57563	+	11.2846i	−0.549127	+	2.40588i
$23$	−2.85155	−	3.57573i	−0.594590	−	0.745592i	0.389934	−	0.920843i	$-0.372498\pi$
$23$	−2.85155	−	3.57573i	−0.594590	−	0.745592i	−0.984524	+	0.175251i	$0.943926\pi$
$24$	0.725086	−	0.909229i	0.148008	−	0.185596i
$25$	−0.0224408	−	0.0983195i	−0.00448816	−	0.0196639i
$26$	0.671949	−	2.94400i	0.131780	−	0.577366i
$27$	−0.623490	+	0.781831i	−0.119991	+	0.150464i
$28$	−1.01678			−0.192154
$29$	−4.68636	−	2.65293i	−0.870235	−	0.492636i
$29$	−4.68636	−	2.65293i	−0.870235	−	0.492636i
$30$	4.14369			0.756531
$31$	−2.20186	+	2.76105i	−0.395466	+	0.495899i	−0.939206	−	0.343355i	$-0.888437\pi$
$31$	−2.20186	+	2.76105i	−0.395466	+	0.495899i	0.543740	+	0.839254i	$0.317008\pi$
$32$	1.46901	−	6.43615i	0.259687	−	1.13776i
$33$	1.40384	+	6.15063i	0.244377	+	1.07069i
$34$	4.76551	−	5.97577i	0.817279	−	1.02484i
$35$	1.04806	+	1.31422i	0.177154	+	0.222144i
$36$	−0.303995	+	1.33189i	−0.0506658	+	0.221981i
$37$	0.969034	+	0.466662i	0.159308	+	0.0767188i	0.511839	−	0.859081i	$-0.328964\pi$
$37$	0.969034	+	0.466662i	0.159308	+	0.0767188i	−0.352531	+	0.935800i	$0.614679\pi$
$38$	−1.72055	−	0.828574i	−0.279110	−	0.134412i
$39$	−0.366244	−	1.60462i	−0.0586460	−	0.256945i
$40$	−2.36642	+	1.13961i	−0.374163	+	0.180187i
$41$	−1.20065			−0.187510			−0.0937548	−	0.995595i	$-0.529887\pi$
$41$	−1.20065			−0.187510			−0.0937548	+	0.995595i	$0.529887\pi$
$42$	−1.23030	+	0.592479i	−0.189839	+	0.0914215i
$43$	−7.99734	−	10.0283i	−1.21958	−	1.52931i	−0.772778	−	0.634676i	$-0.781133\pi$
$43$	−7.99734	−	10.0283i	−1.21958	−	1.52931i	−0.446804	−	0.894632i	$-0.647438\pi$
$44$	5.37367	+	6.73837i	0.810112	+	1.01585i
$45$	2.03484	−	0.979929i	0.303337	−	0.146079i
$46$	−8.39108			−1.23720
$47$	7.10498	−	3.42158i	1.03637	−	0.499088i	0.163243	−	0.986586i	$-0.447804\pi$
$47$	7.10498	−	3.42158i	1.03637	−	0.499088i	0.873124	+	0.487497i	$0.162090\pi$
$48$	−1.08277	−	4.74394i	−0.156285	−	0.684729i
$49$	5.80769	+	2.79684i	0.829671	+	0.399548i
$50$	−0.166703	−	0.0802799i	−0.0235753	−	0.0113533i
$51$	0.927012	−	4.06150i	0.129808	−	0.568724i
$52$	−1.40192	−	1.75795i	−0.194412	−	0.243784i
$53$	−8.22494	+	10.3138i	−1.12978	+	1.41670i	−0.233986	+	0.972240i	$0.575177\pi$
$53$	−8.22494	+	10.3138i	−1.12978	+	1.41670i	−0.895797	+	0.444463i	$0.853395\pi$
$54$	0.408260	+	1.78870i	0.0555572	+	0.243412i
$55$	3.17058	−	13.8912i	0.427521	−	1.87309i
$56$	0.539663	−	0.676716i	0.0721155	−	0.0904300i
$57$	−1.04086			−0.137865
$58$	−9.16625	+	3.68752i	−1.20359	+	0.484195i
$59$	11.0585			1.43970			0.719849	−	0.694131i	$-0.244211\pi$
$59$	11.0585			1.43970			0.719849	+	0.694131i	$0.244211\pi$
$60$	1.92374	−	2.41229i	0.248353	−	0.311425i
$61$	1.43496	−	6.28696i	0.183728	−	0.804963i	−0.796108	−	0.605155i	$-0.793111\pi$
$61$	1.43496	−	6.28696i	0.183728	−	0.804963i	0.979835	−	0.199808i	$-0.0640318\pi$
$62$	1.44178	+	6.31683i	0.183106	+	0.802238i
$63$	−0.464048	+	0.581898i	−0.0584646	+	0.0733122i
$64$	−1.48405	−	1.86094i	−0.185506	−	0.232617i
$65$	−0.827164	+	3.62404i	−0.102597	+	0.449507i
$66$	10.4285	+	5.02211i	1.28366	+	0.618179i
$67$	6.19652	+	2.98409i	0.757026	+	0.364564i	0.772249	−	0.635320i	$-0.219132\pi$
$67$	6.19652	+	2.98409i	0.757026	+	0.364564i	−0.0152236	+	0.999884i	$0.504846\pi$
$68$	−1.26643	−	5.54858i	−0.153577	−	0.672864i
$69$	−4.12061	+	1.98438i	−0.496063	+	0.238892i
$70$	3.08405			0.368614
$71$	2.95303	−	1.42211i	0.350461	−	0.168773i	−0.250368	−	0.968151i	$-0.580552\pi$
$71$	2.95303	−	1.42211i	0.350461	−	0.168773i	0.600829	+	0.799378i	$0.294837\pi$
$72$	−0.725086	−	0.909229i	−0.0854522	−	0.107154i
$73$	4.42081	+	5.54352i	0.517417	+	0.648820i	0.970058	−	0.242872i	$-0.0780896\pi$
$73$	4.42081	+	5.54352i	0.517417	+	0.648820i	−0.452641	+	0.891693i	$0.649518\pi$
$74$	1.77789	−	0.856187i	0.206676	−	0.0995298i
$75$	−0.100848			−0.0116449
$76$	−1.28114	+	0.616965i	−0.146957	+	0.0707707i
$77$	1.04484	+	4.57776i	0.119071	+	0.521684i
$78$	−2.72067	−	1.31020i	−0.308055	−	0.148351i
$79$	−5.75663	−	2.77225i	−0.647672	−	0.311902i	0.0810523	−	0.996710i	$-0.474172\pi$
$79$	−5.75663	−	2.77225i	−0.647672	−	0.311902i	−0.728724	+	0.684808i	$0.759886\pi$
$80$	−2.44545	+	10.7142i	−0.273410	+	1.19789i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	−1.37344	+	1.72224i	−0.151672	+	0.190190i
$83$	1.14686	+	5.02472i	0.125884	+	0.551535i	0.998055	+	0.0623339i	$0.0198544\pi$
$83$	1.14686	+	5.02472i	0.125884	+	0.551535i	−0.872171	+	0.489201i	$0.837288\pi$
$84$	−0.226256	+	0.991291i	−0.0246865	+	0.108159i
$85$	−5.86631	+	7.35612i	−0.636290	+	0.797883i
$86$	−23.5333			−2.53766
$87$	−3.62923	+	3.97853i	−0.389094	+	0.426543i
$88$	−7.33681			−0.782106
$89$	5.80998	−	7.28549i	0.615857	−	0.772260i	−0.371898	−	0.928274i	$-0.621293\pi$
$89$	5.80998	−	7.28549i	0.615857	−	0.772260i	0.987755	+	0.156013i	$0.0498643\pi$
$90$	0.922058	−	4.03980i	0.0971934	−	0.425832i
$91$	−0.272586	−	1.19428i	−0.0285748	−	0.125194i
$92$	−3.89562	+	4.88495i	−0.406146	+	0.509291i
$93$	2.20186	+	2.76105i	0.228322	+	0.286307i
$94$	3.21951	−	14.1056i	0.332067	−	1.45488i
$95$	2.11798	+	1.01997i	0.217301	+	0.104646i
$96$	−5.94790	−	2.86436i	−0.607055	−	0.292342i
$97$	3.37522	+	14.7878i	0.342701	+	1.50147i	0.793347	+	0.608769i	$0.208337\pi$
$97$	3.37522	+	14.7878i	0.342701	+	1.50147i	−0.450646	+	0.892703i	$0.648806\pi$
$98$	10.6554	−	5.13137i	1.07636	−	0.518347i
$99$	6.30880			0.634059
$100$	−0.124129	+	0.0597772i	−0.0124129	+	0.00597772i
$101$	2.76928	+	3.47257i	0.275554	+	0.345534i	0.900281	−	0.435310i	$-0.143361\pi$
$101$	2.76928	+	3.47257i	0.275554	+	0.345534i	−0.624727	+	0.780843i	$0.714790\pi$
$102$	−4.76551	−	5.97577i	−0.471856	−	0.591689i
$103$	−13.8692	+	6.67906i	−1.36657	+	0.658108i	−0.966092	−	0.258197i	$-0.916872\pi$
$103$	−13.8692	+	6.67906i	−1.36657	+	0.658108i	−0.400482	+	0.916305i	$0.631157\pi$
$104$	1.91408			0.187691
$105$	1.51448	−	0.729337i	0.147798	−	0.0711760i
$106$	5.38568	+	23.5962i	0.523103	+	2.29187i
$107$	7.13273	+	3.43494i	0.689547	+	0.332068i	0.745632	−	0.666358i	$-0.232148\pi$
$107$	7.13273	+	3.43494i	0.689547	+	0.332068i	−0.0560855	+	0.998426i	$0.517862\pi$
$108$	1.23085	+	0.592746i	0.118438	+	0.0570370i
$109$	−0.932147	+	4.08400i	−0.0892835	+	0.391177i	−0.999749	−	0.0224086i	$-0.992867\pi$
$109$	−0.932147	+	4.08400i	−0.0892835	+	0.391177i	0.910465	+	0.413585i	$0.135724\pi$
$110$	−16.2991	−	20.4384i	−1.55406	−	1.94873i
$111$	0.670593	−	0.840897i	0.0636498	−	0.0798144i
$112$	−0.805882	−	3.53080i	−0.0761487	−	0.333629i
