LMFDB - Embedded newform 87.2.g.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			49.1
Root			$1.10857 - 1.39010i$ of defining polynomial
Character	$\chi$	$=$	87.49
Dual form			87.2.g.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50290 + 1.20533i) q^{2} +(0.623490 + 0.781831i) q^{3} +(3.56470 - 4.46999i) q^{4} +(2.28635 - 1.10105i) q^{5} +(-2.50290 - 1.20533i) q^{6} +(0.527912 + 0.661981i) q^{7} +(-2.29793 + 10.0679i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})$	\(q+(-2.50290 + 1.20533i) q^{2} +(0.623490 + 0.781831i) q^{3} +(3.56470 - 4.46999i) q^{4} +(2.28635 - 1.10105i) q^{5} +(-2.50290 - 1.20533i) q^{6} +(0.527912 + 0.661981i) q^{7} +(-2.29793 + 10.0679i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(-4.39538 + 5.51163i) q^{10} +(-0.279921 - 1.22641i) q^{11} +5.71733 q^{12} +(0.494312 + 2.16572i) q^{13} +(-2.11922 - 1.02056i) q^{14} +(2.28635 + 1.10105i) q^{15} +(-3.83921 - 16.8207i) q^{16} +3.75587 q^{17} +(-0.618165 - 2.70836i) q^{18} +(-1.84230 + 2.31017i) q^{19} +(3.22848 - 14.1449i) q^{20} +(-0.188410 + 0.825477i) q^{21} +(2.17885 + 2.73219i) q^{22} +(-5.78259 - 2.78475i) q^{23} +(-9.30411 + 4.48063i) q^{24} +(0.897653 - 1.12562i) q^{25} +(-3.84763 - 4.82478i) q^{26} +(-0.900969 + 0.433884i) q^{27} +4.84090 q^{28} +(4.24261 - 3.31666i) q^{29} -7.04965 q^{30} +(-0.518900 + 0.249889i) q^{31} +(17.0064 + 21.3253i) q^{32} +(0.784321 - 0.983507i) q^{33} +(-9.40056 + 4.52707i) q^{34} +(1.93587 + 0.932265i) q^{35} +(3.56470 + 4.46999i) q^{36} +(0.893407 - 3.91427i) q^{37} +(1.82657 - 8.00271i) q^{38} +(-1.38503 + 1.73677i) q^{39} +(5.83136 + 25.5489i) q^{40} -9.29991 q^{41} +(-0.523404 - 2.29318i) q^{42} +(-8.60331 - 4.14313i) q^{43} +(-6.47989 - 3.12055i) q^{44} +(0.564683 + 2.47404i) q^{45} +17.8298 q^{46} +(0.626576 + 2.74521i) q^{47} +(10.7572 - 13.4891i) q^{48} +(1.39812 - 6.12556i) q^{49} +(-0.889987 + 3.89929i) q^{50} +(2.34175 + 2.93646i) q^{51} +(11.4428 + 5.51058i) q^{52} +(-3.55697 + 1.71295i) q^{53} +(1.73206 - 2.17193i) q^{54} +(-1.99034 - 2.49581i) q^{55} +(-7.87785 + 3.79377i) q^{56} -2.95482 q^{57} +(-6.62115 + 13.4150i) q^{58} +2.24563 q^{59} +(13.0718 - 6.29507i) q^{60} +(-2.97162 - 3.72629i) q^{61} +(0.997555 - 1.25089i) q^{62} +(-0.762856 + 0.367372i) q^{63} +(-37.1800 - 17.9050i) q^{64} +(3.51474 + 4.40735i) q^{65} +(-0.777623 + 3.40699i) q^{66} +(0.0320387 - 0.140371i) q^{67} +(13.3885 - 16.7887i) q^{68} +(-1.42818 - 6.25727i) q^{69} -5.96898 q^{70} +(1.13905 + 4.99050i) q^{71} +(-9.30411 - 4.48063i) q^{72} +(-1.24324 - 0.598712i) q^{73} +(2.48189 + 10.8739i) q^{74} +1.43972 