LMFDB - Embedded newform 87.2.g.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.3
Root			$2.87569 + 1.38486i$ of defining polynomial
Character	$\chi$	$=$	87.25
Dual form			87.2.g.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.487716 - 2.13682i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-2.52621 - 1.21656i) q^{4} +(0.533332 - 2.33668i) q^{5} +(0.487716 + 2.13682i) q^{6} +(-1.21803 + 0.586571i) q^{7} +(-1.09855 + 1.37753i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})$	\(q+(0.487716 - 2.13682i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-2.52621 - 1.21656i) q^{4} +(0.533332 - 2.33668i) q^{5} +(0.487716 + 2.13682i) q^{6} +(-1.21803 + 0.586571i) q^{7} +(-1.09855 + 1.37753i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-4.73296 - 2.27927i) q^{10} +(2.18816 + 2.74387i) q^{11} +2.80388 q^{12} +(3.76255 + 4.71809i) q^{13} +(0.659347 + 2.88879i) q^{14} +(0.533332 + 2.33668i) q^{15} +(-1.08862 - 1.36508i) q^{16} +3.05437 q^{17} +(-1.36655 - 1.71360i) q^{18} +(-5.07762 - 2.44525i) q^{19} +(-4.19002 + 5.25412i) q^{20} +(0.842900 - 1.05696i) q^{21} +(6.93036 - 3.33749i) q^{22} +(-0.225809 - 0.989335i) q^{23} +(0.392066 - 1.71776i) q^{24} +(-0.670784 - 0.323033i) q^{25} +(11.9168 - 5.73883i) q^{26} +(-0.222521 + 0.974928i) q^{27} +3.79059 q^{28} +(-5.14766 - 1.58164i) q^{29} +5.25319 q^{30} +(-1.80501 + 7.90829i) q^{31} +(-6.62277 + 3.18936i) q^{32} +(-3.16198 - 1.52273i) q^{33} +(1.48967 - 6.52665i) q^{34} +(0.721015 + 3.15897i) q^{35} +(-2.52621 + 1.21656i) q^{36} +(3.42698 - 4.29729i) q^{37} +(-7.70151 + 9.65739i) q^{38} +(-5.43705 - 2.61834i) q^{39} +(2.63296 + 3.30163i) q^{40} -6.85782 q^{41} +(-1.84745 - 2.31663i) q^{42} +(1.73610 + 7.60636i) q^{43} +(-2.18968 - 9.59361i) q^{44} +(-1.49436 - 1.87387i) q^{45} -2.22416 q^{46} +(-0.260777 - 0.327004i) q^{47} +(1.57310 + 0.757565i) q^{48} +(-3.22491 + 4.04390i) q^{49} +(-1.01742 + 1.27580i) q^{50} +(-2.75189 + 1.32524i) q^{51} +(-3.76517 - 16.4963i) q^{52} +(2.96899 - 13.0080i) q^{53} +(1.97472 + 0.950976i) q^{54} +(7.57855 - 3.64964i) q^{55} +(0.530037 - 2.32225i) q^{56} +5.63574 q^{57} +(-5.89028 + 10.2283i) q^{58} +3.56102 q^{59} +(1.49540 - 6.55177i) q^{60} +(-6.49557 + 3.12810i) q^{61} +(16.0183 + 7.71400i) q^{62} +(-0.300828 + 1.31801i) q^{63} +(2.80802 + 12.3027i) q^{64} +(13.0314 - 6.27557i) q^{65} +(-4.79596 + 6.01394i) q^{66} +(5.18318 - 6.49950i) q^{67} +(-7.71599 - 3.71582i) q^{68} +(0.632703 + 0.793385i) q^{69} +7.10182 q^{70} +(-6.10196 - 7.65161i) q^{71} +(0.392066 + 1.71776i) q^{72} +(0.0675863 + 0.296115i) q^{73} +(-7.51117 - 9.41871i) q^{74} +0.744514 q^{75} +(9.85235 + 12.3545i) q^{76} +(-4.27471 - 2.05859i) q^{77} +(-8.24668 + 10.3410i) q^{78} +(2.49794 - 3.13231i) q^{79} +(-3.77036 + 1.81571i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-3.34467 + 14.6540i) q^{82} +(3.88709 + 1.87192i) q^{83} +(-3.41520 + 1.64468i) q^{84} +(1.62899 - 7.13709i) q^{85} +17.1002 q^{86} +(5.32413 - 0.808479i) q^{87} -6.18356 q^{88} +(-3.11361 + 13.6416i) q^{89} +(-4.73296 + 2.27927i) q^{90} +(-7.35039 - 3.53976i) q^{91} +(-0.633143 + 2.77398i) q^{92} +(-1.80501 - 7.90829i) q^{93} +(-0.825935 + 0.397749i) q^{94} +(-8.42183 + 10.5606i) q^{95} +(4.58310 - 5.74702i) q^{96} +(3.42690 + 1.65031i) q^{97} +(7.06827 + 8.86333i) q^{98} +3.50954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.487716	−	2.13682i	0.344867	−	1.51096i	−0.443791	−	0.896130i	$-0.646367\pi$
$2$	0.487716	−	2.13682i	0.344867	−	1.51096i	0.788658	−	0.614832i	$-0.210776\pi$
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$4$	−2.52621	−	1.21656i	−1.26311	−	0.608280i
$5$	0.533332	−	2.33668i	0.238513	−	1.04499i	−0.703836	−	0.710363i	$-0.748531\pi$
$5$	0.533332	−	2.33668i	0.238513	−	1.04499i	0.942349	−	0.334632i	$-0.108612\pi$
$6$	0.487716	+	2.13682i	0.199109	+	0.872355i
$7$	−1.21803	+	0.586571i	−0.460371	+	0.221703i	−0.649670	−	0.760217i	$-0.725093\pi$
$7$	−1.21803	+	0.586571i	−0.460371	+	0.221703i	0.189299	+	0.981920i	$0.439378\pi$
$8$	−1.09855	+	1.37753i	−0.388395	+	0.487031i
$9$	0.623490	−	0.781831i	0.207830	−	0.260610i
$10$	−4.73296	−	2.27927i	−1.49669	−	0.720769i
$11$	2.18816	+	2.74387i	0.659755	+	0.827307i	0.993317	−	0.115421i	$-0.0368218\pi$
$11$	2.18816	+	2.74387i	0.659755	+	0.827307i	−0.333561	+	0.942728i	$0.608250\pi$
$12$	2.80388			0.809411
$13$	3.76255	+	4.71809i	1.04354	+	1.30856i	0.949763	+	0.312971i	$0.101324\pi$
$13$	3.76255	+	4.71809i	1.04354	+	1.30856i	0.0937822	+	0.995593i	$0.470104\pi$
$14$	0.659347	+	2.88879i	0.176218	+	0.772061i
$15$	0.533332	+	2.33668i	0.137706	+	0.603328i
$16$	−1.08862	−	1.36508i	−0.272155	−	0.341271i
$17$	3.05437			0.740794			0.370397	−	0.928874i	$-0.379222\pi$
$17$	3.05437			0.740794			0.370397	+	0.928874i	$0.379222\pi$
$18$	−1.36655	−	1.71360i	−0.322099	−	0.403899i
$19$	−5.07762	−	2.44525i	−1.16489	−	0.560980i	−0.251414	−	0.967880i	$-0.580895\pi$
$19$	−5.07762	−	2.44525i	−1.16489	−	0.560980i	−0.913473	+	0.406900i	$0.866610\pi$
$20$	−4.19002	+	5.25412i	−0.936916	+	1.17486i
$21$	0.842900	−	1.05696i	0.183936	−	0.230648i
$22$	6.93036	−	3.33749i	1.47756	−	0.711555i
$23$	−0.225809	−	0.989335i	−0.0470845	−	0.206291i	0.945914	−	0.324417i	$-0.105168\pi$
$23$	−0.225809	−	0.989335i	−0.0470845	−	0.206291i	−0.992999	+	0.118127i	$0.962311\pi$
$24$	0.392066	−	1.71776i	0.0800302	−	0.350635i
$25$	−0.670784	−	0.323033i	−0.134157	−	0.0646065i
$26$	11.9168	−	5.73883i	2.33708	−	1.12548i
$27$	−0.222521	+	0.974928i	−0.0428242	+	0.187625i
$28$	3.79059			0.716354
$29$	−5.14766	−	1.58164i	−0.955897	−	0.293703i
$29$	−5.14766	−	1.58164i	−0.955897	−	0.293703i
$30$	5.25319			0.959096
$31$	−1.80501	+	7.90829i	−0.324190	+	1.42037i	0.505828	+	0.862634i	$0.331187\pi$
$31$	−1.80501	+	7.90829i	−0.324190	+	1.42037i	−0.830018	+	0.557736i	$0.811670\pi$
$32$	−6.62277	+	3.18936i	−1.17075	+	0.563804i
$33$	−3.16198	−	1.52273i	−0.550431	−	0.265074i
$34$	1.48967	−	6.52665i	0.255476	−	1.11931i
$35$	0.721015	+	3.15897i	0.121874	+	0.533964i
$36$	−2.52621	+	1.21656i	−0.421035	+	0.202760i
$37$	3.42698	−	4.29729i	0.563392	−	0.706471i	−0.415789	−	0.909461i	$-0.636495\pi$
$37$	3.42698	−	4.29729i	0.563392	−	0.706471i	0.979181	+	0.202990i	$0.0650660\pi$
$38$	−7.70151	+	9.65739i	−1.24935	+	1.56664i
$39$	−5.43705	−	2.61834i	−0.870625	−	0.419271i
$40$	2.63296	+	3.30163i	0.416308	+	0.522034i
$41$	−6.85782			−1.07101			−0.535506	−	0.844531i	$-0.679879\pi$
$41$	−6.85782			−1.07101			−0.535506	+	0.844531i	$0.679879\pi$
$42$	−1.84745	−	2.31663i	−0.285068	−	0.357463i
$43$	1.73610	+	7.60636i	0.264753	+	1.15996i	0.916027	+	0.401116i	$0.131378\pi$
$43$	1.73610	+	7.60636i	0.264753	+	1.15996i	−0.651274	+	0.758843i	$0.725765\pi$
$44$	−2.18968	−	9.59361i	−0.330107	−	1.44629i
$45$	−1.49436	−	1.87387i	−0.222766	−	0.279340i
$46$	−2.22416			−0.327935
$47$	−0.260777	−	0.327004i	−0.0380382	−	0.0476984i	0.762449	−	0.647049i	$-0.223997\pi$
$47$	−0.260777	−	0.327004i	−0.0380382	−	0.0476984i	−0.800487	+	0.599350i	$0.795426\pi$
$48$	1.57310	+	0.757565i	0.227057	+	0.109345i
$49$	−3.22491	+	4.04390i	−0.460701	+	0.577700i
$50$	−1.01742	+	1.27580i	−0.143884	+	0.180425i