$113$	2.40874	−	10.5534i	0.226595	−	0.992779i	−0.725798	−	0.687907i	$-0.758529\pi$
$113$	2.40874	−	10.5534i	0.226595	−	0.992779i	0.952394	−	0.304871i	$-0.0986134\pi$
$114$	−1.19066	+	1.49304i	−0.111515	+	0.139836i
$115$	10.3294			0.963217
$116$	−2.10877	+	7.04818i	−0.195794	+	0.654407i
$117$	−1.64589			−0.152162
$118$	12.6501	−	15.8627i	1.16453	−	1.46028i
$119$	0.689952	−	3.02288i	0.0632478	−	0.277107i
$120$	0.584456	+	2.56067i	0.0533533	+	0.233756i
$121$	17.9571	−	22.5175i	1.63247	−	2.04705i
$122$	−7.37673	−	9.25012i	−0.667858	−	0.837467i
$123$	−0.267169	+	1.17054i	−0.0240898	+	0.105544i
$124$	4.34676	+	2.09329i	0.390350	+	0.187983i
$125$	−9.96901	−	4.80082i	−0.891655	−	0.429398i
$126$	0.303858	+	1.33129i	0.0270698	+	0.118601i
$127$	−7.27053	+	3.50130i	−0.645155	+	0.310690i	−0.727698	−	0.685897i	$-0.759410\pi$
$127$	−7.27053	+	3.50130i	−0.645155	+	0.310690i	0.0825435	+	0.996587i	$0.473696\pi$
$128$	8.83633			0.781029
$129$	−11.5565	+	5.56531i	−1.01749	+	0.489998i
$130$	4.25222	+	5.33212i	0.372945	+	0.467658i
$131$	−11.6622	−	14.6240i	−1.01893	−	1.27770i	−0.960166	−	0.279432i	$-0.909854\pi$
$131$	−11.6622	−	14.6240i	−1.01893	−	1.27770i	−0.0587686	−	0.998272i	$-0.518717\pi$
$132$	7.76518	−	3.73952i	0.675872	−	0.325483i
$133$	−0.774686			−0.0671738
$134$	11.3688	−	5.47492i	0.982113	−	0.472961i
$135$	−0.502565	−	2.20188i	−0.0432539	−	0.189508i
$136$	4.36500	+	2.10207i	0.374296	+	0.180251i
$137$	3.36252	+	1.61931i	0.287280	+	0.138347i	0.571974	−	0.820272i	$-0.306178\pi$
$137$	3.36252	+	1.61931i	0.287280	+	0.138347i	−0.284694	+	0.958618i	$0.591892\pi$
$138$	−1.86719	+	8.18070i	−0.158946	+	0.696388i
$139$	8.44508	+	10.5898i	0.716302	+	0.898214i	0.998122	−	0.0612530i	$-0.0195096\pi$
$139$	8.44508	+	10.5898i	0.716302	+	0.898214i	−0.281820	+	0.959467i	$0.590938\pi$
$140$	1.43179	−	1.79541i	0.121008	−	0.151740i
$141$	−1.75478	−	7.68822i	−0.147780	−	0.647465i
$142$	1.33812	−	5.86270i	0.112293	−	0.491986i
$143$	−6.47405	+	8.11820i	−0.541387	+	0.678878i
$144$	−4.86594			−0.405495
$145$	11.2836	−	4.53931i	0.937051	−	0.376969i
$146$	13.0088			1.07662
$147$	4.01905	−	5.03973i	0.331486	−	0.415670i
$148$	0.326960	−	1.43251i	0.0268760	−	0.117751i
$149$	0.458291	+	2.00790i	0.0375447	+	0.164494i	0.990225	−	0.139481i	$-0.0445433\pi$
$149$	0.458291	+	2.00790i	0.0375447	+	0.164494i	−0.952680	+	0.303975i	$0.901686\pi$
$150$	−0.115362	+	0.144659i	−0.00941927	+	0.0118114i
$151$	−7.77480	−	9.74929i	−0.632704	−	0.793386i	0.357365	−	0.933965i	$-0.383675\pi$
$151$	−7.77480	−	9.74929i	−0.632704	−	0.793386i	−0.990070	+	0.140578i	$0.955104\pi$
$152$	0.269354	−	1.18012i	0.0218475	−	0.0957200i
$153$	−3.75339	−	1.80754i	−0.303444	−	0.146131i
$154$	7.76169	+	3.73783i	0.625455	+	0.301203i
$155$	−1.77481	−	7.77597i	−0.142556	−	0.624581i
$156$	−2.02584	+	0.975591i	−0.162197	+	0.0781098i
$157$	−13.1146			−1.04666			−0.523329	−	0.852131i	$-0.675310\pi$
$157$	−13.1146			−1.04666			−0.523329	+	0.852131i	$0.675310\pi$
$158$	−10.5617	+	5.08625i	−0.840245	+	0.404641i
$159$	8.22494	+	10.3138i	0.652281	+	0.817934i
$160$	9.29618	+	11.6570i	0.734927	+	0.921570i
$161$	−3.06687	+	1.47693i	−0.241703	+	0.116398i
$162$	1.83470			0.144148
$163$	−9.80204	+	4.72041i	−0.767755	+	0.369731i	−0.776407	−	0.630231i	$-0.782960\pi$
$163$	−9.80204	+	4.72041i	−0.767755	+	0.369731i	0.00865246	+	0.999963i	$0.497246\pi$
$164$	0.364990	+	1.59913i	0.0285010	+	0.124871i
$165$	−12.8374	−	6.18218i	−0.999392	−	0.481282i
$166$	8.51952	+	4.10279i	0.661243	+	0.318438i
$167$	4.51248	−	19.7705i	0.349186	−	1.52988i	−0.429847	−	0.902902i	$-0.641432\pi$
$167$	4.51248	−	19.7705i	0.349186	−	1.52988i	0.779033	−	0.626983i	$-0.215710\pi$
$168$	−0.539663	−	0.676716i	−0.0416359	−	0.0522098i
$169$	−6.41637	+	8.04588i	−0.493567	+	0.618914i
$170$	3.84125	+	16.8296i	0.294610	+	1.29077i
$171$	−0.231613	+	1.01476i	−0.0177119	+	0.0776008i
$172$	−10.9255	+	13.7001i	−0.833060	+	1.04462i
$173$	−0.158953			−0.0120850			−0.00604249	−	0.999982i	$-0.501923\pi$
$173$	−0.158953			−0.0120850			−0.00604249	+	0.999982i	$0.501923\pi$
$174$	1.55538	+	9.75699i	0.117913	+	0.739675i
$175$	−0.0750587			−0.00567390
$176$	−19.1401	+	24.0009i	−1.44274	+	1.80913i
$177$	2.46075	−	10.7813i	0.184962	−	0.810369i
$178$	−3.80437	−	16.6680i	−0.285149	−	1.24932i
$179$	−8.97720	+	11.2571i	−0.670988	+	0.841392i	−0.994490	−	0.104836i	$-0.966568\pi$
$179$	−8.97720	+	11.2571i	−0.670988	+	0.841392i	0.323502	+	0.946228i	$0.395140\pi$
$180$	−1.92374	−	2.41229i	−0.143387	−	0.179801i
$181$	−2.87864	+	12.6121i	−0.213968	+	0.937453i	0.747873	+	0.663842i	$0.231075\pi$
$181$	−2.87864	+	12.6121i	−0.213968	+	0.937453i	−0.961840	+	0.273611i	$0.911782\pi$
$182$	−2.02492	−	0.975152i	−0.150097	−	0.0722831i
$183$	−5.81003	−	2.79796i	−0.429490	−	0.206831i
$184$	−1.18354	−	5.18543i	−0.0872517	−	0.382275i
$185$	−2.18857	+	1.05396i	−0.160907	+	0.0774887i
$186$	6.47928			0.475084
$187$	−23.6794	+	11.4034i	−1.73161	+	0.833900i
$188$	−6.71703	−	8.42289i	−0.489890	−	0.614302i
$189$	0.464048	+	0.581898i	0.0337545	+	0.0423268i
$190$	3.88588	−	1.87134i	0.281911	−	0.135761i
$191$	−5.61297			−0.406140			−0.203070	−	0.979164i	$-0.565092\pi$
$191$	−5.61297			−0.406140			−0.203070	+	0.979164i	$0.565092\pi$
$192$	−2.14451	+	1.03274i	−0.154767	+	0.0745317i
$193$	−2.01768	−	8.84002i	−0.145236	−	0.636319i	−0.994170	−	0.107821i	$-0.965613\pi$
$193$	−2.01768	−	8.84002i	−0.145236	−	0.636319i	0.848935	−	0.528498i	$-0.177245\pi$
$194$	25.0730	+	12.0745i	1.80014	+	0.866900i
$195$	3.34912	+	1.61285i	0.239835	+	0.115499i
$196$	1.95957	−	8.58542i	0.139969	−	0.613244i
$197$	6.01235	+	7.53925i	0.428362	+	0.537149i	0.948435	−	0.316973i	$-0.102667\pi$
$197$	6.01235	+	7.53925i	0.428362	+	0.537149i	−0.520072	+	0.854122i	$0.674095\pi$
$198$	7.21676	−	9.04953i	0.512873	−	0.643122i
$199$	−2.64957	−	11.6085i	−0.187823	−	0.822905i	−0.977762	−	0.209720i	$-0.932745\pi$
$199$	−2.64957	−	11.6085i	−0.187823	−	0.822905i	0.789939	−	0.613186i	$-0.210112\pi$
$200$	0.0260975	−	0.114340i	0.00184537	−	0.00808509i
$201$	4.28813	−	5.37714i	0.302461	−	0.379274i
$202$	8.14899			0.573361
$203$	−2.70114	+	2.96112i	−0.189583	+	0.207830i
$204$	−5.69127			−0.398469
$205$	1.69070	−	2.12007i	0.118083	−	0.148072i
$206$	−6.28462	+	27.5347i	−0.437870	+	1.91843i
$207$	1.01771	+	4.45887i	0.0707355	+	0.309913i
$208$	4.99339	−	6.26152i	0.346230	−	0.434158i
$209$	4.09419	+	5.13395i	0.283201	+	0.355123i
$210$	0.686265	−	3.00672i	0.0473568	−	0.207484i
$211$	5.22041	+	2.51402i	0.359388	+	0.173072i	0.604861	−	0.796331i	$-0.293229\pi$