q^{75} +(3.75920 + 16.4701i) q^{76} +(0.664089 - 0.832741i) q^{77} +(1.37320 - 6.01640i) q^{78} +(-0.0599388 + 0.262609i) q^{79} +(-27.2982 - 34.2308i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(23.2767 - 11.2095i) q^{82} +(-4.26140 + 5.34363i) q^{83} +(3.01825 + 3.78477i) q^{84} +(8.58724 - 4.13540i) q^{85} +26.5271 q^{86} +(5.23830 + 1.24910i) q^{87} +12.9906 q^{88} +(4.15363 - 2.00028i) q^{89} +(-4.39538 - 5.51163i) q^{90} +(-1.17271 + 1.47054i) q^{91} +(-33.0610 + 15.9213i) q^{92} +(-0.518900 - 0.249889i) q^{93} +(-4.87715 - 6.11575i) q^{94} +(-1.66853 + 7.31033i) q^{95} +(-6.06950 + 26.5922i) q^{96} +(-2.88047 + 3.61199i) q^{97} +(3.88399 + 17.0169i) q^{98} +1.25795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.50290	+	1.20533i	−1.76982	+	0.852299i	−0.803351	+	0.595506i	$0.796952\pi$
$2$	−2.50290	+	1.20533i	−1.76982	+	0.852299i	−0.966466	+	0.256793i	$0.917334\pi$
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$4$	3.56470	−	4.46999i	1.78235	−	2.23500i
$5$	2.28635	−	1.10105i	1.02249	−	0.492404i	0.153977	−	0.988074i	$-0.450792\pi$
$5$	2.28635	−	1.10105i	1.02249	−	0.492404i	0.868511	+	0.495670i	$0.165077\pi$
$6$	−2.50290	−	1.20533i	−1.02180	−	0.492075i
$7$	0.527912	+	0.661981i	0.199532	+	0.250205i	0.871524	−	0.490353i	$-0.163132\pi$
$7$	0.527912	+	0.661981i	0.199532	+	0.250205i	−0.671992	+	0.740559i	$0.734561\pi$
$8$	−2.29793	+	10.0679i	−0.812440	+	3.55953i
$9$	−0.222521	+	0.974928i	−0.0741736	+	0.324976i
$10$	−4.39538	+	5.51163i	−1.38994	+	1.74293i
$11$	−0.279921	−	1.22641i	−0.0843993	−	0.369778i	0.915036	−	0.403372i	$-0.132162\pi$
$11$	−0.279921	−	1.22641i	−0.0843993	−	0.369778i	−0.999436	+	0.0335941i	$0.989305\pi$
$12$	5.71733			1.65045
$13$	0.494312	+	2.16572i	0.137098	+	0.600663i	0.996064	+	0.0886323i	$0.0282496\pi$
$13$	0.494312	+	2.16572i	0.137098	+	0.600663i	−0.858967	+	0.512031i	$0.828893\pi$
$14$	−2.11922	−	1.02056i	−0.566385	−	0.272757i
$15$	2.28635	+	1.10105i	0.590334	+	0.284290i
$16$	−3.83921	−	16.8207i	−0.959802	−	4.20517i
$17$	3.75587			0.910932			0.455466	−	0.890253i	$-0.349473\pi$
$17$	3.75587			0.910932			0.455466	+	0.890253i	$0.349473\pi$
$18$	−0.618165	−	2.70836i	−0.145703	−	0.638366i
$19$	−1.84230	+	2.31017i	−0.422652	+	0.529989i	−0.946879	−	0.321589i	$-0.895783\pi$
$19$	−1.84230	+	2.31017i	−0.422652	+	0.529989i	0.524227	+	0.851579i	$0.324354\pi$
$20$	3.22848	−	14.1449i	0.721910	−	3.16289i
$21$	−0.188410	+	0.825477i	−0.0411144	+	0.180134i
$22$	2.17885	+	2.73219i	0.464532	+	0.582505i
$23$	−5.78259	−	2.78475i	−1.20575	−	0.580660i	−0.280443	−	0.959871i	$-0.590481\pi$