$51$	−2.75189	+	1.32524i	−0.385342	+	0.185571i
$52$	−3.76517	−	16.4963i	−0.522135	−	2.28762i
$53$	2.96899	−	13.0080i	0.407821	−	1.78678i	−0.186392	−	0.982475i	$-0.559680\pi$
$53$	2.96899	−	13.0080i	0.407821	−	1.78678i	0.594214	−	0.804307i	$-0.297463\pi$
$54$	1.97472	+	0.950976i	0.268726	+	0.129411i
$55$	7.57855	−	3.64964i	1.02189	−	0.492117i
$56$	0.530037	−	2.32225i	0.0708292	−	0.310323i
$57$	5.63574			0.746471
$58$	−5.89028	+	10.2283i	−0.773432	+	1.34304i
$59$	3.56102			0.463606			0.231803	−	0.972763i	$-0.425538\pi$
$59$	3.56102			0.463606			0.231803	+	0.972763i	$0.425538\pi$
$60$	1.49540	−	6.55177i	0.193055	−	0.845830i
$61$	−6.49557	+	3.12810i	−0.831672	+	0.400512i	−0.800742	−	0.599009i	$-0.795561\pi$
$61$	−6.49557	+	3.12810i	−0.831672	+	0.400512i	−0.0309301	+	0.999522i	$0.509847\pi$
$62$	16.0183	+	7.71400i	2.03432	+	0.979679i
$63$	−0.300828	+	1.31801i	−0.0379007	+	0.166054i
$64$	2.80802	+	12.3027i	0.351002	+	1.53784i
$65$	13.0314	−	6.27557i	1.61634	−	0.778389i
$66$	−4.79596	+	6.01394i	−0.590342	+	0.740265i
$67$	5.18318	−	6.49950i	0.633226	−	0.794040i	−0.356912	−	0.934138i	$-0.616170\pi$
$67$	5.18318	−	6.49950i	0.633226	−	0.794040i	0.990138	+	0.140098i	$0.0447418\pi$
$68$	−7.71599	−	3.71582i	−0.935701	−	0.450610i
$69$	0.632703	+	0.793385i	0.0761685	+	0.0955123i
$70$	7.10182			0.848830
$71$	−6.10196	−	7.65161i	−0.724169	−	0.908079i	0.274397	−	0.961617i	$-0.411522\pi$
$71$	−6.10196	−	7.65161i	−0.724169	−	0.908079i	−0.998566	+	0.0535372i	$0.982950\pi$
$72$	0.392066	+	1.71776i	0.0462055	+	0.202439i
$73$	0.0675863	+	0.296115i	0.00791038	+	0.0346577i	0.978729	−	0.205157i	$-0.0657705\pi$
$73$	0.0675863	+	0.296115i	0.00791038	+	0.0346577i	−0.970819	+	0.239815i	$0.922913\pi$
$74$	−7.51117	−	9.41871i	−0.873156	−	1.09490i
$75$	0.744514			0.0859691
$76$	9.85235	+	12.3545i	1.13014	+	1.41715i
$77$	−4.27471	−	2.05859i	−0.487148	−	0.234598i
$78$	−8.24668	+	10.3410i	−0.933752	+	1.17089i
$79$	2.49794	−	3.13231i	0.281040	−	0.352413i	−0.621196	−	0.783655i	$-0.713353\pi$
$79$	2.49794	−	3.13231i	0.281040	−	0.352413i	0.902236	+	0.431242i	$0.141924\pi$
$80$	−3.77036	+	1.81571i	−0.421539	+	0.203002i
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	−3.34467	+	14.6540i	−0.369357	+	1.61826i
$83$	3.88709	+	1.87192i	0.426663	+	0.205470i	0.634877	−	0.772613i	$-0.281051\pi$
$83$	3.88709	+	1.87192i	0.426663	+	0.205470i	−0.208214	+	0.978083i	$0.566765\pi$
$84$	−3.41520	+	1.64468i	−0.372629	+	0.179449i
$85$	1.62899	−	7.13709i	0.176689	−	0.774126i
$86$	17.1002			1.84396
$87$	5.32413	−	0.808479i	0.570807	−	0.0866780i
$88$	−6.18356			−0.659170
$89$	−3.11361	+	13.6416i	−0.330042	+	1.44601i	0.489004	+	0.872282i	$0.337360\pi$
$89$	−3.11361	+	13.6416i	−0.330042	+	1.44601i	−0.819046	+	0.573728i	$0.805497\pi$
$90$	−4.73296	+	2.27927i	−0.498898	+	0.240256i
$91$	−7.35039	−	3.53976i	−0.770530	−	0.371068i
$92$	−0.633143	+	2.77398i	−0.0660097	+	0.289207i
$93$	−1.80501	−	7.90829i	−0.187171	−	0.820051i
$94$	−0.825935	+	0.397749i	−0.0851887	+	0.0410247i
$95$	−8.42183	+	10.5606i	−0.864062	+	1.08350i
$96$	4.58310	−	5.74702i	0.467761	−	0.586553i
$97$	3.42690	+	1.65031i	0.347949	+	0.167563i	0.599692	−	0.800231i	$-0.295290\pi$
$97$	3.42690	+	1.65031i	0.347949	+	0.167563i	−0.251743	+	0.967794i	$0.581004\pi$
$98$	7.06827	+	8.86333i	0.714003	+	0.895332i
$99$	3.50954			0.352722
$100$	1.30155	+	1.63210i	0.130155	+	0.163210i
$101$	0.00939526	+	0.0411633i	0.000934863	+	0.00409590i	0.975393	−	0.220472i	$-0.0707599\pi$
$101$	0.00939526	+	0.0411633i	0.000934863	+	0.00409590i	−0.974458	+	0.224568i	$0.927903\pi$
$102$	1.48967	+	6.52665i	0.147499	+	0.646235i
$103$	7.34494	+	9.21026i	0.723718	+	0.907514i	0.998542	−	0.0539808i	$-0.0171910\pi$
$103$	7.34494	+	9.21026i	0.723718	+	0.907514i	−0.274824	+	0.961495i	$0.588620\pi$
$104$	−10.6327			−1.04262
$105$	−2.02024	−	2.53330i	−0.197155	−	0.247225i
$106$	−26.3477	−	12.6884i	−2.55912	−	1.23241i
$107$	−3.90752	+	4.89987i	−0.377754	+	0.473688i	−0.933971	−	0.357349i	$-0.883681\pi$
$107$	−3.90752	+	4.89987i	−0.377754	+	0.473688i	0.556217	+	0.831037i	$0.312252\pi$
$108$	1.74819	−	2.19216i	0.168220	−	0.210941i
$109$	13.3409	−	6.42464i	1.27783	−	0.615369i	0.332996	−	0.942928i	$-0.391940\pi$
$109$	13.3409	−	6.42464i	1.27783	−	0.615369i	0.944831	+	0.327559i	$0.106226\pi$
$110$	−4.10245	−	17.9740i	−0.391154	−	1.71376i
$111$	−1.22307	+	5.35864i	−0.116089	+	0.508619i
$112$	2.12668	+	1.02416i	0.200953	+	0.0967737i
$113$	−10.7154	+	5.16029i	−1.00802	+	0.485439i	−0.863654	−	0.504085i	$-0.831830\pi$
$113$	−10.7154	+	5.16029i	−1.00802	+	0.485439i	−0.144370	+	0.989524i	$0.546116\pi$
$114$	2.74864	−	12.0426i	0.257434	−	1.12789i
$115$	−2.43219			−0.226803
$116$	11.0799	+	10.2580i	1.02874	+	0.952430i
$117$	6.03467			0.557905
$118$	1.73677	−	7.60928i	0.159883	−	0.700491i
$119$	−3.72031	+	1.79160i	−0.341040	+	0.164236i
$120$	−3.80474	−	1.83227i	−0.347324	−	0.167262i
$121$	−0.293028	+	1.28384i	−0.0266389	+	0.116713i
$122$	3.51621	+	15.4055i	0.318342	+	1.39475i
$123$	6.17868	−	2.97550i	0.557113	−	0.268292i
$124$	14.1807	−	17.7821i	1.27347	−	1.59688i
$125$	6.35924	−	7.97423i	0.568788	−	0.713237i
$126$	2.66964	+	1.28563i	0.237831	+	0.114533i
$127$	−9.41080	−	11.8008i	−0.835074	−	1.04715i	−0.998166	−	0.0605385i	$-0.980718\pi$
$127$	−9.41080	−	11.8008i	−0.835074	−	1.04715i	0.163092	−	0.986611i	$-0.447853\pi$
$128$	12.9568			1.14523
$129$	−4.86445	−	6.09983i	−0.428291	−	0.537060i
$130$	−7.05419	−	30.9064i	−0.618693	−	2.71067i
$131$	−2.32463	−	10.1849i	−0.203103	−	0.889855i	−0.969033	−	0.246930i	$-0.920578\pi$
$131$	−2.32463	−	10.1849i	−0.203103	−	0.889855i	0.765930	−	0.642924i	$-0.222279\pi$
$132$	6.13535	+	7.69348i	0.534013	+	0.669632i
$133$	7.61899			0.660650
$134$	−11.3604	−	14.2454i	−0.981386	−	1.23062i
$135$	2.15942	+	1.03992i	0.185853	+	0.0895021i
$136$	−3.35537	+	4.20750i	−0.287720	+	0.360790i
$137$	−2.28953	+	2.87098i	−0.195608	+	0.245284i	−0.869956	−	0.493129i	$-0.835853\pi$
$137$	−2.28953	+	2.87098i	−0.195608	+	0.245284i	0.674348	+	0.738413i	$0.264425\pi$
$138$	2.00390	−	0.965029i	0.170584	−	0.0821487i
$139$	−1.28647	−	5.63639i	−0.109117	−	0.478072i	−0.999728	−	0.0233073i	$-0.992580\pi$
$139$	−1.28647	−	5.63639i	−0.109117	−	0.478072i	0.890611	−	0.454765i	$-0.150277\pi$
$140$	2.02164	−	8.85739i	0.170860	−	0.748586i
$141$	0.376834	+	0.181474i	0.0317351	+	0.0152828i
$142$	−19.3262	+	9.30699i	−1.62182	+	0.781025i
$143$	−4.71275	+	20.6479i	−0.394100	+	1.72666i
$144$	−1.74601			−0.145501
$145$	−6.44120	+	11.1849i	−0.534912	+	0.928855i
$146$	0.665709			0.0550944
$147$	1.15096	−	5.04267i	0.0949292	−	0.415912i
$148$	−13.8852	+	6.68675i	−1.14135	+	0.549648i
$149$	7.73406	+	3.72453i	0.633599	+	0.305125i	0.722977	−	0.690873i	$-0.242773\pi$
$149$	7.73406	+	3.72453i	0.633599	+	0.305125i	−0.0893774	+	0.995998i	$0.528488\pi$
$150$	0.363111	−	1.59090i	0.0296479	−	0.129896i
$151$	−2.65704	−	11.6412i	−0.216227	−	0.947351i	−0.960238	−	0.279184i	$-0.909936\pi$
$151$	−2.65704	−	11.6412i	−0.216227	−	0.947351i	0.744011	−	0.668168i	$-0.232921\pi$
$152$	8.94642	−	4.30837i	0.725650	−	0.349455i