$211$	5.22041	+	2.51402i	0.359388	+	0.173072i	−0.245473	+	0.969404i	$0.578943\pi$
$212$	16.2371	+	7.81937i	1.11517	+	0.537037i
$213$	−0.729339	−	3.19544i	−0.0499735	−	0.218948i
$214$	13.0864	−	6.30210i	0.894571	−	0.430803i
$215$	28.9692			1.97569
$216$	−1.04778	+	0.504584i	−0.0712923	+	0.0343326i
$217$	1.63879	+	2.05498i	0.111248	+	0.139501i
$218$	4.79191	+	6.00887i	0.324549	+	0.406972i
$219$	6.38826	−	3.07642i	0.431678	−	0.207885i
$220$	−19.4654			−1.31236
$221$	6.17765	−	2.97500i	0.415554	−	0.200120i
$222$	−0.439103	−	1.92384i	−0.0294707	−	0.129119i
$223$	9.35393	+	4.50461i	0.626385	+	0.301651i	0.720018	−	0.693956i	$-0.244134\pi$
$223$	9.35393	+	4.50461i	0.626385	+	0.301651i	−0.0936325	+	0.995607i	$0.529848\pi$
$224$	−4.42687	−	2.13187i	−0.295783	−	0.142442i
$225$	−0.0224408	+	0.0983195i	−0.00149605	+	0.00655464i
$226$	−12.3827	−	15.5274i	−0.823683	−	1.03287i
$227$	0.871753	−	1.09314i	0.0578603	−	0.0725545i	−0.752059	−	0.659095i	$-0.770939\pi$
$227$	0.871753	−	1.09314i	0.0578603	−	0.0725545i	0.809920	+	0.586541i	$0.199511\pi$
$228$	0.316415	+	1.38631i	0.0209551	+	0.0918104i
$229$	1.53344	−	6.71844i	0.101333	−	0.443967i	−0.898653	−	0.438660i	$-0.855453\pi$
$229$	1.53344	−	6.71844i	0.101333	−	0.443967i	0.999986	−	0.00530751i	$-0.00168944\pi$
$230$	11.8159	−	14.8167i	0.779121	−	0.976986i
$231$	4.69549			0.308940
$232$	−3.57165	−	5.14434i	−0.234490	−	0.337743i
$233$	−0.133957			−0.00877579			−0.00438789	−	0.999990i	$-0.501397\pi$
$233$	−0.133957			−0.00877579			−0.00438789	+	0.999990i	$0.501397\pi$
$234$	−1.88276	+	2.36091i	−0.123080	+	0.154337i
$235$	−3.96319	+	17.3639i	−0.258530	+	1.13269i
$236$	−3.36173	−	14.7287i	−0.218830	−	0.958757i
$237$	−3.98371	+	4.99542i	−0.258770	+	0.324487i
$238$	−3.54685	−	4.44761i	−0.229908	−	0.288296i
$239$	−2.30911	+	10.1169i	−0.149364	+	0.654405i	0.843699	+	0.536817i	$0.180373\pi$
$239$	−2.30911	+	10.1169i	−0.149364	+	0.654405i	−0.993062	+	0.117588i	$0.962484\pi$
$240$	9.90143	+	4.76828i	0.639135	+	0.307791i
$241$	−7.62763	−	3.67328i	−0.491339	−	0.236616i	0.171773	−	0.985137i	$-0.445050\pi$
$241$	−7.62763	−	3.67328i	−0.491339	−	0.236616i	−0.663112	+	0.748520i	$0.730765\pi$
$242$	−11.7583	−	51.5165i	−0.755852	−	3.31160i
$243$	0.900969	−	0.433884i	0.0577972	−	0.0278337i
$244$	−8.80974			−0.563986
$245$	−13.1167	+	6.31668i	−0.837996	+	0.403558i
$246$	1.37344	+	1.72224i	0.0875676	+	0.109806i
$247$	−1.06812	−	1.33938i	−0.0679630	−	0.0852229i
$248$	−3.70024	+	1.78194i	−0.234966	+	0.113154i
$249$	5.15394			0.326618
$250$	−18.2902	+	8.80809i	−1.15677	+	0.557072i
$251$	−1.68037	−	7.36218i	−0.106064	−	0.464697i	−0.999868	−	0.0162393i	$-0.994831\pi$
$251$	−1.68037	−	7.36218i	−0.106064	−	0.464697i	0.893804	−	0.448458i	$-0.148026\pi$
$252$	0.916090	+	0.441166i	0.0577083	+	0.0277908i
$253$	25.9961	+	12.5191i	1.63436	+	0.787068i
$254$	−3.29453	+	14.4343i	−0.206717	+	0.905686i
$255$	5.86631	+	7.35612i	0.367362	+	0.460658i
$256$	13.0761	−	16.3970i	0.817259	−	1.02481i
$257$	−4.74187	−	20.7755i	−0.295789	−	1.29594i	−0.876332	−	0.481708i	$-0.840017\pi$
$257$	−4.74187	−	20.7755i	−0.295789	−	1.29594i	0.580542	−	0.814230i	$-0.302841\pi$
$258$	−5.23664	+	22.9432i	−0.326019	+	1.42838i
$259$	0.499105	−	0.625858i	0.0310129	−	0.0388890i
$260$	5.07827			0.314941
$261$	3.07120	+	4.42354i	0.190103	+	0.273810i
$262$	−34.3177			−2.12016
$263$	−16.0972	+	20.1853i	−0.992597	+	1.24468i	−0.0230593	+	0.999734i	$0.507341\pi$
$263$	−16.0972	+	20.1853i	−0.992597	+	1.24468i	−0.969537	+	0.244943i	$0.921231\pi$
$264$	−1.63259	+	7.15286i	−0.100479	+	0.440228i
$265$	−6.62973	−	29.0467i	−0.407261	−	1.78433i
$266$	−0.886178	+	1.11123i	−0.0543350	+	0.0681340i
$267$	−5.80998	−	7.28549i	−0.355565	−	0.445865i
$268$	2.09076	−	9.16021i	0.127713	−	0.559549i
$269$	−17.2204	−	8.29293i	−1.04995	−	0.505629i	−0.172356	−	0.985035i	$-0.555138\pi$
$269$	−17.2204	−	8.29293i	−1.04995	−	0.505629i	−0.877593	+	0.479406i	$0.840852\pi$
$270$	−3.73334	−	1.79788i	−0.227204	−	0.109415i
$271$	0.775056	+	3.39574i	0.0470813	+	0.206277i	0.992998	−	0.118134i	$-0.0376912\pi$
$271$	0.775056	+	3.39574i	0.0470813	+	0.206277i	−0.945916	+	0.324411i	$0.894834\pi$
$272$	18.2638	−	8.79538i	1.10741	−	0.533298i
$273$	−1.22499			−0.0741399
$274$	6.16924	−	2.97095i	0.372697	−	0.179481i
$275$	0.396683	+	0.497425i	0.0239209	+	0.0299958i
$276$	3.89562	+	4.88495i	0.234489	+	0.294039i
$277$	9.16006	−	4.41125i	0.550375	−	0.265047i	−0.137962	−	0.990437i	$-0.544055\pi$
$277$	9.16006	−	4.41125i	0.550375	−	0.265047i	0.688337	+	0.725391i	$0.258341\pi$
$278$	24.8508			1.49045
$279$	3.18178	−	1.53227i	0.190488	−	0.0917343i
$280$	0.434996	+	1.90584i	0.0259960	+	0.113896i
$281$	0.969638	+	0.466953i	0.0578437	+	0.0278561i	0.462582	−	0.886576i	$-0.346923\pi$
$281$	0.969638	+	0.466953i	0.0578437	+	0.0278561i	−0.404738	+	0.914433i	$0.632637\pi$
$282$	−13.0355	−	6.27758i	−0.776255	−	0.373825i
$283$	−2.03116	+	8.89909i	−0.120740	+	0.528996i	0.877993	+	0.478673i	$0.158882\pi$
$283$	−2.03116	+	8.89909i	−0.120740	+	0.528996i	−0.998733	+	0.0503227i	$0.983975\pi$
$284$	−2.79179	−	3.50080i	−0.165662	−	0.207734i
$285$	1.46569	−	1.83792i	0.0868200	−	0.108869i
$286$	4.23919	+	18.5731i	0.250669	+	1.09825i
$287$	−0.198847	+	0.871208i	−0.0117376	+	0.0514258i
$288$	−4.11607	+	5.16139i	−0.242542	+	0.304138i
$289$	0.355162			0.0208919
$290$	6.39619	−	21.3781i	0.375597	−	1.25537i
$291$	15.1681			0.889169
$292$	6.03944	−	7.57322i	0.353432	−	0.443189i
$293$	3.06458	−	13.4268i	0.179035	−	0.784402i	−0.803042	−	0.595922i	$-0.796787\pi$
$293$	3.06458	−	13.4268i	0.179035	−	0.784402i	0.982077	−	0.188480i	$-0.0603562\pi$
$294$	−2.63167	−	11.5301i	−0.153482	−	0.672448i
$295$	−15.5721	+	19.5268i	−0.906644	+	1.13690i
$296$	0.779864	+	0.977918i	0.0453287	+	0.0568403i
$297$	1.40384	−	6.15063i	0.0814591	−	0.356896i
$298$	3.40445	+	1.63949i	0.197214	+	0.0949734i
$299$	−6.78205	−	3.26607i	−0.392216	−	0.188881i
$300$	0.0306572	+	0.134318i	0.00177000	+	0.00775486i
$301$	−8.60121	+	4.14212i	−0.495765	+	0.238748i
$302$	−22.8784			−1.31651
$303$	4.00173	−	1.92713i	0.229893	−	0.110711i
$304$	−3.15783	−	3.95979i	−0.181114	−	0.227109i
$305$	9.08069	+	11.3868i	0.519959	+	0.652008i
$306$	−6.88637	+	3.31630i	−0.393667	+	0.189580i
$307$	3.43747			0.196187			0.0980934	−	0.995177i	$-0.468726\pi$
$307$	3.43747			0.196187			0.0980934	+	0.995177i	$0.468726\pi$
$308$	5.77943	−	2.78323i	0.329314	−	0.158589i
$309$	3.42541	+	15.0077i	0.194865	+	0.853759i
$310$	−13.1843	−	6.34923i	−0.748819	−	0.360612i