$23$	−5.78259	−	2.78475i	−1.20575	−	0.580660i	−0.925310	+	0.379211i	$0.876196\pi$
$24$	−9.30411	+	4.48063i	−1.89919	+	0.914604i
$25$	0.897653	−	1.12562i	0.179531	−	0.225124i
$26$	−3.84763	−	4.82478i	−0.754582	−	0.946216i
$27$	−0.900969	+	0.433884i	−0.173392	+	0.0835010i
$28$	4.84090			0.914844
$29$	4.24261	−	3.31666i	0.787833	−	0.615889i
$29$	4.24261	−	3.31666i	0.787833	−	0.615889i
$30$	−7.04965			−1.28708
$31$	−0.518900	+	0.249889i	−0.0931972	+	0.0448814i	−0.479902	−	0.877322i	$-0.659328\pi$
$31$	−0.518900	+	0.249889i	−0.0931972	+	0.0448814i	0.386704	+	0.922204i	$0.373613\pi$
$32$	17.0064	+	21.3253i	3.00633	+	3.76982i
$33$	0.784321	−	0.983507i	0.136533	−	0.171207i
$34$	−9.40056	+	4.52707i	−1.61218	+	0.776386i
$35$	1.93587	+	0.932265i	0.327222	+	0.157582i
$36$	3.56470	+	4.46999i	0.594117	+	0.744999i
$37$	0.893407	−	3.91427i	0.146875	−	0.643502i	−0.846867	−	0.531805i	$-0.821514\pi$
$37$	0.893407	−	3.91427i	0.146875	−	0.643502i	0.993742	−	0.111698i	$-0.0356288\pi$
$38$	1.82657	−	8.00271i	0.296308	−	1.29821i
$39$	−1.38503	+	1.73677i	−0.221783	+	0.278107i
$40$	5.83136	+	25.5489i	0.922019	+	4.03963i
$41$	−9.29991			−1.45240			−0.726201	−	0.687482i	$-0.758716\pi$
$41$	−9.29991			−1.45240			−0.726201	+	0.687482i	$0.758716\pi$
$42$	−0.523404	−	2.29318i	−0.0807630	−	0.353846i
$43$	−8.60331	−	4.14313i	−1.31199	−	0.631822i	−0.358582	−	0.933498i	$-0.616740\pi$
$43$	−8.60331	−	4.14313i	−1.31199	−	0.631822i	−0.953410	+	0.301676i	$0.902454\pi$
$44$	−6.47989	−	3.12055i	−0.976880	−	0.470441i
$45$	0.564683	+	2.47404i	0.0841779	+	0.368808i
$46$	17.8298			2.62886
$47$	0.626576	+	2.74521i	0.0913956	+	0.400430i	0.999846	−	0.0175630i	$-0.00559076\pi$
$47$	0.626576	+	2.74521i	0.0913956	+	0.400430i	−0.908450	+	0.417993i	$0.862734\pi$
$48$	10.7572	−	13.4891i	1.55267	−	1.94699i
$49$	1.39812	−	6.12556i	0.199731	−	0.875080i
$50$	−0.889987	+	3.89929i	−0.125863	+	0.551443i
$51$	2.34175	+	2.93646i	0.327910	+	0.411186i
$52$	11.4428	+	5.51058i	1.58684	+	0.764180i
$53$	−3.55697	+	1.71295i	−0.488587	+	0.235291i	−0.661923	−	0.749571i	$-0.730260\pi$
$53$	−3.55697	+	1.71295i	−0.488587	+	0.235291i	0.173336	+	0.984863i	$0.444545\pi$
$54$	1.73206	−	2.17193i	0.235704	−	0.295563i
$55$	−1.99034	−	2.49581i	−0.268377	−	0.336535i
$56$	−7.87785	+	3.79377i	−1.05272	+	0.506964i
$57$	−2.95482			−0.391375
$58$	−6.62115	+	13.4150i	−0.869400	+	1.76148i
$59$	2.24563			0.292356			0.146178	−	0.989258i	$-0.453303\pi$
$59$	2.24563			0.292356			0.146178	+	0.989258i	$0.453303\pi$
$60$	13.0718	−	6.29507i	1.68757	−	0.812690i
$61$	−2.97162	−	3.72629i	−0.380477	−	0.477103i	0.554311	−	0.832310i	$-0.312982\pi$