$153$	1.90437	−	2.38800i	0.153959	−	0.193059i
$154$	−6.48369	+	8.13029i	−0.522471	+	0.655158i
$155$	17.5165	+	8.43548i	1.40696	+	0.677554i
$156$	10.5498	+	13.2290i	0.844657	+	1.05917i
$157$	−12.2535			−0.977936			−0.488968	−	0.872302i	$-0.662626\pi$
$157$	−12.2535			−0.977936			−0.488968	+	0.872302i	$0.662626\pi$
$158$	−5.47492	−	6.86533i	−0.435561	−	0.546176i
$159$	2.96899	+	13.0080i	0.235456	+	1.03160i
$160$	3.92037	+	17.1763i	0.309933	+	1.35790i
$161$	0.855356	+	1.07258i	0.0674115	+	0.0845314i
$162$	−2.19178			−0.172202
$163$	−4.94515	−	6.20102i	−0.387334	−	0.485701i	0.549491	−	0.835499i	$-0.314822\pi$
$163$	−4.94515	−	6.20102i	−0.387334	−	0.485701i	−0.936825	+	0.349798i	$0.886250\pi$
$164$	17.3243	+	8.34295i	1.35280	+	0.651475i
$165$	−5.24452	+	6.57642i	−0.408286	+	0.511974i
$166$	5.89576	−	7.39305i	0.457600	−	0.573812i
$167$	−11.6445	+	5.60770i	−0.901080	+	0.433937i	−0.826279	−	0.563261i	$-0.809546\pi$
$167$	−11.6445	+	5.60770i	−0.901080	+	0.433937i	−0.0748008	+	0.997198i	$0.523832\pi$
$168$	0.530037	+	2.32225i	0.0408933	+	0.179165i
$169$	−5.21082	+	22.8301i	−0.400833	+	1.75616i
$170$	−14.4562	−	6.96175i	−1.10874	−	0.533941i
$171$	−5.07762	+	2.44525i	−0.388295	+	0.186993i
$172$	4.86783	−	21.3273i	0.371168	−	1.62619i
$173$	2.65357			0.201747			0.100874	−	0.994899i	$-0.467836\pi$
$173$	2.65357			0.201747			0.100874	+	0.994899i	$0.467836\pi$
$174$	0.869087	−	11.7710i	0.0658853	−	0.892360i
$175$	1.00651			0.0760853
$176$	1.36354	−	5.97405i	0.102781	−	0.450311i
$177$	−3.20837	+	1.54507i	−0.241156	+	0.116135i
$178$	27.6312	+	13.3065i	2.07105	+	0.997363i
$179$	2.98150	−	13.0628i	0.222848	−	0.976361i	−0.732474	−	0.680795i	$-0.761635\pi$
$179$	2.98150	−	13.0628i	0.222848	−	0.976361i	0.955322	−	0.295566i	$-0.0955083\pi$
$180$	1.49540	+	6.55177i	0.111461	+	0.488340i
$181$	−1.36397	+	0.656854i	−0.101383	+	0.0488236i	−0.483888	−	0.875130i	$-0.660776\pi$
$181$	−1.36397	+	0.656854i	−0.101383	+	0.0488236i	0.382505	+	0.923953i	$0.375062\pi$
$182$	−11.1487	+	13.9801i	−0.826400	+	1.03627i
$183$	4.49507	−	5.63664i	0.332285	−	0.416673i
$184$	1.61090	+	0.775770i	0.118757	+	0.0571905i
$185$	−8.21368	−	10.2996i	−0.603882	−	0.757244i
$186$	−17.7790			−1.30362
$187$	6.68346	+	8.38079i	0.488743	+	0.612864i
$188$	0.260958	+	1.14333i	0.0190323	+	0.0833860i
$189$	−0.300828	−	1.31801i	−0.0218820	−	0.0958713i
$190$	18.4588	+	23.1466i	1.33914	+	1.67923i
$191$	−11.6187			−0.840696			−0.420348	−	0.907363i	$-0.638092\pi$
$191$	−11.6187			−0.840696			−0.420348	+	0.907363i	$0.638092\pi$
$192$	−7.86789	−	9.86602i	−0.567816	−	0.712019i
$193$	5.55158	+	2.67350i	0.399612	+	0.192443i	0.622886	−	0.782313i	$-0.285960\pi$
$193$	5.55158	+	2.67350i	0.399612	+	0.192443i	−0.223274	+	0.974756i	$0.571674\pi$
$194$	5.19777	−	6.51780i	0.373178	−	0.467951i
$195$	−9.01798	+	11.3082i	−0.645791	+	0.809797i
$196$	13.0664	−	6.29246i	0.933317	−	0.449462i
$197$	0.562248	+	2.46337i	0.0400585	+	0.175508i	0.991000	−	0.133864i	$-0.0427385\pi$
$197$	0.562248	+	2.46337i	0.0400585	+	0.175508i	−0.950941	+	0.309372i	$0.899881\pi$
$198$	1.71166	−	7.49926i	0.121642	−	0.532949i
$199$	−11.9665	−	5.76277i	−0.848284	−	0.408512i	−0.0413438	−	0.999145i	$-0.513164\pi$
$199$	−11.9665	−	5.76277i	−0.848284	−	0.408512i	−0.806940	+	0.590633i	$0.798878\pi$
$200$	1.18187	−	0.569161i	0.0835712	−	0.0402458i
$201$	−1.84985	+	8.10474i	−0.130479	+	0.571664i
$202$	0.0925410			0.00651116
$203$	7.19773	−	1.09299i	0.505182	−	0.0767128i
$204$	8.56410			0.599607
$205$	−3.65749	+	16.0245i	−0.255451	+	1.11920i
$206$	23.2629	−	11.2028i	1.62081	−	0.780539i
$207$	−0.914283	−	0.440295i	−0.0635471	−	0.0306026i
$208$	2.34461	−	10.2724i	0.162569	−	0.712263i
$209$	−4.40120	−	19.2829i	−0.304438	−	1.33383i
$210$	−6.39852	+	3.08136i	−0.441540	+	0.212634i
$211$	−5.17794	+	6.49294i	−0.356464	+	0.446992i	−0.927438	−	0.373976i	$-0.877994\pi$
$211$	−5.17794	+	6.49294i	−0.356464	+	0.446992i	0.570974	+	0.820968i	$0.306566\pi$
$212$	−23.3253	+	29.2489i	−1.60198	+	2.00883i
$213$	8.81758	+	4.24632i	0.604171	+	0.290953i
$214$	8.56440	+	10.7394i	0.585450	+	0.734132i
$215$	18.6995			1.27530
$216$	−1.09855	−	1.37753i	−0.0747466	−	0.0937292i
$217$	−2.44021	−	10.6913i	−0.165652	−	0.725771i
$218$	−7.22175	−	31.6406i	−0.489119	−	2.14297i
$219$	−0.189373	−	0.237466i	−0.0127966	−	0.0160465i
$220$	−23.5850			−1.59010
$221$	11.4922	+	14.4108i	0.773052	+	0.969376i
$222$	10.8540	+	5.22699i	0.728470	+	0.350812i
$223$	15.5947	−	19.5551i	1.04430	−	1.30951i	0.0948805	−	0.995489i	$-0.469753\pi$
$223$	15.5947	−	19.5551i	1.04430	−	1.30951i	0.949417	−	0.314019i	$-0.101675\pi$
$224$	6.19592	−	7.76944i	0.413983	−	0.519118i
$225$	−0.670784	+	0.323033i	−0.0447189	+	0.0215355i
$226$	5.80053	+	25.4138i	0.385845	+	1.69050i
$227$	−0.677325	+	2.96756i	−0.0449556	+	0.196964i	−0.992419	−	0.122901i	$-0.960780\pi$
$227$	−0.677325	+	2.96756i	−0.0449556	+	0.196964i	0.947463	+	0.319865i	$0.103637\pi$
$228$	−14.2371	−	6.85620i	−0.942872	−	0.454063i
$229$	19.7389	−	9.50577i	1.30439	−	0.628159i	0.352845	−	0.935682i	$-0.385214\pi$
$229$	19.7389	−	9.50577i	1.30439	−	0.628159i	0.951541	+	0.307523i	$0.0995001\pi$
$230$	−1.18622	+	5.19716i	−0.0782169	+	0.342691i
$231$	4.74457			0.312170
$232$	7.83370	−	5.35357i	0.514308	−	0.351479i
$233$	9.96464			0.652805			0.326403	−	0.945231i	$-0.394163\pi$
$233$	9.96464			0.652805			0.326403	+	0.945231i	$0.394163\pi$
$234$	2.94320	−	12.8950i	0.192403	−	0.842974i
$235$	−0.903184	+	0.434951i	−0.0589173	+	0.0283731i
$236$	−8.99590	−	4.33220i	−0.585583	−	0.282002i
$237$	−0.891504	+	3.90593i	−0.0579094	+	0.253718i
$238$	2.01389	+	8.82343i	0.130541	+	0.571938i
$239$	7.01041	−	3.37604i	0.453466	−	0.218378i	−0.193187	−	0.981162i	$-0.561882\pi$
$239$	7.01041	−	3.37604i	0.453466	−	0.218378i	0.646653	+	0.762784i	$0.276168\pi$
$240$	2.60917	−	3.27179i	0.168421	−	0.211193i
$241$	−14.4582	+	18.1300i	−0.931334	+	1.16786i	0.0542254	+	0.998529i	$0.482731\pi$
$241$	−14.4582	+	18.1300i	−0.931334	+	1.16786i	−0.985560	+	0.169328i	$0.945840\pi$
$242$	2.60043	+	1.25230i	0.167162	+	0.0805009i
$243$	0.623490	+	0.781831i	0.0399969	+	0.0501545i
$244$	20.2147			1.29411
$245$	7.72936	+	9.69231i	0.493811	+	0.619219i
$246$	−3.34467	−	14.6540i	−0.213248	−	0.934302i
$247$	−7.56789	−	33.1571i	−0.481533	−	2.10974i
$248$	−8.91103	−	11.1741i	−0.565851	−	0.709555i
$249$	−4.31434			−0.273410
$250$	−13.9380	−	17.4777i	−0.881518	−	1.10539i
$251$	−1.06363	−	0.512217i	−0.0671357	−	0.0323308i	0.400015	−	0.916509i	$-0.369005\pi$
$251$	−1.06363	−	0.512217i	−0.0671357	−	0.0323308i	−0.467150	+	0.884178i	$0.654719\pi$
$252$	2.36339	−	2.96360i	0.148880	−	0.186689i
$253$	2.22050	−	2.78441i	0.139601	−	0.175055i
$254$	−29.8060	+	14.3538i	−1.87019	+	0.900637i
$255$	1.62899	+	7.13709i	0.102012	+	0.446942i
$256$	0.703222	−	3.08102i	0.0439514	−	0.192564i
$257$	−14.3925	−	6.93107i	−0.897781	−	0.432348i	−0.0726939	−	0.997354i	$-0.523160\pi$
$257$	−14.3925	−	6.93107i	−0.897781	−	0.432348i	−0.825087	+	0.565006i	$0.808874\pi$
$258$	−15.4067	+	7.41949i	−0.959181	+	0.461917i
$259$	−1.65348	+	7.24438i	−0.102742	+	0.450144i
$260$	−40.5546			−2.51509