$311$	26.9582	+	12.9824i	1.52866	+	0.736163i	0.994049	−	0.108937i	$-0.0347446\pi$
$311$	26.9582	+	12.9824i	1.52866	+	0.736163i	0.534609	+	0.845100i	$0.320459\pi$
$312$	0.425922	−	1.86609i	0.0241131	−	0.105646i
$313$	19.0975	+	23.9476i	1.07946	+	1.35360i	0.931142	+	0.364657i	$0.118814\pi$
$313$	19.0975	+	23.9476i	1.07946	+	1.35360i	0.148315	+	0.988940i	$0.452615\pi$
$314$	−15.0020	+	18.8119i	−0.846613	+	1.06162i
$315$	−0.374047	−	1.63880i	−0.0210751	−	0.0923362i
$316$	−1.94234	+	8.50993i	−0.109265	+	0.478721i
$317$	2.76481	−	3.46696i	0.155287	−	0.194724i	−0.698102	−	0.715998i	$-0.745972\pi$
$317$	2.76481	−	3.46696i	0.155287	−	0.194724i	0.853389	+	0.521274i	$0.174543\pi$
$318$	24.2030			1.35724
$319$	33.8993	+	2.25141i	1.89799	+	0.126055i
$320$	5.37575			0.300514
$321$	4.93600	−	6.18955i	0.275501	−	0.345467i
$322$	−1.38970	+	6.08869i	−0.0774452	+	0.339310i
$323$	−0.964888	−	4.22745i	−0.0536878	−	0.235222i
$324$	0.851774	−	1.06809i	0.0473208	−	0.0593384i
$325$	−0.103489	−	0.129772i	−0.00574056	−	0.00719844i
$326$	−4.44164	+	19.4601i	−0.246000	+	1.07780i
$327$	3.77419	+	1.81755i	0.208713	+	0.100511i
$328$	−1.25801	−	0.605827i	−0.0694622	−	0.0334512i
$329$	−1.30604	−	5.72215i	−0.0720045	−	0.315472i
$330$	−23.5529	+	11.3425i	−1.29654	+	0.624382i
$331$	−12.6242			−0.693891			−0.346946	−	0.937885i	$-0.612781\pi$
$331$	−12.6242			−0.693891			−0.346946	+	0.937885i	$0.612781\pi$
$332$	6.34372	−	3.05498i	0.348157	−	0.167664i
$333$	−0.670593	−	0.840897i	−0.0367482	−	0.0460808i
$334$	−23.1974	−	29.0887i	−1.26931	−	1.59166i
$335$	−13.9949	+	6.73958i	−0.764622	+	0.368223i
$336$	−3.62160			−0.197574
$337$	15.3978	−	7.41521i	0.838774	−	0.403932i	0.0353753	−	0.999374i	$-0.488737\pi$
$337$	15.3978	−	7.41521i	0.838774	−	0.403932i	0.803398	+	0.595442i	$0.203023\pi$
$338$	4.20143	+	18.4077i	0.228528	+	1.00125i
$339$	−9.75279	−	4.69670i	−0.529699	−	0.255090i
$340$	11.5808	+	5.57704i	0.628059	+	0.302458i
$341$	4.95768	−	21.7210i	0.268473	−	1.17626i
$342$	1.19066	+	1.49304i	0.0643834	+	0.0807343i
$343$	6.23961	−	7.82423i	0.336908	−	0.422469i
$344$	−3.31930	−	14.5428i	−0.178965	−	0.784096i
$345$	2.29850	−	10.0704i	0.123747	−	0.542171i
$346$	−0.181830	+	0.228007i	−0.00977522	+	0.0122577i
$347$	5.48266			0.294325			0.147162	−	0.989112i	$-0.452986\pi$
$347$	5.48266			0.294325			0.147162	+	0.989112i	$0.452986\pi$
$348$	6.40222	+	3.62427i	0.343195	+	0.194281i
$349$	−20.4824			−1.09640			−0.548198	−	0.836349i	$-0.684686\pi$
$349$	−20.4824			−1.09640			−0.548198	+	0.836349i	$0.684686\pi$
$350$	−0.0858611	+	0.107666i	−0.00458947	+	0.00575501i
$351$	−0.366244	+	1.60462i	−0.0195487	+	0.0856482i
$352$	9.26769	+	40.6044i	0.493970	+	2.16422i
$353$	−11.7746	+	14.7649i	−0.626699	+	0.785856i	−0.989270	−	0.146100i	$-0.953328\pi$
$353$	−11.7746	+	14.7649i	−0.626699	+	0.785856i	0.362571	+	0.931956i	$0.381899\pi$
$354$	−12.6501	−	15.8627i	−0.672343	−	0.843092i
$355$	−1.64722	+	7.21693i	−0.0874252	+	0.383035i
$356$	−11.4697	−	5.52349i	−0.607890	−	0.292745i
$357$	−2.79356	−	1.34531i	−0.147851	−	0.0712012i
$358$	5.87826	+	25.7543i	0.310676	+	1.36116i
$359$	3.87037	−	1.86387i	0.204270	−	0.0983714i	−0.328952	−	0.944347i	$-0.606695\pi$
$359$	3.87037	−	1.86387i	0.204270	−	0.0983714i	0.533222	+	0.845975i	$0.320981\pi$
$360$	2.62652			0.138430
$361$	16.1423	−	7.77373i	0.849595	−	0.409144i
$362$	14.7983	+	18.5565i	0.777781	+	0.975307i
$363$	−17.9571	−	22.5175i	−0.942505	−	1.18186i
$364$	−1.50778	+	0.726108i	−0.0790291	+	0.0380584i
$365$	−16.0138			−0.838199
$366$	−10.6597	+	5.13343i	−0.557190	+	0.268329i
$367$	−3.04134	−	13.3250i	−0.158757	−	0.695558i	−0.990166	−	0.139898i	$-0.955323\pi$
$367$	−3.04134	−	13.3250i	−0.158757	−	0.695558i	0.831409	−	0.555660i	$-0.187534\pi$
$368$	−20.0507	−	9.65589i	−1.04521	−	0.503348i
$369$	1.08175	+	0.520941i	0.0563135	+	0.0271191i
$370$	−0.991716	+	4.34499i	−0.0515569	+	0.225885i
$371$	6.12162	+	7.67627i	0.317819	+	0.398532i
$372$	3.00805	−	3.77197i	0.155960	−	0.195568i
$373$	−2.78499	−	12.2018i	−0.144201	−	0.631787i	−0.994432	−	0.105377i	$-0.966395\pi$
$373$	−2.78499	−	12.2018i	−0.144201	−	0.631787i	0.850231	−	0.526409i	$-0.176462\pi$
$374$	−10.7300	+	47.0110i	−0.554833	+	2.43088i
$375$	−6.89877	+	8.65078i	−0.356251	+	0.446724i
$376$	9.17092			0.472954
$377$	−8.84388	−	0.587364i	−0.455483	−	0.0302508i
$378$	1.36552			0.0702350
$379$	6.92755	−	8.68688i	0.355845	−	0.446215i	−0.571400	−	0.820672i	$-0.693599\pi$
$379$	6.92755	−	8.68688i	0.355845	−	0.446215i	0.927244	+	0.374457i	$0.122171\pi$
$380$	0.714626	−	3.13098i	0.0366595	−	0.160616i
$381$	1.79567	+	7.86735i	0.0919951	+	0.403057i
$382$	−6.42079	+	8.05141i	−0.328516	+	0.411946i
$383$	9.69544	+	12.1577i	0.495414	+	0.621229i	0.965188	−	0.261557i	$-0.0842360\pi$
$383$	9.69544	+	12.1577i	0.495414	+	0.621229i	−0.469774	+	0.882787i	$0.655665\pi$
$384$	1.96627	−	8.61478i	0.100341	−	0.439621i
$385$	−9.55458	−	4.60124i	−0.486946	−	0.234501i
$386$	−14.9885	−	7.21806i	−0.762892	−	0.367389i
$387$	2.85422	+	12.5051i	0.145088	+	0.635672i
$388$	18.6696	−	8.99081i	0.947806	−	0.456439i
$389$	−0.482991			−0.0244886			−0.0122443	−	0.999925i	$-0.503898\pi$
$389$	−0.482991			−0.0244886			−0.0122443	+	0.999925i	$0.503898\pi$
$390$	6.14464	−	2.95910i	0.311146	−	0.149840i
$391$	−11.8794	−	14.8963i	−0.600769	−	0.753340i
$392$	4.67394	+	5.86094i	0.236070	+	0.296022i
$393$	−16.8524	+	8.11570i	−0.850092	+	0.409383i
$394$	17.6922			0.891318
$395$	13.0014	−	6.26114i	0.654171	−	0.315032i
$396$	−1.91784	−	8.40261i	−0.0963752	−	0.422247i
$397$	7.00415	+	3.37302i	0.351528	+	0.169287i	0.601311	−	0.799015i	$-0.294645\pi$
$397$	7.00415	+	3.37302i	0.351528	+	0.169287i	−0.249783	+	0.968302i	$0.580359\pi$
$398$	−19.6825	−	9.47858i	−0.986593	−	0.475118i
$399$	−0.172384	+	0.755263i	−0.00862998	+	0.0378104i
$400$	−0.305959	−	0.383661i	−0.0152980	−	0.0191830i
$401$	−0.967205	+	1.21284i	−0.0482999	+	0.0605662i	−0.805395	−	0.592739i	$-0.798047\pi$
$401$	−0.967205	+	1.21284i	−0.0482999	+	0.0605662i	0.757095	+	0.653305i	$0.226618\pi$
$402$	−2.80786	−	12.3020i	−0.140043	−	0.613569i
$403$	−1.29339	+	5.66673i	−0.0644286	+	0.282280i
$404$	3.78323	−	4.74401i	0.188222	−	0.236024i
$405$	−2.25851			−0.112226
$406$	1.15763	+	7.26188i	0.0574524	+	0.360401i
$407$	−6.78542			−0.336341
$408$	3.02067	−	3.78780i	0.149546	−	0.187524i
$409$	−2.26265	+	9.91331i	−0.111881	+	0.490182i	0.887678	+	0.460465i	$0.152317\pi$
$409$	−2.26265	+	9.91331i	−0.111881	+	0.490182i	−0.999558	+	0.0297161i	$0.990540\pi$