$261$	−4.44609	+	3.03847i	−0.275206	+	0.188076i
$262$	−22.8970			−1.41458
$263$	−3.25116	+	14.2443i	−0.200475	+	0.878339i	0.770173	+	0.637835i	$0.220170\pi$
$263$	−3.25116	+	14.2443i	−0.200475	+	0.878339i	−0.970648	+	0.240504i	$0.922687\pi$
$264$	5.57120	−	2.68295i	0.342883	−	0.165124i
$265$	−28.8120	−	13.8751i	−1.76991	−	0.852343i
$266$	3.71590	−	16.2804i	0.227837	−	0.998218i
$267$	−3.11361	−	13.6416i	−0.190550	−	0.834854i
$268$	−21.0008	+	10.1135i	−1.28283	+	0.617778i
$269$	13.7882	−	17.2899i	0.840681	−	1.05418i	−0.157099	−	0.987583i	$-0.550214\pi$
$269$	13.7882	−	17.2899i	0.840681	−	1.05418i	0.997780	−	0.0665980i	$-0.0212145\pi$
$270$	3.27531	−	4.10711i	0.199329	−	0.249951i
$271$	20.8260	+	10.0293i	1.26509	+	0.609236i	0.941516	−	0.336967i	$-0.109401\pi$
$271$	20.8260	+	10.0293i	1.26509	+	0.609236i	0.323574	+	0.946203i	$0.395115\pi$
$272$	−3.32504	−	4.16947i	−0.201610	−	0.252812i
$273$	8.15831			0.493764
$274$	5.01814	+	6.29255i	0.303157	+	0.380147i
$275$	−0.581425	−	2.54739i	−0.0350613	−	0.153613i
$276$	−0.633143	−	2.77398i	−0.0381107	−	0.166974i
$277$	11.6674	+	14.6304i	0.701024	+	0.879056i	0.997100	−	0.0761086i	$-0.0242496\pi$
$277$	11.6674	+	14.6304i	0.701024	+	0.879056i	−0.296076	+	0.955164i	$0.595678\pi$
$278$	−12.6714			−0.759980
$279$	5.05754	+	6.34195i	0.302787	+	0.379683i
$280$	−5.14366	−	2.47706i	−0.307392	−	0.148032i
$281$	−5.40308	+	6.77525i	−0.322321	+	0.404177i	−0.916422	−	0.400213i	$-0.868936\pi$
$281$	−5.40308	+	6.77525i	−0.322321	+	0.404177i	0.594102	+	0.804390i	$0.297508\pi$
$282$	0.571565	−	0.716720i	0.0340362	−	0.0426800i
$283$	−5.03188	+	2.42322i	−0.299114	+	0.144046i	−0.577421	−	0.816446i	$-0.695941\pi$
$283$	−5.03188	+	2.42322i	−0.299114	+	0.144046i	0.278307	+	0.960492i	$0.410227\pi$
$284$	6.10619	+	26.7530i	0.362336	+	1.58750i
$285$	3.00572	−	13.1689i	0.178043	−	0.780059i
$286$	41.8224	+	20.1406i	2.47301	+	1.19094i
$287$	8.35301	−	4.02260i	0.493063	−	0.237446i
$288$	−1.63569	+	7.16642i	−0.0963839	+	0.422285i
$289$	−7.67081			−0.451224
$290$	20.7587	+	19.2188i	1.21899	+	1.12856i
$291$	−3.80357			−0.222969
$292$	0.189504	−	0.830272i	0.0110899	−	0.0485880i
$293$	4.25166	−	2.04749i	0.248385	−	0.119616i	−0.305549	−	0.952176i	$-0.598840\pi$
$293$	4.25166	−	2.04749i	0.248385	−	0.119616i	0.553934	+	0.832560i	$0.313126\pi$
$294$	−10.2139	−	4.91878i	−0.595689	−	0.286869i
$295$	1.89921	−	8.32097i	0.110576	−	0.484466i
$296$	2.15497	+	9.44155i	0.125255	+	0.548779i
$297$	−3.16198	+	1.52273i	−0.183477	+	0.0883578i
$298$	11.7307	−	14.7098i	0.679540	−	0.852117i
$299$	3.81816	−	4.78782i	0.220810	−	0.276887i
$300$	−1.88080	−	0.905745i	−0.108588	−	0.0522932i
$301$	−6.57628	−	8.24640i	−0.379051	−	0.475315i
$302$	−26.1712			−1.50598
$303$	−0.0263249	−	0.0330104i	−0.00151233	−	0.00189640i
$304$	2.18961	+	9.59333i	0.125583	+	0.550215i
$305$	3.84508	+	16.8464i	0.220168	+	0.964621i
$306$	−4.17395	−	5.23397i	−0.238609	−	0.299206i
$307$	11.7362			0.669821			0.334910	−	0.942250i	$-0.391294\pi$
$307$	11.7362			0.669821			0.334910	+	0.942250i	$0.391294\pi$
$308$	8.29442	+	10.4009i	0.472618	+	0.592645i
$309$	−10.6137	−	5.11131i	−0.603795	−	0.290772i
$310$	26.5682	−	33.3155i	1.50897	−	1.89219i
$311$	10.4770	−	13.1378i	0.594097	−	0.744974i	−0.390348	−	0.920667i	$-0.627645\pi$
$311$	10.4770	−	13.1378i	0.594097	−	0.744974i	0.984445	+	0.175693i	$0.0562167\pi$
$312$	9.57970	−	4.61334i	0.542344	−	0.261179i
$313$	2.66132	+	11.6600i	0.150427	+	0.659063i	0.992761	+	0.120107i	$0.0383239\pi$
$313$	2.66132	+	11.6600i	0.150427	+	0.659063i	−0.842334	+	0.538956i	$0.818819\pi$
$314$	−5.97623	+	26.1836i	−0.337258	+	1.47762i
$315$	2.91933	+	1.40588i	0.164486	+	0.0792121i
$316$	−10.1210	+	4.87400i	−0.569349	+	0.274184i
$317$	3.14555	−	13.7815i	0.176671	−	0.774048i	−0.806481	−	0.591260i	$-0.798631\pi$
$317$	3.14555	−	13.7815i	0.176671	−	0.774048i	0.983152	−	0.182788i	$-0.0585122\pi$
$318$	29.2438			1.63991
$319$	−6.92410	−	17.5854i	−0.387675	−	0.984592i
$320$	30.2451			1.69075
$321$	1.39458	−	6.11004i	0.0778377	−	0.341029i
$322$	2.70909	−	1.30463i	0.150972	−	0.0727042i
$323$	−15.5089	−	7.46871i	−0.862941	−	0.415570i
$324$	−0.623923	+	2.73358i	−0.0346624	+	0.151866i
$325$	−0.999763	−	4.38025i	−0.0554569	−	0.242973i
$326$	−15.6623	+	7.54257i	−0.867455	+	0.417744i
$327$	−9.23220	+	11.5768i	−0.510542	+	0.640199i
$328$	7.53363	−	9.44687i	0.415975	−	0.521616i
$329$	0.509444	+	0.245335i	0.0280866	+	0.0135258i
$330$	11.4948	+	14.4140i	0.632769	+	0.793467i
$331$	23.0236			1.26549			0.632747	−	0.774359i	$-0.281927\pi$
$331$	23.0236			1.26549			0.632747	+	0.774359i	$0.281927\pi$
$332$	−7.54230	−	9.45774i	−0.413937	−	0.519061i
$333$	−1.22307	−	5.35864i	−0.0670241	−	0.293652i
$334$	6.30346	+	27.6172i	0.344910	+	1.51115i
$335$	−12.4229	−	15.5778i	−0.678735	−	0.851107i
$336$	−2.36044			−0.128773
$337$	−1.59382	−	1.99859i	−0.0868212	−	0.108870i	0.736524	−	0.676412i	$-0.236466\pi$
$337$	−1.59382	−	1.99859i	−0.0868212	−	0.108870i	−0.823345	+	0.567542i	$0.807895\pi$
$338$	46.2425	+	22.2692i	2.51526	+	1.21129i
$339$	7.41532	−	9.29852i	0.402745	−	0.505026i
$340$	−12.7979	+	16.0480i	−0.694062	+	0.870326i
$341$	−25.6490	+	12.3519i	−1.38897	+	0.668892i
$342$	2.74864	+	12.0426i	0.148629	+	0.651188i
$343$	3.66178	−	16.0433i	0.197717	−	0.866257i
$344$	−12.3852	−	5.96440i	−0.667765	−	0.321579i
$345$	2.19133	−	1.05529i	0.117977	−	0.0568148i
$346$	1.29419	−	5.67022i	0.0695761	−	0.304833i
$347$	−0.891885			−0.0478789			−0.0239394	−	0.999713i	$-0.507621\pi$
$347$	−0.891885			−0.0478789			−0.0239394	+	0.999713i	$0.507621\pi$
$348$	−14.4334	−	4.43473i	−0.773713	−	0.237726i
$349$	−0.755575			−0.0404450			−0.0202225	−	0.999796i	$-0.506437\pi$
$349$	−0.755575			−0.0404450			−0.0202225	+	0.999796i	$0.506437\pi$
$350$	0.490893	−	2.15074i	0.0262393	−	0.114962i
$351$	−5.43705	+	2.61834i	−0.290208	+	0.139757i
$352$	−23.2429	−	11.1932i	−1.23885	−	0.596598i
$353$	−4.28143	+	18.7582i	−0.227878	+	0.998397i	0.723489	+	0.690336i	$0.242537\pi$
$353$	−4.28143	+	18.7582i	−0.227878	+	0.998397i	−0.951367	+	0.308061i	$0.900320\pi$
$354$	1.73677	+	7.60928i	0.0923082	+	0.404429i
$355$	−21.1337	+	10.1775i	−1.12166	+	0.540164i
$356$	24.4615	−	30.6737i	1.29646	−	1.62570i
$357$	2.57453	−	3.22836i	0.136259	−	0.170863i
$358$	−26.4588	−	12.7419i	−1.39839	−	0.673430i
$359$	10.9825	+	13.7716i	0.579634	+	0.726838i	0.982050	−	0.188619i	$-0.0604010\pi$
$359$	10.9825	+	13.7716i	0.579634	+	0.726838i	−0.402416	+	0.915457i	$0.631830\pi$
$360$	4.22294			0.222569
$361$	7.95667	+	9.97735i	0.418772	+	0.525124i
$362$	0.738351	+	3.23493i	0.0388068	+	0.170024i
$363$	−0.293028	−	1.28384i	−0.0153800	−	0.0673842i
$364$	14.2623	+	17.8844i	0.747548	+	0.937395i
$365$	0.727972			0.0381038
$366$	−9.85219	−	12.3543i	−0.514982	−	0.645767i
$367$	−3.42176	−	1.64783i	−0.178614	−	0.0860162i	0.342440	−	0.939540i	$-0.388747\pi$
$367$	−3.42176	−	1.64783i	−0.178614	−	0.0860162i	−0.521054	+	0.853524i	$0.674461\pi$
$368$	−1.10471	+	1.38526i	−0.0575867	+	0.0722115i
$369$	−4.27578	+	5.36166i	−0.222588	+	0.279117i
$370$	−26.0144	+	12.5279i	−1.35243	+	0.651294i
$371$	4.01379	+	17.5856i	0.208386	+	0.912998i