$410$	−1.10707	−	4.85037i	−0.0546741	−	0.239543i
$411$	2.32694	−	2.91789i	0.114779	−	0.143929i
$412$	13.1119	+	16.4418i	0.645978	+	0.810031i
$413$	1.83148	−	8.02423i	0.0901211	−	0.394846i
$414$	7.56010	+	3.64075i	0.371559	+	0.178933i
$415$	−10.4875	−	5.05050i	−0.514809	−	0.247919i
$416$	−2.41782	−	10.5932i	−0.118543	−	0.519373i
$417$	12.2035	−	5.87689i	0.597607	−	0.287793i
$418$	12.0477			0.589273
$419$	13.5322	−	6.51676i	0.661091	−	0.318364i	−0.0730834	−	0.997326i	$-0.523284\pi$
$419$	13.5322	−	6.51676i	0.661091	−	0.318364i	0.734174	+	0.678961i	$0.237570\pi$
$420$	−1.43179	−	1.79541i	−0.0698641	−	0.0876069i
$421$	−5.34856	−	6.70689i	−0.260673	−	0.326874i	0.634221	−	0.773151i	$-0.281321\pi$
$421$	−5.34856	−	6.70689i	−0.260673	−	0.326874i	−0.894894	+	0.446278i	$0.852749\pi$
$422$	9.57791	−	4.61248i	0.466246	−	0.224532i
$423$	−7.88593			−0.383427
$424$	−13.8221	+	6.65636i	−0.671260	+	0.323262i
$425$	−0.0934873	−	0.409595i	−0.00453480	−	0.0198683i
$426$	−5.41794	−	2.60914i	−0.262500	−	0.126413i
$427$	−4.32426	−	2.08245i	−0.209266	−	0.100777i
$428$	2.40664	−	10.5442i	0.116329	−	0.509673i
$429$	6.47405	+	8.11820i	0.312570	+	0.391950i
$430$	33.1385	−	41.5543i	1.59808	−	2.00393i
$431$	2.09048	+	9.15897i	0.100695	+	0.441172i	0.999993	+	0.00383572i	$0.00122095\pi$
$431$	2.09048	+	9.15897i	0.100695	+	0.441172i	−0.899298	+	0.437336i	$0.855922\pi$
$432$	−1.08277	+	4.74394i	−0.0520950	+	0.228243i
$433$	13.8607	−	17.3808i	0.666102	−	0.835266i	−0.327890	−	0.944716i	$-0.606338\pi$
$433$	13.8607	−	17.3808i	0.666102	−	0.835266i	0.993992	+	0.109450i	$0.0349090\pi$
$434$	4.82237			0.231481
$435$	−1.91466	−	12.0108i	−0.0918011	−	0.575872i
$436$	5.72280			0.274072
$437$	−2.96806	+	3.72183i	−0.141982	+	0.178039i
$438$	2.89474	−	12.6827i	0.138316	−	0.606002i
$439$	0.625294	+	2.73959i	0.0298437	+	0.130754i	0.987655	−	0.156643i	$-0.0500673\pi$
$439$	0.625294	+	2.73959i	0.0298437	+	0.130754i	−0.957812	+	0.287397i	$0.907210\pi$
$440$	10.3314	−	12.9551i	0.492528	−	0.617611i
$441$	−4.01905	−	5.03973i	−0.191383	−	0.239987i
$442$	2.79931	−	12.2646i	0.133150	−	0.583366i
$443$	4.43329	+	2.13496i	0.210632	+	0.101435i	0.536225	−	0.844075i	$-0.319850\pi$
$443$	4.43329	+	2.13496i	0.210632	+	0.101435i	−0.325593	+	0.945510i	$0.605564\pi$
$444$	−1.32384	−	0.637526i	−0.0628265	−	0.0302556i
$445$	4.68314	+	20.5182i	0.222002	+	0.972656i
$446$	17.1617	−	8.26464i	0.812630	−	0.391342i
$447$	2.05954			0.0974130
$448$	−1.59611	+	0.768644i	−0.0754089	+	0.0363150i
$449$	−23.6873	−	29.7029i	−1.11787	−	1.40177i	−0.905378	−	0.424606i	$-0.860413\pi$
$449$	−23.6873	−	29.7029i	−1.11787	−	1.40177i	−0.212494	−	0.977162i	$-0.568159\pi$
$450$	0.115362	+	0.144659i	0.00543822	+	0.00681931i
$451$	6.82452	−	3.28652i	0.321354	−	0.154756i
$452$	−14.7882			−0.695576
$453$	−11.2349	+	5.41045i	−0.527862	+	0.254205i
$454$	−0.570822	−	2.50094i	−0.0267900	−	0.117375i
$455$	2.49267	+	1.20040i	0.116858	+	0.0562758i
$456$	−1.09059	−	0.525201i	−0.0510716	−	0.0245948i
$457$	1.03622	−	4.53998i	0.0484723	−	0.212371i	−0.944892	−	0.327383i	$-0.893833\pi$
$457$	1.03622	−	4.53998i	0.0484723	−	0.212371i	0.993364	+	0.115012i	$0.0366905\pi$
$458$	−7.88300	−	9.88497i	−0.368348	−	0.461894i
$459$	−2.59743	+	3.25707i	−0.121238	+	0.152027i
$460$	−3.14007	−	13.7575i	−0.146406	−	0.641448i
$461$	4.44300	−	19.4661i	0.206931	−	0.906625i	−0.759664	−	0.650316i	$-0.774636\pi$
$461$	4.44300	−	19.4661i	0.206931	−	0.906625i	0.966595	−	0.256309i	$-0.0825064\pi$
$462$	5.37126	−	6.73534i	0.249893	−	0.313357i
$463$	−19.4998			−0.906230			−0.453115	−	0.891452i	$-0.649687\pi$
$463$	−19.4998			−0.906230			−0.453115	+	0.891452i	$0.649687\pi$
$464$	−26.1463	−	1.73650i	−1.21381	−	0.0806150i
$465$	−7.97594			−0.369875
$466$	−0.153236	+	0.192151i	−0.00709850	+	0.00890123i
$467$	−7.69529	+	33.7153i	−0.356095	+	1.56016i	0.406728	+	0.913549i	$0.366670\pi$
$467$	−7.69529	+	33.7153i	−0.356095	+	1.56016i	−0.762824	+	0.646607i	$0.776188\pi$
$468$	0.500340	+	2.19213i	0.0231282	+	0.101331i
$469$	3.19155	−	4.00207i	0.147372	−	0.184799i
$470$	20.3737	+	25.5478i	0.939768	+	1.17843i
$471$	−2.91827	+	12.7858i	−0.134467	+	0.589137i
$472$	11.5869	+	5.57995i	0.533330	+	0.256838i
$473$	72.9076	+	35.1104i	3.35230	+	1.61438i
$474$	2.60853	+	11.4287i	0.119814	+	0.524938i
$475$	−0.0945734	+	0.0455441i	−0.00433932	+	0.00208971i
$476$	−4.23587			−0.194151
$477$	11.8854	−	5.72370i	0.544195	−	0.262070i
$478$	11.8705	+	14.8851i	0.542943	+	0.680829i
$479$	3.84596	+	4.82268i	0.175726	+	0.220354i	0.861893	−	0.507091i	$-0.169279\pi$
$479$	3.84596	+	4.82268i	0.175726	+	0.220354i	−0.686166	+	0.727445i	$0.740708\pi$
$480$	13.4334	−	6.46917i	0.613146	−	0.295276i
$481$	1.77023			0.0807154
$482$	−13.9945	+	6.73937i	−0.637430	+	0.306970i
$483$	0.757454	+	3.31862i	0.0344654	+	0.151003i
$484$	−35.4497	−	17.0717i	−1.61135	−	0.775985i
$485$	−30.8647	−	14.8636i	−1.40149	−	0.674923i
$486$	0.408260	−	1.78870i	0.0185191	−	0.0811373i
$487$	4.08151	+	5.11806i	0.184951	+	0.231921i	0.865660	−	0.500633i	$-0.166899\pi$
$487$	4.08151	+	5.11806i	0.184951	+	0.231921i	−0.680709	+	0.732554i	$0.738328\pi$
$488$	4.67582	−	5.86329i	0.211664	−	0.265419i
$489$	2.42090	+	10.6067i	0.109477	+	0.479650i
$490$	−5.94363	+	26.0408i	−0.268506	+	1.17640i
$491$	11.3529	−	14.2361i	0.512349	−	0.642465i	−0.456616	−	0.889664i	$-0.650939\pi$
$491$	11.3529	−	14.2361i	0.512349	−	0.642465i	0.968965	+	0.247199i	$0.0795100\pi$
$492$	1.64025			0.0739483
$493$	−19.5232	−	11.0520i	−0.879279	−	0.497756i
$494$	−3.14309			−0.141414
$495$	−8.88377	+	11.1399i	−0.399296	+	0.500701i
$496$	−3.82383	+	16.7533i	−0.171695	+	0.752245i
$497$	−0.542829	−	2.37829i	−0.0243492	−	0.106681i
$498$	5.89569	−	7.39296i	0.264192	−	0.331287i
$499$	10.4457	+	13.0985i	0.467614	+	0.586369i	0.958585	−	0.284806i	$-0.0919293\pi$
$499$	10.4457	+	13.0985i	0.467614	+	0.586369i	−0.490971	+	0.871176i	$0.663358\pi$
$500$	−3.36363	+	14.7370i	−0.150426	+	0.659059i
$501$	−18.2707	−	8.79869i	−0.816273	−	0.393096i
$502$	−12.4827	−	6.01137i	−0.557132	−	0.268301i
$503$	−0.739155	−	3.23845i	−0.0329573	−	0.144395i	0.955772	−	0.294108i	$-0.0950224\pi$
$503$	−0.739155	−	3.23845i	−0.0329573	−	0.144395i	−0.988730	+	0.149712i	$0.952165\pi$
$504$	−0.779836	+	0.375549i	−0.0347367	+	0.0167283i
$505$	−10.0313			−0.446389
$506$	47.6952	−	22.9688i	2.12031	−	1.02109i
$507$	6.41637	+	8.04588i	0.284961	+	0.357330i
$508$	6.87354	+	8.61914i	0.304964	+	0.382413i
$509$	−16.9609	+	8.16792i	−0.751777	+	0.362036i	−0.770207	−	0.637794i	$-0.779847\pi$