$372$	−5.06105	+	22.1739i	−0.262403	+	1.14966i
$373$	7.47141	+	3.59804i	0.386855	+	0.186299i	0.617194	−	0.786811i	$-0.288269\pi$
$373$	7.47141	+	3.59804i	0.386855	+	0.186299i	−0.230339	+	0.973110i	$0.573984\pi$
$374$	21.1679	−	10.1939i	1.09457	−	0.527115i
$375$	−2.26959	+	9.94371i	−0.117201	+	0.513491i
$376$	0.736934			0.0380045
$377$	−11.9060	−	30.2382i	−0.613192	−	1.55734i
$378$	−2.96308			−0.152404
$379$	1.98764	−	8.70843i	0.102098	−	0.447322i	−0.897877	−	0.440247i	$-0.854891\pi$
$379$	1.98764	−	8.70843i	0.102098	−	0.447322i	0.999975	−	0.00707478i	$-0.00225199\pi$
$380$	34.1230	−	16.4328i	1.75047	−	0.842983i
$381$	13.5990	+	6.54894i	0.696698	+	0.335512i
$382$	−5.66660	+	24.8270i	−0.289929	+	1.27026i
$383$	−7.97804	−	34.9541i	−0.407659	−	1.78607i	−0.594947	−	0.803765i	$-0.702827\pi$
$383$	−7.97804	−	34.9541i	−0.407659	−	1.78607i	0.187288	−	0.982305i	$-0.440030\pi$
$384$	−11.6737	+	5.62176i	−0.595721	+	0.286884i
$385$	−7.09011	+	8.89072i	−0.361345	+	0.453113i
$386$	8.42040	−	10.5588i	0.428587	−	0.537431i
$387$	7.02933	+	3.38515i	0.357321	+	0.172077i
$388$	−6.64938	−	8.33806i	−0.337571	−	0.423301i
$389$	11.3446			0.575194			0.287597	−	0.957752i	$-0.407144\pi$
$389$	11.3446			0.575194			0.287597	+	0.957752i	$0.407144\pi$
$390$	19.7654	+	24.7850i	1.00086	+	1.25504i
$391$	−0.689705	−	3.02180i	−0.0348799	−	0.152819i
$392$	−2.02790	−	8.88482i	−0.102425	−	0.448751i
$393$	6.51346	+	8.16762i	0.328560	+	0.412002i
$394$	5.53800			0.279001
$395$	−5.98699	−	7.50744i	−0.301238	−	0.377740i
$396$	−8.86583	−	4.26956i	−0.445525	−	0.214553i
$397$	−15.0481	+	18.8697i	−0.755242	+	0.947043i	−0.999744	−	0.0226053i	$-0.992804\pi$
$397$	−15.0481	+	18.8697i	−0.755242	+	0.947043i	0.244503	+	0.969649i	$0.421375\pi$
$398$	−18.1503	+	22.7598i	−0.909792	+	1.14084i
$399$	−6.86447	+	3.30576i	−0.343654	+	0.165495i
$400$	0.289261	+	1.26734i	0.0144631	+	0.0633668i
$401$	−4.30720	+	18.8711i	−0.215091	+	0.942376i	0.745957	+	0.665994i	$0.231992\pi$
$401$	−4.30720	+	18.8711i	−0.215091	+	0.942376i	−0.961048	+	0.276381i	$0.910865\pi$
$402$	16.4162	+	7.90562i	0.818765	+	0.394297i
$403$	−44.1035	+	21.2391i	−2.19695	+	1.05800i
$404$	0.0263432	−	0.115417i	0.00131062	−	0.00574222i
$405$	−2.39677			−0.119097
$406$	1.17492	−	15.9133i	0.0583105	−	0.789766i
$407$	19.2900			0.956169
$408$	1.19752	−	5.24666i	0.0592859	−	0.259749i
$409$	−10.3124	+	4.96618i	−0.509915	+	0.245562i	−0.671106	−	0.741361i	$-0.734181\pi$
$409$	−10.3124	+	4.96618i	−0.509915	+	0.245562i	0.161192	+	0.986923i	$0.448466\pi$
$410$	32.4578	+	15.6308i	1.60298	+	0.771952i
$411$	0.817124	−	3.58006i	0.0403058	−	0.176591i
$412$	−7.35003	−	32.2026i	−0.362110	−	1.58651i
$413$	−4.33742	+	2.08879i	−0.213431	+	0.102783i
$414$	−1.38674	+	1.73892i	−0.0681548	+	0.0854634i
$415$	6.44719	−	8.08452i	0.316480	−	0.396853i
$416$	−39.9662	−	19.2467i	−1.95951	−	0.943648i
$417$	3.60461	+	4.52003i	0.176518	+	0.221347i
$418$	−43.3508			−2.12036
$419$	−13.1672	−	16.5111i	−0.643259	−	0.806621i	0.348147	−	0.937440i	$-0.386811\pi$
$419$	−13.1672	−	16.5111i	−0.643259	−	0.806621i	−0.991406	+	0.130819i	$0.958239\pi$
$420$	2.02164	+	8.85739i	0.0986460	+	0.432196i
$421$	−6.12223	−	26.8233i	−0.298379	−	1.30729i	−0.872540	−	0.488543i	$-0.837529\pi$
$421$	−6.12223	−	26.8233i	−0.298379	−	1.30729i	0.574161	−	0.818743i	$-0.305329\pi$
$422$	11.3489	+	14.2311i	0.552455	+	0.692757i
$423$	−0.418254			−0.0203362
$424$	14.6573	+	18.3797i	0.711823	+	0.892598i
$425$	−2.04882	−	0.986662i	−0.0993826	−	0.0478601i
$426$	13.3741	−	16.7706i	0.647978	−	0.812539i
$427$	6.07692	−	7.62022i	0.294083	−	0.368768i
$428$	15.8322	−	7.62438i	0.765278	−	0.368538i
$429$	−4.71275	−	20.6479i	−0.227534	−	0.996890i
$430$	9.12007	−	39.9576i	0.439809	−	1.92693i
$431$	1.75647	+	0.845873i	0.0846064	+	0.0407443i	0.475708	−	0.879603i	$-0.342192\pi$
$431$	1.75647	+	0.845873i	0.0846064	+	0.0407443i	−0.391102	+	0.920347i	$0.627906\pi$
$432$	1.57310	−	0.757565i	0.0756858	−	0.0364483i
$433$	−1.74340	+	7.63835i	−0.0837826	+	0.367076i	−0.999387	−	0.0350044i	$-0.988855\pi$
$433$	−1.74340	+	7.63835i	−0.0837826	+	0.367076i	0.915605	+	0.402080i	$0.131713\pi$
$434$	−24.0355			−1.15374
$435$	0.950372	−	12.8720i	0.0455669	−	0.617164i
$436$	−41.5179			−1.98835
$437$	−1.27260	+	5.57563i	−0.0608768	+	0.266719i
$438$	−0.599783	+	0.288840i	−0.0286587	+	0.0138013i
$439$	−2.15322	−	1.03694i	−0.102768	−	0.0494903i	0.381794	−	0.924248i	$-0.375306\pi$
$439$	−2.15322	−	1.03694i	−0.102768	−	0.0494903i	−0.484561	+	0.874757i	$0.661021\pi$
$440$	−3.29789	+	14.4490i	−0.157221	+	0.688829i
$441$	1.15096	+	5.04267i	0.0548074	+	0.240127i
$442$	36.3983	−	17.5285i	1.73129	−	0.833746i
$443$	23.9106	−	29.9830i	1.13603	−	1.42453i	0.245623	−	0.969366i	$-0.421008\pi$
$443$	23.9106	−	29.9830i	1.13603	−	1.42453i	0.890405	−	0.455168i	$-0.150421\pi$
$444$	9.60884	−	12.0491i	0.456016	−	0.571825i
$445$	30.2155	+	14.5510i	1.43235	+	0.689785i
$446$	−34.1801	−	42.8604i	−1.61847	−	2.02950i
$447$	−8.58416			−0.406017
$448$	−10.6367	−	13.3379i	−0.502535	−	0.630159i
$449$	6.97471	+	30.5582i	0.329157	+	1.44213i	0.820741	+	0.571301i	$0.193561\pi$
$449$	6.97471	+	30.5582i	0.329157	+	1.44213i	−0.491584	+	0.870830i	$0.663582\pi$
$450$	0.363111	+	1.59090i	0.0171172	+	0.0749955i
$451$	−15.0060	−	18.8170i	−0.706606	−	0.886056i
$452$	33.3473			1.56852
$453$	7.44486	+	9.33556i	0.349790	+	0.438623i
$454$	6.01080	+	2.89465i	0.282101	+	0.135853i
$455$	−12.1915	+	15.2876i	−0.571545	+	0.716695i
$456$	−6.19111	+	7.76341i	−0.289925	+	0.363555i
$457$	29.0691	−	13.9989i	1.35980	−	0.654843i	0.395204	−	0.918593i	$-0.370674\pi$
$457$	29.0691	−	13.9989i	1.35980	−	0.654843i	0.964591	+	0.263750i	$0.0849595\pi$
$458$	−10.6852	−	46.8147i	−0.499285	−	2.18751i
$459$	−0.679662	+	2.97779i	−0.0317239	+	0.138991i
$460$	6.14422	+	2.95890i	0.286476	+	0.137960i
$461$	5.11576	−	2.46362i	0.238265	−	0.114742i	−0.310942	−	0.950429i	$-0.600644\pi$
$461$	5.11576	−	2.46362i	0.238265	−	0.114742i	0.549206	+	0.835687i	$0.314930\pi$
$462$	2.31400	−	10.1383i	0.107657	−	0.471677i
$463$	23.2339			1.07977			0.539886	−	0.841738i	$-0.318467\pi$
$463$	23.2339			1.07977			0.539886	+	0.841738i	$0.318467\pi$
$464$	3.44477	+	8.74879i	0.159919	+	0.406152i
$465$	−19.4418			−0.901592
$466$	4.85991	−	21.2927i	0.225131	−	0.986364i
$467$	−10.8811	+	5.24005i	−0.503516	+	0.242481i	−0.668358	−	0.743839i	$-0.733003\pi$
$467$	−10.8811	+	5.24005i	−0.503516	+	0.242481i	0.164842	+	0.986320i	$0.447288\pi$
$468$	−15.2448	−	7.34153i	−0.704693	−	0.339362i
$469$	−2.50083	+	10.9569i	−0.115478	+	0.505941i
$470$	0.488915	+	2.14208i	0.0225520	+	0.0988067i
$471$	11.0400	−	5.31659i	0.508697	−	0.244976i
$472$	−3.91195	+	4.90543i	−0.180062	+	0.225791i
$473$	−17.0720	+	21.4076i	−0.784970	+	0.984321i
$474$	7.91149	+	3.80997i	0.363387	+	0.174998i
$475$	2.61609	+	3.28047i	0.120034	+	0.150518i
$476$	11.5779			0.530671
$477$	−8.31891	−	10.4316i	−0.380897	−	0.477629i
$478$	−3.79490	−	16.6266i	−0.173575	−	0.760481i
$479$	6.78931	+	29.7459i	0.310212	+	1.35913i	0.854161	+	0.520008i	$0.174071\pi$
$479$	6.78931	+	29.7459i	0.310212	+	1.35913i	−0.543950	+	0.839118i	$0.683072\pi$
$480$	−10.9846	−	13.7743i	−0.501378	−	0.628708i
$481$	33.1692			1.51239
$482$	31.6891	+	39.7369i	1.44340	+	1.80997i
$483$	−1.23603	−	0.595239i	−0.0562411	−	0.0270843i
$484$	2.30212	−	2.88677i	0.104642	−	0.131217i
$485$	5.68392	−	7.12741i	0.258093	−	0.323639i
$486$	1.97472	−	0.950976i	0.0895752	−	0.0431371i
$487$	5.23476	+	22.9350i	0.237210	+	1.03928i	0.943503	+	0.331364i	$0.107509\pi$
$487$	5.23476	+	22.9350i	0.237210	+	1.03928i	−0.706293	+	0.707919i	$0.749634\pi$
$488$	2.82662	−	12.3842i	0.127955	−	0.560607i
$489$	7.14595	+	3.44131i	0.323151	+	0.155621i
$490$	24.4805	−	11.7892i	1.10592	−	0.532581i
$491$	−6.13907	+	26.8970i	−0.277052	+	1.21385i	0.624447	+	0.781067i	$0.285324\pi$
$491$	−6.13907	+	26.8970i	−0.277052	+	1.21385i	−0.901500	+	0.432779i	$0.857533\pi$
$492$	−19.2285			−0.866889
$493$	−15.7229	−	4.83091i	−0.708123	−	0.217573i
$494$	−74.5419			−3.35380
$495$	1.87175	−	8.20067i	0.0841288	−	0.368593i
$496$	12.7604	−	6.14511i	0.572961	−	0.275924i
$497$	11.9206	+	5.74064i	0.534710	+	0.257503i
$498$	−2.10417	+	9.21898i	−0.0942902	+	0.413113i
$499$	8.53765	+	37.4059i	0.382198	+	1.67452i	0.690580	+	0.723256i	$0.257355\pi$
$499$	8.53765	+	37.4059i	0.382198	+	1.67452i	−0.308383	+	0.951262i	$0.599788\pi$
$500$	−25.7659	+	12.4082i	−1.15229	+	0.554912i
$501$	8.05825	−	10.1047i	0.360016	−	0.451446i
$502$	−1.61327	+	2.02297i	−0.0720036	+	0.0902896i
$503$	4.46853	+	2.15193i	0.199242	+	0.0959498i	0.530844	−	0.847469i	$-0.321875\pi$
$503$	4.46853	+	2.15193i	0.199242	+	0.0959498i	−0.331602	+	0.943419i	$0.607589\pi$
$504$	−1.48513	−	1.86230i	−0.0661530	−	0.0829533i
$505$	0.101196			0.00450318
$506$	−4.86683	−	6.10281i	−0.216357	−	0.271303i
$507$	−5.21082	−	22.8301i	−0.231421	−	1.01392i
$508$	9.41733	+	41.2600i	0.417827	+	1.83062i
$509$	−10.2436	−	12.8450i	−0.454038	−	0.569345i	0.501144	−	0.865364i	$-0.332913\pi$
$509$	−10.2436	−	12.8450i	−0.454038	−	0.569345i	−0.955182	+	0.296018i	$0.904341\pi$
$510$	16.0452			0.710493
$511$	−0.256014	−	0.321032i	−0.0113254	−	0.0142016i
$512$	17.1068	+	8.23820i	0.756020	+	0.364080i
$513$	3.51382	−	4.40620i	0.155139	−	0.194538i
$514$	−21.8299	+	27.3739i	−0.962878	+	1.20741i
$515$	25.4387	−	12.2506i	1.12096	−	0.539828i
$516$	4.86783	+	21.3273i	0.214294	+	0.938884i
$517$	0.326634	−	1.43108i	0.0143653	−	0.0629386i
$518$	14.6735	+	7.06640i	0.644718	+	0.310480i
$519$	−2.39079	+	1.15134i	−0.104944	+	0.0505383i
$520$	−5.67074	+	24.8451i	−0.248678	+	1.08953i
$521$	−30.7040			−1.34517			−0.672583	−	0.740021i	$-0.734815\pi$
$521$	−30.7040			−1.34517			−0.672583	+	0.740021i	$0.734815\pi$
$522$	4.32424	+	10.9824i	0.189267	+	0.480687i
$523$	37.0601			1.62052			0.810262	−	0.586068i	$-0.199325\pi$
$523$	37.0601			1.62052			0.810262	+	0.586068i	$0.199325\pi$
$524$	−6.51798	+	28.5571i	−0.284739	+	1.24752i
$525$	−0.906838	+	0.436710i	−0.0395776	+	0.0190596i
$526$	28.8518	+	13.8943i	1.25800	+	0.605821i
$527$	−5.51319	+	24.1548i	−0.240158	+	1.05220i
$528$	1.36354	+	5.97405i	0.0593404	+	0.259987i
$529$	19.7945	−	9.53252i	0.860630	−	0.414458i
$530$	−43.7008	+	54.7991i	−1.89824	+	2.38032i
$531$	2.22026	−	2.78412i	0.0963512	−	0.120821i
$532$	−19.2472	−	9.26895i	−0.834471	−	0.401860i
$533$	−25.8029	−	32.3558i	−1.11765	−	1.40149i
$534$	−30.6683			−1.32715
$535$	9.36542	+	11.7439i	0.404903	+	0.507732i
$536$	3.25931	+	14.2800i	0.140781	+	0.616801i
$537$	2.98150	+	13.0628i	0.128661	+	0.563702i
$538$	−30.2206	−	37.8955i	−1.30290	−	1.63379i
$539$	−18.1525			−0.781886
$540$	−4.19002	−	5.25412i	−0.180310	−	0.226101i
$541$	−30.6558	−	14.7631i	−1.31800	−	0.634714i	−0.363128	−	0.931739i	$-0.618291\pi$
$541$	−30.6558	−	14.7631i	−1.31800	−	0.634714i	−0.954870	+	0.297025i	$0.904006\pi$
$542$	31.5880	−	39.6101i	1.35682	−	1.70140i
$543$	0.943898	−	1.18361i	0.0405065	−	0.0507936i
$544$	−20.2284	+	9.74148i	−0.867285	+	0.417663i
$545$	−7.89720	−	34.5999i	−0.338279	−	1.48210i
$546$	3.97894	−	17.4329i	0.170283	−	0.746058i
$547$	−15.4934	−	7.46124i	−0.662451	−	0.319020i	0.0722738	−	0.997385i	$-0.476974\pi$
$547$	−15.4934	−	7.46124i	−0.662451	−	0.319020i	−0.734725	+	0.678365i	$0.762689\pi$
$548$	9.27656	−	4.46735i	0.396275	−	0.190836i
$549$	−1.60427	+	7.02878i	−0.0684687	+	0.299981i
$550$	−5.72689			−0.244196
$551$	22.2704	+	20.6183i	0.948750	+	0.878369i
$552$	−1.78797			−0.0761009
$553$	−1.20523	+	5.28046i	−0.0512516	+	0.224548i
$554$	36.9530	−	17.7956i	1.56998	−	0.756063i
$555$	11.8691	+	5.71587i	0.503816	+	0.242625i
$556$	−3.60711	+	15.8038i	−0.152975	+	0.670229i
$557$	6.60546	+	28.9404i	0.279882	+	1.22624i	0.897942	+	0.440114i	$0.145062\pi$
$557$	6.60546	+	28.9404i	0.279882	+	1.22624i	−0.618060	+	0.786131i	$0.712081\pi$
$558$	16.0183	−	7.71400i	0.678108	−	0.326560i
$559$	−29.3553	+	36.8104i	−1.24160	+	1.55692i
$560$	3.52736	−	4.42316i	0.149058	−	0.186913i
$561$	−9.65788	−	4.65099i	−0.407756	−	0.196365i
$562$	11.8423	+	14.8498i	0.499539	+	0.626402i
$563$	−27.8621			−1.17425			−0.587125	−	0.809497i	$-0.699740\pi$
$563$	−27.8621			−1.17425			−0.587125	+	0.809497i	$0.699740\pi$
$564$	−0.731188	−	0.916881i	−0.0307886	−	0.0386077i
$565$	6.34305	+	27.7907i	0.266854	+	1.16916i
$566$	2.72387	+	11.9341i	0.114493	+	0.501627i
$567$	0.842900	+	1.05696i	0.0353985	+	0.0443883i
$568$	17.2436			0.723526
$569$	−6.10300	−	7.65292i	−0.255851	−	0.320827i	0.637272	−	0.770639i	$-0.280063\pi$
$569$	−6.10300	−	7.65292i	−0.255851	−	0.320827i	−0.893124	+	0.449811i	$0.851491\pi$
$570$	−26.6737	−	12.8454i	−1.11724	−	0.538034i
$571$	−20.1541	+	25.2725i	−0.843424	+	1.05762i	0.154153	+	0.988047i	$0.450735\pi$
$571$	−20.1541	+	25.2725i	−0.843424	+	1.05762i	−0.997577	+	0.0695735i	$0.977836\pi$
$572$	37.0248	−	46.4276i	1.54808	−	1.94124i
$573$	10.4680	−	5.04115i	0.437309	−	0.210597i
$574$	−4.52168	−	19.8108i	−0.188731	−	0.826886i
$575$	−0.168118	+	0.736574i	−0.00701101	+	0.0307172i
$576$	11.3694	+	5.47523i	0.473726	+	0.228135i
$577$	39.2874	−	18.9198i	1.63555	−	0.787641i	0.635677	−	0.771955i	$-0.280721\pi$
$577$	39.2874	−	18.9198i	1.63555	−	0.787641i	0.999877	−	0.0156861i	$-0.00499325\pi$
$578$	−3.74118	+	16.3912i	−0.155613	+	0.681783i
$579$	−6.16179			−0.256075
$580$	29.8789	−	20.4193i	1.24065	−	0.847866i
$581$	−5.83259			−0.241977
$582$	−1.85506	+	8.12757i	−0.0768949	+	0.336898i
$583$	42.1888	−	20.3170i	1.74728	−	0.841446i
$584$	−0.482155	−	0.232194i	−0.0199517	−	0.00960824i
$585$	3.21848	−	14.1011i	0.133068	−	0.583008i
$586$	−2.30153	−	10.0837i	−0.0950752	−	0.416552i
$587$	39.3393	−	18.9448i	1.62371	−	0.781935i	0.623705	−	0.781660i	$-0.285627\pi$
$587$	39.3393	−	18.9448i	1.62371	−	0.781935i	1.00000		0.000275397i	$-8.76615e-5\pi$
$588$	−9.04226	+	11.3386i	−0.372896	+	0.467597i
$589$	28.5030	−	35.7416i	1.17444	−	1.47271i
$590$	−16.8542	−	8.11654i	−0.693876	−	0.334153i
$591$	−1.57538	−	1.97547i	−0.0648026	−	0.0812599i
$592$	−9.59684			−0.394428
$593$	14.9685	+	18.7699i	0.614682	+	0.770787i	0.987585	−	0.157083i	$-0.0502091\pi$
$593$	14.9685	+	18.7699i	0.614682	+	0.770787i	−0.372903	+	0.927870i	$0.621638\pi$
$594$	1.71166	+	7.49926i	0.0702302	+	0.307699i
$595$	2.20225	+	9.64868i	0.0902834	+	0.395557i