$509$	−16.9609	+	8.16792i	−0.751777	+	0.362036i	0.0184308	+	0.999830i	$0.494133\pi$
$510$	17.2624			0.764393
$511$	4.75462	−	2.28971i	0.210332	−	0.101291i
$512$	−4.62970	−	20.2840i	−0.204606	−	0.896436i
$513$	0.937782	+	0.451612i	0.0414041	+	0.0199391i
$514$	−35.2253	−	16.9636i	−1.55372	−	0.748232i
$515$	7.73632	−	33.8950i	0.340903	−	1.49359i
$516$	10.9255	+	13.7001i	0.480967	+	0.603114i
$517$	−31.0191	+	38.8967i	−1.36422	+	1.71068i
$518$	−0.326813	−	1.43186i	−0.0143594	−	0.0629125i
$519$	−0.0353704	+	0.154968i	−0.00155259	+	0.00680234i
$520$	−2.69532	+	3.37982i	−0.118198	+	0.148215i
$521$	−3.09335			−0.135522			−0.0677611	−	0.997702i	$-0.521586\pi$
$521$	−3.09335			−0.135522			−0.0677611	+	0.997702i	$0.521586\pi$
$522$	9.85847	+	0.654748i	0.431493	+	0.0286575i
$523$	34.6039			1.51312			0.756561	−	0.653924i	$-0.226878\pi$
$523$	34.6039			1.51312			0.756561	+	0.653924i	$0.226878\pi$
$524$	−15.9322	+	19.9784i	−0.696003	+	0.872760i
$525$	−0.0167021	+	0.0731768i	−0.000728940	+	0.00319370i
$526$	10.5404	+	46.1806i	0.459585	+	2.01357i
$527$	−9.17285	+	11.5024i	−0.399576	+	0.501052i
$528$	19.1401	+	24.0009i	0.832964	+	1.04450i
$529$	0.463462	−	2.03056i	0.0201505	−	0.0882852i
$530$	−49.2494	−	23.7172i	−2.13926	−	1.03021i
$531$	−9.96339	−	4.79811i	−0.432374	−	0.208220i
$532$	0.235500	+	1.03179i	0.0102102	+	0.0447339i
$533$	−1.78043	+	0.857410i	−0.0771190	+	0.0371385i
$534$	−17.0967			−0.739845
$535$	−16.1093	+	7.75783i	−0.696466	+	0.335400i
$536$	4.98686	+	6.25333i	0.215400	+	0.270103i
$537$	8.97720	+	11.2571i	0.387395	+	0.485778i
$538$	−31.5944	+	15.2151i	−1.36213	+	0.655968i
$539$	−40.6669			−1.75165
$540$	−2.77988	+	1.33872i	−0.119627	+	0.0576093i
$541$	−6.17721	−	27.0641i	−0.265579	−	1.16358i	−0.915098	−	0.403232i	$-0.867887\pi$
$541$	−6.17721	−	27.0641i	−0.265579	−	1.16358i	0.649518	−	0.760346i	$-0.274971\pi$
$542$	5.75755	+	2.77269i	0.247308	+	0.119097i
$543$	11.6554	+	5.61293i	0.500180	+	0.240874i
$544$	6.11982	−	26.8127i	0.262385	−	1.14959i
$545$	−5.89881	−	7.39687i	−0.252677	−	0.316847i
$546$	−1.40129	+	1.75716i	−0.0599697	+	0.0751997i
$547$	7.27014	+	31.8526i	0.310849	+	1.36192i	0.853120	+	0.521714i	$0.174707\pi$
$547$	7.27014	+	31.8526i	0.310849	+	1.36192i	−0.542272	+	0.840203i	$0.682436\pi$
$548$	1.13454	−	4.97076i	0.0484653	−	0.212340i
$549$	−4.02066	+	5.04175i	−0.171598	+	0.215177i
$550$	1.16729			0.0497736
$551$	−1.60667	+	5.37000i	−0.0684464	+	0.228769i
$552$	−5.31878			−0.226382
$553$	−2.96498	+	3.71796i	−0.126084	+	0.158104i
$554$	4.15074	−	18.1856i	0.176348	−	0.772631i
$555$	0.540532	+	2.36823i	0.0229443	+	0.100526i
$556$	11.5371	−	14.4671i	0.489284	−	0.613543i
$557$	27.0722	+	33.9474i	1.14708	+	1.43840i	0.880157	+	0.474683i	$0.157437\pi$
$557$	27.0722	+	33.9474i	1.14708	+	1.43840i	0.266928	+	0.963717i	$0.413991\pi$
$558$	1.44178	−	6.31683i	0.0610352	−	0.267413i
$559$	−19.0206	−	9.15986i	−0.804488	−	0.387421i
$560$	7.36939	+	3.54891i	0.311414	+	0.149969i
$561$	5.84833	+	25.6232i	0.246917	+	1.08181i
$562$	1.77900	−	0.856721i	0.0750425	−	0.0361386i
$563$	−0.551999			−0.0232640			−0.0116320	−	0.999932i	$-0.503703\pi$
$563$	−0.551999			−0.0232640			−0.0116320	+	0.999932i	$0.503703\pi$
$564$	−9.70639	+	4.67435i	−0.408713	+	0.196826i
$565$	15.2430	+	19.1141i	0.641277	+	0.804136i
$566$	10.4416	+	13.0934i	0.438895	+	0.550356i
$567$	0.670569	−	0.322929i	0.0281612	−	0.0135617i
$568$	3.81170			0.159935
$569$	25.1874	−	12.1296i	1.05591	−	0.508499i	0.176369	−	0.984324i	$-0.443565\pi$
$569$	25.1874	−	12.1296i	1.05591	−	0.508499i	0.879540	+	0.475825i	$0.157850\pi$
$570$	−0.959732	−	4.20486i	−0.0401988	−	0.176122i
$571$	−29.9930	−	14.4439i	−1.25517	−	0.604457i	−0.316276	−	0.948667i	$-0.602432\pi$
$571$	−29.9930	−	14.4439i	−1.25517	−	0.604457i	−0.938893	+	0.344210i	$0.888147\pi$
$572$	12.7806	+	6.15481i	0.534384	+	0.257346i
$573$	−1.24900	+	5.47224i	−0.0521779	+	0.228606i
$574$	1.02222	+	1.28182i	0.0426667	+	0.0535023i
$575$	−0.287573	+	0.360606i	−0.0119926	+	0.0150383i
$576$	0.529650	+	2.32055i	0.0220688	+	0.0966895i
$577$	−4.30983	+	18.8826i	−0.179421	+	0.786093i	0.802477	+	0.596682i	$0.203515\pi$
$577$	−4.30983	+	18.8826i	−0.179421	+	0.786093i	−0.981898	+	0.189410i	$0.939342\pi$
$578$	0.406277	−	0.509455i	0.0168989	−	0.0211905i
$579$	−9.06736			−0.376827
$580$	−9.47599	−	13.6485i	−0.393469	−	0.566725i
$581$	3.83595			0.159142
$582$	17.3511	−	21.7575i	0.719225	−	0.901879i
$583$	18.5192	−	81.1378i	0.766986	−	3.36038i
$584$	1.83486	+	8.03906i	0.0759271	+	0.332659i
$585$	2.31766	−	2.90626i	0.0958235	−	0.120159i
$586$	−15.7542	−	19.7551i	−0.650799	−	0.816076i
$587$	−1.29711	+	5.68302i	−0.0535376	+	0.234564i	−0.994617	−	0.103623i	$-0.966956\pi$
$587$	−1.29711	+	5.68302i	−0.0535376	+	0.234564i	0.941079	+	0.338187i	$0.109814\pi$
$588$	−7.93412	−	3.82087i	−0.327198	−	0.157570i
$589$	3.31179	+	1.59487i	0.136460	+	0.0657156i
$590$	10.1966	+	44.6742i	0.419787	+	1.83921i
$591$	8.68809	−	4.18397i	0.357380	−	0.172105i
$592$	5.23355			0.215098
$593$	2.04748	−	0.986017i	0.0840801	−	0.0404909i	−0.391371	−	0.920233i	$-0.627999\pi$
$593$	2.04748	−	0.986017i	0.0840801	−	0.0404909i	0.475451	+	0.879742i	$0.342285\pi$
$594$	−7.21676	−	9.04953i	−0.296107	−	0.371307i
$595$	4.36615	+	5.47498i	0.178995	+	0.224452i
$596$	2.53498	−	1.22078i	0.103837	−	0.0500053i
$597$	−11.9070			−0.487323
$598$	−12.4431	+	5.99226i	−0.508835	+	0.245042i
$599$	−6.75720	−	29.6052i	−0.276092	−	1.20964i	−0.902689	−	0.430294i	$-0.858410\pi$
$599$	−6.75720	−	29.6052i	−0.276092	−	1.20964i	0.626597	−	0.779343i	$-0.284447\pi$
$600$	−0.105666	−	0.0508863i	−0.00431381	−	0.00207742i
$601$	−17.9698	−	8.65379i	−0.733003	−	0.352996i	0.0298616	−	0.999554i	$-0.490493\pi$
$601$	−17.9698	−	8.65379i	−0.733003	−	0.352996i	−0.762864	+	0.646559i	$0.776208\pi$
$602$	−3.89750	+	17.0761i	−0.158850	+	0.695969i
$603$	−4.28813	−	5.37714i	−0.174626	−	0.218974i
$604$	−10.6215	+	13.3189i	−0.432181	+	0.541938i
$605$	14.4744	+	63.4164i	0.588467	+	2.57824i
$606$	1.81332	−	7.94468i	0.0736612	−	0.322731i
$607$	21.1629	−	26.5375i	0.858977	−	1.07712i	−0.137267	−	0.990534i	$-0.543832\pi$
$607$	21.1629	−	26.5375i	0.858977	−	1.07712i	0.996244	−	0.0865894i	$-0.0275968\pi$
$608$	−6.87141			−0.278672
$609$	2.28582	+	3.29233i	0.0926261	+	0.133412i
$610$	26.7212			1.08191
$611$	8.09248	−	10.1477i	0.327387	−	0.410530i
$612$	−1.26643	+	5.54858i	−0.0511923	+	0.224288i
$613$	−5.90946	−	25.8910i	−0.238681	−	1.04573i	−0.942200	−	0.335052i	$-0.891246\pi$
$613$	−5.90946	−	25.8910i	−0.238681	−	1.04573i	0.703519	−	0.710677i	$-0.251611\pi$
$614$	3.93219	−	4.93081i	0.158690	−	0.198991i
$615$	−1.69070	−	2.12007i	−0.0681755	−	0.0854894i
$616$	−1.21510	+	5.32369i	−0.0489577	+	0.214498i
$617$	0.763697	+	0.367777i	0.0307453	+	0.0148062i	0.449193	−	0.893435i	$-0.351711\pi$
$617$	0.763697	+	0.367777i	0.0307453	+	0.0148062i	−0.418448	+	0.908241i	$0.637426\pi$
$618$	25.4459	+	12.2541i	1.02358	+	0.492932i
$619$	−9.82554	−	43.0485i	−0.394922	−	1.73027i	−0.646938	−	0.762543i	$-0.723951\pi$
$619$	−9.82554	−	43.0485i	−0.394922	−	1.73027i	0.252016	−	0.967723i	$-0.418906\pi$
$620$	−9.81718	+	4.72770i	−0.394267	+	0.189869i
$621$	4.57353			0.183530
$622$	49.4603	−	23.8188i	1.98318	−	0.955047i
$623$	−4.32423	−	5.42241i	−0.173246	−	0.217244i
$624$	−4.99339	−	6.26152i	−0.199896	−	0.250661i
$625$	22.9694	−	11.0615i	0.918775	−	0.442458i
$626$	56.1972			2.24609
$627$	5.91628	−	2.84913i	0.236273	−	0.113783i
$628$	3.98676	+	17.4671i	0.159089	+	0.697015i
$629$	4.03695	+	1.94409i	0.160964	+	0.0775161i
$630$	−2.77863	−	1.33812i	−0.110703	−	0.0533119i
$631$	1.04715	−	4.58785i	0.0416862	−	0.182639i	−0.949798	−	0.312862i	$-0.898712\pi$
$631$	1.04715	−	4.58785i	0.0416862	−	0.182639i	0.991485	+	0.130223i	$0.0415693\pi$
$632$	−4.63285	−	5.80941i	−0.184285	−	0.231086i
$633$	3.61264	−	4.53011i	0.143589	−	0.180056i
$634$	−1.81039	−	7.93185i	−0.0718999	−	0.315014i
$635$	4.05554	−	17.7685i	0.160939	−	0.705120i
$636$	11.2364	−	14.0900i	0.445553	−	0.558706i
$637$	10.6095			0.420362
$638$	42.0075	−	46.0507i	1.66309	−	1.82316i
$639$	−3.27762			−0.129661
$640$	−12.4429	+	15.6029i	−0.491850	+	0.616760i
$641$	−5.84782	+	25.6210i	−0.230975	+	1.01197i	0.717858	+	0.696190i	$0.245123\pi$
$641$	−5.84782	+	25.6210i	−0.230975	+	1.01197i	−0.948833	+	0.315778i	$0.897734\pi$
$642$	−3.23208	−	14.1607i	−0.127560	−	0.558878i
$643$	−13.3662	+	16.7607i	−0.527111	+	0.660976i	−0.972102	−	0.234559i	$-0.924636\pi$
$643$	−13.3662	+	16.7607i	−0.527111	+	0.660976i	0.444991	+	0.895535i	$0.353207\pi$
$644$	2.89941	+	3.63575i	0.114253	+	0.143268i
$645$	6.44626	−	28.2429i	0.253821	−	1.11206i
$646$	−7.16774	−	3.45180i	−0.282011	−	0.135809i
$647$	−28.2997	−	13.6284i	−1.11258	−	0.535788i	−0.214985	−	0.976617i	$-0.568970\pi$
$647$	−28.2997	−	13.6284i	−1.11258	−	0.535788i	−0.897591	+	0.440829i	$0.854685\pi$
$648$	0.258780	+	1.13379i	0.0101658	+	0.0445395i
$649$	−62.8570	+	30.2704i	−2.46735	+	1.18822i
$650$	−0.304532			−0.0119447
$651$	2.36812	−	1.14043i	0.0928140	−	0.0446969i
$652$	9.26682	+	11.6202i	0.362917	+	0.455083i
$653$	−21.5031	−	26.9641i	−0.841483	−	1.05519i	−0.997722	−	0.0674669i	$-0.978508\pi$
$653$	−21.5031	−	26.9641i	−0.841483	−	1.05519i	0.156239	−	0.987719i	$-0.450063\pi$
$654$	6.92452	−	3.33467i	0.270770	−	0.130396i
$655$	42.2448			1.65064
$656$	−5.26371	+	2.53487i	−0.205514	+	0.0989701i
$657$	−1.57777	−	6.91266i	−0.0615546	−	0.269689i
$658$	−9.70202	−	4.67225i	−0.378224	−	0.182143i
$659$	−21.3410	−	10.2773i	−0.831326	−	0.400346i	−0.0307137	−	0.999528i	$-0.509778\pi$
$659$	−21.3410	−	10.2773i	−0.831326	−	0.400346i	−0.800612	+	0.599183i	$0.795492\pi$
$660$	−4.33146	+	18.9774i	−0.168602	+	0.738692i
$661$	−19.9534	−	25.0208i	−0.776099	−	0.973197i	0.223900	−	0.974612i	$-0.428121\pi$
$661$	−19.9534	−	25.0208i	−0.776099	−	0.973197i	−0.999999	+	0.00141483i	$0.999550\pi$
$662$	−14.4411	+	18.1086i	−0.561270	+	0.703810i
$663$	−1.52575	−	6.68477i	−0.0592554	−	0.259615i
$664$	−1.33374	+	5.84348i	−0.0517590	+	0.226771i
$665$	1.09088	−	1.36792i	0.0423024	−	0.0530456i
$666$	−1.97331			−0.0764642
$667$	3.87725	+	24.3221i	0.150128	+	0.941757i
$668$	−27.7038			−1.07189
$669$	6.47312	−	8.11704i	0.250265	−	0.313823i
$670$	−6.34156	+	27.7842i	−0.244996	+	1.07340i
$671$	9.05287	+	39.6632i	0.349482	+	1.53118i
$672$	−3.06349	+	3.84150i	−0.118177	+	0.148189i
$673$	7.45946	+	9.35386i	0.287541	+	0.360565i	0.904532	−	0.426405i	$-0.140220\pi$
$673$	7.45946	+	9.35386i	0.287541	+	0.360565i	−0.616991	+	0.786970i	$0.711649\pi$
$674$	6.97729	−	30.5695i	0.268755	−	1.17749i
$675$	0.0908609	+	0.0437563i	0.00349724	+	0.00168418i
$676$	12.6667	+	6.09998i	0.487182	+	0.234615i
$677$	8.91349	+	39.0526i	0.342573	+	1.50091i	0.793621	+	0.608412i	$0.208193\pi$
$677$	8.91349	+	39.0526i	0.342573	+	1.50091i	−0.451048	+	0.892500i	$0.648950\pi$
$678$	−17.8935	+	8.61705i	−0.687195	+	0.330936i
$679$	11.2892			0.433241
$680$	−9.85837	+	4.74754i	−0.378051	+	0.182060i
$681$	−0.871753	−	1.09314i	−0.0334056	−	0.0418893i
$682$	−25.4861	−	31.9585i	−0.975912	−	1.22376i
$683$	18.7031	−	9.00695i	0.715655	−	0.344641i	−0.0403691	−	0.999185i	$-0.512853\pi$
$683$	18.7031	−	9.00695i	0.715655	−	0.344641i	0.756024	+	0.654543i	$0.227139\pi$
$684$	1.42196			0.0543699
$685$	−7.59428	+	3.65721i	−0.290162	+	0.139735i
$686$	−4.08569	−	17.9006i	−0.155992	−	0.683447i
$687$	−6.20877	−	2.98999i	−0.236879	−	0.114075i
$688$	−56.2332	−	27.0805i	−2.14387	−	1.03243i
$689$	−4.83141	+	21.1678i	−0.184062	+	0.806429i
$690$	−11.8159	−	14.8167i	−0.449825	−	0.564063i
$691$	2.08045	−	2.60881i	0.0791442	−	0.0992437i	−0.740683	−	0.671855i	$-0.765498\pi$
$691$	2.08045	−	2.60881i	0.0791442	−	0.0992437i	0.819827	+	0.572611i	$0.194069\pi$
$692$	0.0483209	+	0.211708i	0.00183688	+	0.00804792i
$693$	1.04484	−	4.57776i	0.0396903	−	0.173895i
$694$	6.27173	−	7.86449i	0.238071	−	0.298532i
$695$	−30.5911			−1.16039
$696$	−5.81013	+	2.33738i	−0.220232	+	0.0885980i
$697$	−5.00184			−0.189458
$698$	−23.4302	+	29.3805i	−0.886845	+	1.11207i
$699$	−0.0298081	+	0.130598i	−0.00112745	+	0.00493967i
$700$	0.0228174	+	0.0999697i	0.000862418	+	0.00377850i
$701$	14.9843	−	18.7898i	0.565951	−	0.709680i	−0.413695	−	0.910416i	$-0.635762\pi$
$701$	14.9843	−	18.7898i	0.565951	−	0.709680i	0.979645	+	0.200736i	$0.0643334\pi$
$702$	1.88276	+	2.36091i	0.0710602	+	0.0891067i
$703$	0.249111	−	1.09142i	0.00939538	−	0.0411639i
$704$	13.5293	+	6.51536i	0.509904	+	0.245557i
$705$	16.0466	+	7.72765i	0.604351	+	0.291040i
$706$	7.70999	+	33.7797i	0.290169	+	1.27132i
$707$	2.97839	−	1.43432i	0.112014	−	0.0539430i
$708$	−15.1075			−0.567774
$709$	42.6554	−	20.5417i	1.60196	−	0.771461i	0.602315	−	0.798258i	$-0.294245\pi$
$709$	42.6554	−	20.5417i	1.60196	−	0.771461i	0.999641	+	0.0267971i	$0.00853079\pi$
$710$	8.46789	+	10.6184i	0.317794	+	0.398502i
$711$	3.98371	+	4.99542i	0.149401	+	0.187343i
$712$	9.76372	−	4.70196i	0.365911	−	0.176213i
$713$	16.1515			0.604878
$714$	−5.12535	+	2.46824i	−0.191811	+	0.0923715i
$715$	−5.21841	−	22.8634i	−0.195158	−	0.855041i