$596$	−15.0068	−	18.8179i	−0.614701	−	0.770811i
$597$	13.2818			0.543589
$598$	−8.36854	−	10.4938i	−0.342215	−	0.429124i
$599$	−3.27503	−	1.57717i	−0.133814	−	0.0644415i	0.365779	−	0.930702i	$-0.380803\pi$
$599$	−3.27503	−	1.57717i	−0.133814	−	0.0644415i	−0.499593	+	0.866260i	$0.666517\pi$
$600$	−0.817883	+	1.02559i	−0.0333899	+	0.0418696i
$601$	−9.51453	+	11.9308i	−0.388106	+	0.486669i	−0.937053	−	0.349188i	$-0.886458\pi$
$601$	−9.51453	+	11.9308i	−0.388106	+	0.486669i	0.548947	+	0.835857i	$0.315029\pi$
$602$	−20.8285	+	10.0305i	−0.848905	+	0.408811i
$603$	−1.84985	−	8.10474i	−0.0753319	−	0.330051i
$604$	−7.45003	+	32.6407i	−0.303137	+	1.32813i
$605$	2.84364	+	1.36943i	0.115611	+	0.0556751i
$606$	−0.0833766	+	0.0401520i	−0.00338694	+	0.00163106i
$607$	0.643106	−	2.81763i	0.0261029	−	0.114364i	−0.960198	−	0.279320i	$-0.909891\pi$
$607$	0.643106	−	2.81763i	0.0261029	−	0.114364i	0.986301	+	0.164956i	$0.0527482\pi$
$608$	41.4267			1.68007
$609$	−6.01070	+	4.10773i	−0.243566	+	0.166453i
$610$	37.8730			1.53343
$611$	0.561648	−	2.46074i	0.0227219	−	0.0995509i
$612$	−7.71599	+	3.71582i	−0.311900	+	0.150203i
$613$	3.96789	+	1.91083i	0.160261	+	0.0771778i	0.512295	−	0.858810i	$-0.328795\pi$
$613$	3.96789	+	1.91083i	0.160261	+	0.0771778i	−0.352034	+	0.935987i	$0.614510\pi$
$614$	5.72394	−	25.0782i	0.230999	−	1.01207i
$615$	−3.65749	−	16.0245i	−0.147484	−	0.646172i
$616$	7.53174	−	3.62710i	0.303463	−	0.146140i
$617$	4.33910	−	5.44106i	0.174686	−	0.219049i	−0.686779	−	0.726866i	$-0.740976\pi$
$617$	4.33910	−	5.44106i	0.174686	−	0.219049i	0.861465	+	0.507817i	$0.169547\pi$
$618$	−16.0985	+	20.1868i	−0.647575	+	0.812033i
$619$	−11.8459	−	5.70468i	−0.476127	−	0.229291i	0.180400	−	0.983593i	$-0.442261\pi$
$619$	−11.8459	−	5.70468i	−0.476127	−	0.229291i	−0.656527	+	0.754303i	$0.727975\pi$
$620$	−33.9880	−	42.6196i	−1.36499	−	1.71165i
$621$	1.01478			0.0407216
$622$	−22.9633	−	28.7950i	−0.920743	−	1.15458i
$623$	−4.20932	−	18.4422i	−0.168643	−	0.738872i
$624$	2.34461	+	10.2724i	0.0938595	+	0.411225i
$625$	−17.5626	−	22.0228i	−0.702505	−	0.880914i
$626$	26.2134			1.04770
$627$	12.3319	+	15.4637i	0.492489	+	0.617561i
$628$	30.9549	+	14.9071i	1.23524	+	0.594858i
$629$	10.4673	−	13.1255i	0.417357	−	0.523349i
$630$	4.42791	−	5.55243i	0.176412	−	0.221214i
$631$	11.9773	−	5.76796i	0.476808	−	0.229619i	−0.180014	−	0.983664i	$-0.557614\pi$
$631$	11.9773	−	5.76796i	0.476808	−	0.229619i	0.656823	+	0.754045i	$0.271900\pi$
$632$	1.57077	+	6.88198i	0.0624818	+	0.273750i
$633$	1.84799	−	8.09656i	0.0734509	−	0.321809i
$634$	−27.9146	−	13.4430i	−1.10863	−	0.533888i
$635$	−32.5937	+	15.6963i	−1.29344	+	0.622889i
$636$	8.32469	−	36.4728i	0.330095	−	1.44624i
$637$	−31.2134			−1.23672
$638$	−40.9539	+	6.21892i	−1.62138	+	0.246209i
$639$	−9.78678			−0.387159
$640$	6.91029	−	30.2760i	0.273153	−	1.19676i
$641$	−18.1431	+	8.73725i	−0.716609	+	0.345101i	−0.756402	−	0.654107i	$-0.773045\pi$
$641$	−18.1431	+	8.73725i	−0.716609	+	0.345101i	0.0397927	+	0.999208i	$0.487330\pi$
$642$	−12.3759	−	5.95993i	−0.488439	−	0.235220i
$643$	−9.82444	+	43.0437i	−0.387438	+	1.69748i	0.285997	+	0.958231i	$0.407675\pi$
$643$	−9.82444	+	43.0437i	−0.387438	+	1.69748i	−0.673435	+	0.739247i	$0.735182\pi$
$644$	−0.855950	−	3.75016i	−0.0337292	−	0.147777i
$645$	−16.8477	+	8.11343i	−0.663378	+	0.319466i
$646$	−23.5233	+	29.4973i	−0.925511	+	1.16055i
$647$	11.3676	−	14.2546i	0.446908	−	0.560404i	−0.506442	−	0.862274i	$-0.669039\pi$
$647$	11.3676	−	14.2546i	0.446908	−	0.560404i	0.953349	+	0.301870i	$0.0976108\pi$
$648$	1.58744	+	0.764473i	0.0623607	+	0.0300313i
$649$	7.79210	+	9.77098i	0.305866	+	0.383544i
$650$	−9.84742			−0.386248
$651$	6.83732	+	8.57373i	0.267976	+	0.336031i
$652$	4.94858	+	21.6811i	0.193801	+	0.849099i
$653$	3.38155	+	14.8156i	0.132330	+	0.579778i	0.996998	+	0.0774324i	$0.0246722\pi$
$653$	3.38155	+	14.8156i	0.132330	+	0.579778i	−0.864667	+	0.502345i	$0.832471\pi$
$654$	20.2349	+	25.3738i	0.791247	+	0.992193i
$655$	−25.0385			−0.978336
$656$	7.46555	+	9.36150i	0.291481	+	0.365505i
$657$	0.273652	+	0.131784i	0.0106762	+	0.00514137i
$658$	0.772703	−	0.968939i	0.0301231	−	0.0377732i
$659$	−10.4628	+	13.1200i	−0.407574	+	0.511082i	−0.942678	−	0.333704i	$-0.891701\pi$
$659$	−10.4628	+	13.1200i	−0.407574	+	0.511082i	0.535103	+	0.844787i	$0.320273\pi$
$660$	21.2494	−	10.2332i	0.827131	−	0.398325i
$661$	0.299039	+	1.31018i	0.0116313	+	0.0509599i	0.980411	−	0.196965i	$-0.0631085\pi$
$661$	0.299039	+	1.31018i	0.0116313	+	0.0509599i	−0.968779	+	0.247925i	$0.920251\pi$
$662$	11.2290	−	49.1975i	0.436428	−	1.91211i
$663$	−16.6068	−	7.99740i	−0.644953	−	0.310593i
$664$	−6.84877	+	3.29820i	−0.265784	+	0.127995i
$665$	4.06345	−	17.8031i	0.157574	−	0.690376i
$666$	−12.0470			−0.466811
$667$	−0.402381	+	5.44991i	−0.0155803	+	0.211021i
$668$	36.2386			1.40211
$669$	−5.56568	+	24.3848i	−0.215182	+	0.942772i
$670$	−39.3459	+	18.9480i	−1.52006	+	0.732024i
$671$	−22.7964	−	10.9782i	−0.880047	−	0.423808i
$672$	−2.21130	+	9.68834i	−0.0853027	+	0.373736i
$673$	−2.65230	−	11.6205i	−0.102239	−	0.447937i	−0.999973	−	0.00739895i	$-0.997645\pi$
$673$	−2.65230	−	11.6205i	−0.102239	−	0.447937i	0.897734	−	0.440538i	$-0.145212\pi$
$674$	−5.04797	+	2.43098i	−0.194441	+	0.0936377i
$675$	0.464197	−	0.582085i	0.0178669	−	0.0224044i
$676$	40.9378	−	51.3344i	1.57453	−	1.97440i
$677$	−14.6012	−	7.03155i	−0.561169	−	0.270245i	0.131723	−	0.991287i	$-0.457949\pi$
$677$	−14.6012	−	7.03155i	−0.561169	−	0.270245i	−0.692891	+	0.721042i	$0.743663\pi$
$678$	−16.2527	−	20.3803i	−0.624182	−	0.782700i
$679$	−5.14208			−0.197335
$680$	8.04205	+	10.0844i	0.308398	+	0.386719i
$681$	−0.677325	−	2.96756i	−0.0259552	−	0.113717i
$682$	13.8844	+	60.8315i	0.531661	+	2.32936i
$683$	−17.9645	−	22.5268i	−0.687393	−	0.861964i	0.308619	−	0.951186i	$-0.400133\pi$
$683$	−17.9645	−	22.5268i	−0.687393	−	0.861964i	−0.996012	+	0.0892221i	$0.971562\pi$
$684$	15.8019			0.604202
$685$	5.48748	+	6.88109i	0.209666	+	0.262913i
$686$	−32.4958	−	15.6492i	−1.24070	−	0.597487i
$687$	−13.6598	+	17.1288i	−0.521152	+	0.653505i
$688$	8.49337	−	10.6503i	0.323807	−	0.406041i
$689$	72.5438	−	34.9353i	2.76370	−	1.33093i
$690$	−1.18622	−	5.19716i	−0.0451585	−	0.197853i
$691$	5.64168	−	24.7178i	0.214620	−	0.940310i	−0.746762	−	0.665092i	$-0.768393\pi$
$691$	5.64168	−	24.7178i	0.214620	−	0.940310i	0.961382	−	0.275219i	$-0.0887503\pi$
$692$	−6.70349	−	3.22823i	−0.254828	−	0.122719i
$693$	−4.27471	+	2.05859i	−0.162383	+	0.0781994i
$694$	−0.434987	+	1.90580i	−0.0165119	+	0.0723432i
$695$	−13.8566			−0.525609
$696$	−4.73509	+	8.22231i	−0.179483	+	0.311666i
$697$	−20.9463			−0.793399
$698$	−0.368506	+	1.61453i	−0.0139482	+	0.0611109i
$699$	−8.97783	+	4.32349i	−0.339573	+	0.163530i
$700$	−2.54267	−	1.22448i	−0.0961038	−	0.0462811i
$701$	−2.93968	+	12.8796i	−0.111030	+	0.486455i	0.888585	+	0.458712i	$0.151689\pi$
$701$	−2.93968	+	12.8796i	−0.111030	+	0.486455i	−0.999615	+	0.0277426i	$0.991168\pi$
$702$	2.94320	+	12.8950i	0.111084	+	0.486691i
$703$	−27.9089	+	13.4402i	−1.05260	+	0.506907i
$704$	−27.6127	+	34.6252i	−1.04069	+	1.30499i