$716$	17.7221	+	8.53454i	0.662308	+	0.318951i
$717$	9.34938	+	4.50242i	0.349159	+	0.168146i
$718$	1.75380	−	7.68389i	0.0654512	−	0.286760i
$719$	18.0229	+	22.6001i	0.672142	+	0.842840i	0.994604	−	0.103743i	$-0.0330819\pi$
$719$	18.0229	+	22.6001i	0.672142	+	0.842840i	−0.322462	+	0.946582i	$0.604510\pi$
$720$	6.85200	−	8.59214i	0.255359	−	0.320210i
$721$	2.54945	+	11.1699i	0.0949465	+	0.415988i
$722$	7.31464	−	32.0475i	0.272223	−	1.19269i
$723$	−5.27849	+	6.61901i	−0.196309	+	0.246164i
$724$	17.6730			0.656813
$725$	−0.155669	+	0.520295i	−0.00578140	+	0.0193233i
$726$	−52.8413			−1.96113
$727$	2.28644	−	2.86711i	0.0847994	−	0.106335i	−0.737622	−	0.675214i	$-0.764051\pi$
$727$	2.28644	−	2.86711i	0.0847994	−	0.106335i	0.822421	+	0.568879i	$0.192623\pi$
$728$	0.317003	−	1.38888i	0.0117489	−	0.0514754i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−18.3185	+	22.9706i	−0.677997	+	0.850181i
$731$	−33.3165	−	41.7776i	−1.23226	−	1.54520i
$732$	−1.96035	+	8.58887i	−0.0724567	+	0.317454i
$733$	37.0632	+	17.8487i	1.36896	+	0.659257i	0.966616	−	0.256231i	$-0.0824808\pi$
$733$	37.0632	+	17.8487i	1.36896	+	0.659257i	0.402345	+	0.915488i	$0.368195\pi$
$734$	−22.5928	−	10.8801i	−0.833915	−	0.401592i
$735$	3.23956	+	14.1934i	0.119493	+	0.523533i
$736$	−27.2029	+	13.1002i	−1.00271	+	0.482881i
$737$	−43.3896			−1.59827
$738$	1.98468	−	0.955773i	0.0730572	−	0.0351825i
$739$	26.7814	+	33.5828i	0.985168	+	1.23536i	0.971886	+	0.235450i	$0.0756563\pi$
$739$	26.7814	+	33.5828i	0.985168	+	1.23536i	0.0132816	+	0.999912i	$0.495772\pi$
$740$	2.06907	+	2.59453i	0.0760605	+	0.0953768i
$741$	−1.54348	+	0.743301i	−0.0567012	+	0.0273058i
$742$	18.0137			0.661304
$743$	−25.4955	+	12.2780i	−0.935340	+	0.450436i	−0.838523	−	0.544866i	$-0.816580\pi$
$743$	−25.4955	+	12.2780i	−0.935340	+	0.450436i	−0.0968168	+	0.995302i	$0.530866\pi$
$744$	0.913885	+	4.00399i	0.0335046	+	0.146793i
$745$	−4.19084	−	2.01820i	−0.153541	−	0.0739413i
$746$	−20.6885	−	9.96304i	−0.757458	−	0.364773i
$747$	1.14686	−	5.02472i	0.0419614	−	0.183845i
$748$	22.3865	+	28.0717i	0.818530	+	1.02640i
$749$	3.67374	−	4.60673i	0.134236	−	0.168326i
$750$	4.51730	+	19.7916i	0.164949	+	0.722687i
$751$	−11.6033	+	50.8373i	−0.423410	+	1.85508i	0.0885513	+	0.996072i	$0.471776\pi$
$751$	−11.6033	+	50.8373i	−0.423410	+	1.85508i	−0.511961	+	0.859009i	$0.671081\pi$
$752$	23.9249	−	30.0008i	0.872450	−	1.09402i
$753$	−7.55152			−0.275193
$754$	−10.9592	+	12.0140i	−0.399111	+	0.437525i
$755$	28.1631			1.02496
$756$	0.633954	−	0.794953i	0.0230567	−	0.0289122i
$757$	9.09782	−	39.8602i	0.330666	−	1.44874i	−0.487179	−	0.873302i	$-0.661974\pi$
$757$	9.09782	−	39.8602i	0.330666	−	1.44874i	0.817844	−	0.575439i	$-0.195169\pi$
$758$	−4.53615	−	19.8742i	−0.164760	−	0.721863i
$759$	17.9899	−	22.5586i	0.652991	−	0.818825i
$760$	1.70452	+	2.13740i	0.0618295	+	0.0775317i
$761$	2.91709	−	12.7806i	0.105744	−	0.463296i	−0.894136	−	0.447796i	$-0.852209\pi$
$761$	2.91709	−	12.7806i	0.105744	−	0.463296i	0.999880	−	0.0154996i	$-0.00493387\pi$
$762$	13.3393	+	6.42385i	0.483231	+	0.232712i
$763$	2.80903	+	1.35276i	0.101694	+	0.0489732i
$764$	1.70631	+	7.47584i	0.0617322	+	0.270467i
$765$	8.47706	−	4.08234i	0.306489	−	0.147597i

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)

\(f(q)\)	\(=\)	\(q+(1.14392 - 1.43443i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.303995 - 1.33189i) q^{4} +(-1.40816 + 1.76577i) q^{5} +(-1.14392 - 1.43443i) q^{6} +(0.165617 - 0.725615i) q^{7} +(1.04778 + 0.504584i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(1.14392 - 1.43443i) q^{2} +(0.222521 - 0.974928i) q^{3} +(-0.303995 - 1.33189i) q^{4} +(-1.40816 + 1.76577i) q^{5} +(-1.14392 - 1.43443i) q^{6} +(0.165617 - 0.725615i) q^{7} +(1.04778 + 0.504584i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.922058 + 4.03980i) q^{10} +(-5.68404 + 2.73729i) q^{11} -1.36614 q^{12} +(1.48289 - 0.714123i) q^{13} +(-0.851391 - 1.06761i) q^{14} +(1.40816 + 1.76577i) q^{15} +(4.38406 - 2.11125i) q^{16} +4.16595 q^{17} +(-1.65301 + 0.796048i) q^{18} +(-0.231613 - 1.01476i) q^{19} +(2.77988 + 1.33872i) q^{20} +(-0.670569 - 0.322929i) q^{21} +(-2.57563 + 11.2846i) q^{22} +(-2.85155 - 3.57573i) q^{23} +(0.725086 - 0.909229i) q^{24} +(-0.0224408 - 0.0983195i) q^{25} +(0.671949 - 2.94400i) q^{26} +(-0.623490 + 0.781831i) q^{27} -1.01678 q^{28} +(-4.68636 - 2.65293i) q^{29} +4.14369 q^{30} +(-2.20186 + 2.76105i) q^{31} +(1.46901 - 6.43615i) q^{32} +(1.40384 + 6.15063i) q^{33} +(4.76551 - 5.97577i) q^{34} +(1.04806 + 1.31422i) q^{35} +(-0.303995 + 1.33189i) q^{36} +(0.969034 + 0.466662i) q^{37} +(-1.72055 - 0.828574i) q^{38} +(-0.366244 - 1.60462i) q^{39} +(-2.36642 + 1.13961i) q^{40} -1.20065 q^{41} +(-1.23030 + 0.592479i) q^{42} +(-7.99734 - 10.0283i) q^{43} +(5.37367 + 6.73837i) q^{44} +(2.03484 - 0.979929i) q^{45} -8.39108 q^{46} +(7.10498 - 3.42158i) q^{47} +(-1.08277 - 4.74394i) q^{48} +(5.80769 + 2.79684i) q^{49} +(-0.166703 - 0.0802799i) q^{50} +(0.927012 - 4.06150i) q^{51} +(-1.40192 - 1.75795i) q^{52} +(-8.22494 + 10.3138i) q^{53} +(0.408260 + 1.78870i) q^{54} +(3.17058 - 13.8912i) q^{55} +(0.539663 - 0.676716i) q^{56} -1.04086 q^{57} +(-9.16625 + 3.68752i) q^{58} +11.0585 q^{59} +(1.92374 - 2.41229i) q^{60} +(1.43496 - 6.28696i) q^{61} +(1.44178 + 6.31683i) q^{62} +(-0.464048 + 0.581898i) q^{63} +(-1.48405 - 1.86094i) q^{64} +(-0.827164 + 3.62404i) q^{65} +(10.4285 + 5.02211i) q^{66} +(6.19652 + 2.98409i) q^{67} +(-1.26643 - 5.54858i) q^{68} +(-4.12061 + 1.98438i) q^{69} +3.08405 q^{70} +(2.95303 - 1.42211i) q^{71} +(-0.725086 - 0.909229i) q^{72} +(4.42081 + 5.54352i) q^{73} +(1.77789 - 0.856187i) q^{74} -0.100848 q^{75} +(-1.28114 + 0.616965i) q^{76} +(1.04484 + 4.57776i) q^{77} +(-2.72067 - 1.31020i) q^{78} +(-5.75663 - 2.77225i) q^{79} +(-2.44545 + 10.7142i) q^{80} +(0.623490 + 0.781831i) q^{81} +(-1.37344 + 1.72224i) q^{82} +(1.14686 + 5.02472i) q^{83} +(-0.226256 + 0.991291i) q^{84} +(-5.86631 + 7.35612i) q^{85} -23.5333 q^{86} +(-3.62923 + 3.97853i) q^{87} -7.33681 q^{88} +(5.80998 - 7.28549i) q^{89} +(0.922058 - 4.03980i) q^{90} +(-0.272586 - 1.19428i) q^{91} +(-3.89562 + 4.88495i) q^{92} +(2.20186 + 2.76105i) q^{93} +(3.21951 - 14.1056i) q^{94} +(2.11798 + 1.01997i) q^{95} +(-5.94790 - 2.86436i) q^{96} +(3.37522 + 14.7878i) q^{97} +(10.6554 - 5.13137i) q^{98} +6.30880 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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