$705$	0.625023	−	0.783754i	0.0235397	−	0.0295179i
$706$	37.9948	+	18.2973i	1.42995	+	0.688629i
$707$	−0.0355889	−	0.0446270i	−0.00133846	−	0.00167837i
$708$	9.98469			0.375248
$709$	−22.2400	−	27.8881i	−0.835240	−	1.04736i	−0.998155	−	0.0607181i	$-0.980661\pi$
$709$	−22.2400	−	27.8881i	−0.835240	−	1.04736i	0.162915	−	0.986640i	$-0.447911\pi$
$710$	11.4402	+	50.1228i	0.429343	+	1.88107i
$711$	−0.891504	−	3.90593i	−0.0334340	−	0.146484i
$712$	−15.3713	−	19.2751i	−0.576065	−	0.722363i
$713$	8.23153			0.308273
$714$	−5.64280	−	7.07584i	−0.211176	−	0.264807i
$715$	45.7341	+	22.0244i	1.71036	+	0.823665i
$716$	−23.4236	+	29.3723i	−0.875381	+	1.09769i
$717$	−4.85135	+	6.08341i	−0.181177	+	0.227189i
$718$	34.7839	−	16.7510i	1.29812	−	0.625143i
$719$	−0.450188	−	1.97240i	−0.0167892	−	0.0735583i	0.965839	−	0.259142i	$-0.0834397\pi$
$719$	−0.450188	−	1.97240i	−0.0167892	−	0.0735583i	−0.982629	+	0.185583i	$0.940583\pi$
$720$	−0.931202	+	4.07986i	−0.0347038	+	0.152047i
$721$	−14.3488	−	6.91002i	−0.534377	−	0.257342i
$722$	25.2004	−	12.1359i	0.937863	−	0.451651i
$723$	5.16007	−	22.6077i	0.191905	−	0.840791i
$724$	4.24478			0.157756
$725$	2.94205	+	2.72380i	0.109265	+	0.101159i
$726$	−2.88626			−0.107119
$727$	2.34647	−	10.2806i	0.0870258	−	0.381285i	−0.912594	−	0.408868i	$-0.865924\pi$
$727$	2.34647	−	10.2806i	0.0870258	−	0.381285i	0.999620	+	0.0275826i	$0.00878092\pi$
$728$	12.9509	−	6.23681i	0.479991	−	0.231152i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	0.355044	−	1.55555i	0.0131408	−	0.0575734i
$731$	5.30270	+	23.2326i	0.196127	+	0.859291i
$732$	−18.2128	+	8.77083i	−0.673165	+	0.324179i
$733$	−11.8578	+	14.8692i	−0.437979	+	0.549208i	−0.951009	−	0.309162i	$-0.899951\pi$
$733$	−11.8578	+	14.8692i	−0.437979	+	0.549208i	0.513030	+	0.858370i	$0.328523\pi$
$734$	−5.18998	+	6.50802i	−0.191566	+	0.240216i
$735$	−11.1693	−	5.37883i	−0.411984	−	0.198401i
$736$	4.65083	+	5.83195i	0.171432	+	0.214969i
$737$	29.1754			1.07469
$738$	9.37156	+	11.7516i	0.344972	+	0.432581i
$739$	9.57638	+	41.9569i	0.352273	+	1.54341i	0.771919	+	0.635721i	$0.219297\pi$
$739$	9.57638	+	41.9569i	0.352273	+	1.54341i	−0.419646	+	0.907688i	$0.637846\pi$
$740$	8.21938	+	36.0115i	0.302151	+	1.32381i
$741$	21.2048	+	26.5899i	0.778976	+	0.976805i
$742$	39.5349			1.45137
$743$	−2.07331	−	2.59985i	−0.0760625	−	0.0953794i	0.742344	−	0.670019i	$-0.233714\pi$
$743$	−2.07331	−	2.59985i	−0.0760625	−	0.0953794i	−0.818407	+	0.574639i	$0.805142\pi$
$744$	12.8768	+	6.20115i	0.472087	+	0.227345i
$745$	12.8279	−	16.0856i	0.469976	−	0.589331i
$746$	11.3323	−	14.2103i	0.414905	−	0.520275i
$747$	3.88709	−	1.87192i	0.142221	−	0.0684900i
$748$	−6.68810	−	29.3025i	−0.244541	−	1.07140i
$749$	1.88534	−	8.26021i	0.0688888	−	0.301821i
$750$	20.1410	+	9.69941i	0.735447	+	0.354172i
$751$	−18.4506	+	8.88532i	−0.673271	+	0.324230i	−0.739095	−	0.673601i	$-0.764747\pi$
$751$	−18.4506	+	8.88532i	−0.673271	+	0.324230i	0.0658243	+	0.997831i	$0.479032\pi$
$752$	−0.162501	+	0.711965i	−0.00592582	+	0.0259627i
$753$	1.18054			0.0430212
$754$	−70.4204	+	10.6935i	−2.56456	+	0.389433i
$755$	−28.6190			−1.04155
$756$	−0.843485	+	3.69555i	−0.0306773	+	0.134406i
$757$	7.59189	−	3.65606i	0.275932	−	0.132882i	−0.290801	−	0.956784i	$-0.593922\pi$
$757$	7.59189	−	3.65606i	0.275932	−	0.132882i	0.566732	+	0.823902i	$0.308207\pi$
$758$	−17.6390	−	8.49448i	−0.640676	−	0.308533i
$759$	−0.792486	+	3.47211i	−0.0287654	+	0.126030i
$760$	−5.29586	−	23.2027i	−0.192101	−	0.841650i
$761$	23.5526	−	11.3423i	0.853780	−	0.411159i	0.0448010	−	0.998996i	$-0.485735\pi$
$761$	23.5526	−	11.3423i	0.853780	−	0.411159i	0.808979	+	0.587837i	$0.200020\pi$
$762$	20.6264	−	25.8647i	0.747215	−	0.936978i
$763$	−12.4811	+	15.6508i	−0.451845	+	0.566596i
$764$	29.3512	+	14.1348i	1.06189	+	0.511378i
$765$	−4.56434	−	5.72350i	−0.165024	−	0.206934i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.487716 - 2.13682i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-2.52621 - 1.21656i) q^{4} +(0.533332 - 2.33668i) q^{5} +(0.487716 + 2.13682i) q^{6} +(-1.21803 + 0.586571i) q^{7} +(-1.09855 + 1.37753i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})\)	\(q+(0.487716 - 2.13682i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(-2.52621 - 1.21656i) q^{4} +(0.533332 - 2.33668i) q^{5} +(0.487716 + 2.13682i) q^{6} +(-1.21803 + 0.586571i) q^{7} +(-1.09855 + 1.37753i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-4.73296 - 2.27927i) q^{10} +(2.18816 + 2.74387i) q^{11} +2.80388 q^{12} +(3.76255 + 4.71809i) q^{13} +(0.659347 + 2.88879i) q^{14} +(0.533332 + 2.33668i) q^{15} +(-1.08862 - 1.36508i) q^{16} +3.05437 q^{17} +(-1.36655 - 1.71360i) q^{18} +(-5.07762 - 2.44525i) q^{19} +(-4.19002 + 5.25412i) q^{20} +(0.842900 - 1.05696i) q^{21} +(6.93036 - 3.33749i) q^{22} +(-0.225809 - 0.989335i) q^{23} +(0.392066 - 1.71776i) q^{24} +(-0.670784 - 0.323033i) q^{25} +(11.9168 - 5.73883i) q^{26} +(-0.222521 + 0.974928i) q^{27} +3.79059 q^{28} +(-5.14766 - 1.58164i) q^{29} +5.25319 q^{30} +(-1.80501 + 7.90829i) q^{31} +(-6.62277 + 3.18936i) q^{32} +(-3.16198 - 1.52273i) q^{33} +(1.48967 - 6.52665i) q^{34} +(0.721015 + 3.15897i) q^{35} +(-2.52621 + 1.21656i) q^{36} +(3.42698 - 4.29729i) q^{37} +(-7.70151 + 9.65739i) q^{38} +(-5.43705 - 2.61834i) q^{39} +(2.63296 + 3.30163i) q^{40} -6.85782 q^{41} +(-1.84745 - 2.31663i) q^{42} +(1.73610 + 7.60636i) q^{43} +(-2.18968 - 9.59361i) q^{44} +(-1.49436 - 1.87387i) q^{45} -2.22416 q^{46} +(-0.260777 - 0.327004i) q^{47} +(1.57310 + 0.757565i) q^{48} +(-3.22491 + 4.04390i) q^{49} +(-1.01742 + 1.27580i) q^{50} +(-2.75189 + 1.32524i) q^{51} +(-3.76517 - 16.4963i) q^{52} +(2.96899 - 13.0080i) q^{53} +(1.97472 + 0.950976i) q^{54} +(7.57855 - 3.64964i) q^{55} +(0.530037 - 2.32225i) q^{56} +5.63574 q^{57} +(-5.89028 + 10.2283i) q^{58} +3.56102 q^{59} +(1.49540 - 6.55177i) q^{60} +(-6.49557 + 3.12810i) q^{61} +(16.0183 + 7.71400i) q^{62} +(-0.300828 + 1.31801i) q^{63} +(2.80802 + 12.3027i) q^{64} +(13.0314 - 6.27557i) q^{65} +(-4.79596 + 6.01394i) q^{66} +(5.18318 - 6.49950i) q^{67} +(-7.71599 - 3.71582i) q^{68} +(0.632703 + 0.793385i) q^{69} +7.10182 q^{70} +(-6.10196 - 7.65161i) q^{71} +(0.392066 + 1.71776i) q^{72} +(0.0675863 + 0.296115i) q^{73} +(-7.51117 - 9.41871i) q^{74} +0.744514 q^{75} +(9.85235 + 12.3545i) q^{76} +(-4.27471 - 2.05859i) q^{77} +(-8.24668 + 10.3410i) q^{78} +(2.49794 - 3.13231i) q^{79} +(-3.77036 + 1.81571i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-3.34467 + 14.6540i) q^{82} +(3.88709 + 1.87192i) q^{83} +(-3.41520 + 1.64468i) q^{84} +(1.62899 - 7.13709i) q^{85} +17.1002 q^{86} +(5.32413 - 0.808479i) q^{87} -6.18356 q^{88} +(-3.11361 + 13.6416i) q^{89} +(-4.73296 + 2.27927i) q^{90} +(-7.35039 - 3.53976i) q^{91} +(-0.633143 + 2.77398i) q^{92} +(-1.80501 - 7.90829i) q^{93} +(-0.825935 + 0.397749i) q^{94} +(-8.42183 + 10.5606i) q^{95} +(4.58310 - 5.74702i) q^{96} +(3.42690 + 1.65031i) q^{97} +(7.06827 + 8.86333i) q^{98} +3.50954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

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