$61$	−2.97162	−	3.72629i	−0.380477	−	0.477103i	−0.934788	+	0.355207i	$0.884410\pi$
$62$	0.997555	−	1.25089i	0.126690	−	0.158864i
$63$	−0.762856	+	0.367372i	−0.0961108	+	0.0462845i
$64$	−37.1800	−	17.9050i	−4.64750	−	2.23812i
$65$	3.51474	+	4.40735i	0.435950	+	0.546664i
$66$	−0.777623	+	3.40699i	−0.0957187	+	0.419371i
$67$	0.0320387	−	0.140371i	0.00391415	−	0.0171490i	−0.972933	−	0.231087i	$-0.925772\pi$
$67$	0.0320387	−	0.140371i	0.00391415	−	0.0171490i	0.976847	+	0.213938i	$0.0686290\pi$
$68$	13.3885	−	16.7887i	1.62360	−	2.03593i
$69$	−1.42818	−	6.25727i	−0.171933	−	0.753287i
$70$	−5.96898			−0.713429
$71$	1.13905	+	4.99050i	0.135180	+	0.592264i	0.996455	+	0.0841244i	$0.0268093\pi$
$71$	1.13905	+	4.99050i	0.135180	+	0.592264i	−0.861275	+	0.508139i	$0.830334\pi$
$72$	−9.30411	−	4.48063i	−1.09650	−	0.528047i
$73$	−1.24324	−	0.598712i	−0.145510	−	0.0700739i	0.359712	−	0.933063i	$-0.382875\pi$
$73$	−1.24324	−	0.598712i	−0.145510	−	0.0700739i	−0.505222	+	0.862990i	$0.668589\pi$
$74$	2.48189	+	10.8739i	0.288514	+	1.26406i
$75$	1.43972			0.166245
$76$	3.75920	+	16.4701i	0.431210	+	1.88925i
$77$	0.664089	−	0.832741i	0.0756800	−	0.0948997i
$78$	1.37320	−	6.01640i	0.155485	−	0.681223i
$79$	−0.0599388	+	0.262609i	−0.00674364	+	0.0295458i	−0.978188	−	0.207722i	$-0.933395\pi$
$79$	−0.0599388	+	0.262609i	−0.00674364	+	0.0295458i	0.971444	+	0.237268i	$0.0762520\pi$
$80$	−27.2982	−	34.2308i	−3.05203	−	3.82712i
$81$	−0.900969	−	0.433884i	−0.100108	−	0.0482093i
$82$	23.2767	−	11.2095i	2.57049	−	1.23788i
$83$	−4.26140	+	5.34363i	−0.467750	+	0.586540i	−0.958619	−	0.284694i	$-0.908108\pi$
$83$	−4.26140	+	5.34363i	−0.467750	+	0.586540i	0.490869	+	0.871234i	$0.336680\pi$
$84$	3.01825	+	3.78477i	0.329318	+	0.412952i
$85$	8.58724	−	4.13540i	0.931417	−	0.448547i
$86$	26.5271			2.86049
$87$	5.23830	+	1.24910i	0.561604	+	0.133918i
$88$	12.9906			1.38480
$89$	4.15363	−	2.00028i	0.440284	−	0.212030i	−0.200590	−	0.979675i	$-0.564286\pi$
$89$	4.15363	−	2.00028i	0.440284	−	0.212030i	0.640875	+	0.767645i	$0.278572\pi$
$90$	−4.39538	−	5.51163i	−0.463314	−	0.580977i
$91$	−1.17271	+	1.47054i	−0.122934	+	0.154154i
$92$	−33.0610	+	15.9213i	−3.44685	+	1.65991i
$93$	−0.518900	−	0.249889i	−0.0538074	−	0.0259123i
$94$	−4.87715	−	6.11575i	−0.503040	−	0.630792i
$95$	−1.66853	+	7.31033i	−0.171188	+	0.750024i
$96$	−6.06950	+	26.5922i	−0.619466	+	2.71406i
$97$	−2.88047	+	3.61199i	−0.292467	+	0.366742i	−0.906257	−	0.422727i	$-0.861073\pi$
$97$	−2.88047	+	3.61199i	−0.292467	+	0.366742i	0.613790	+	0.789469i	$0.289644\pi$
$98$	3.88399	+	17.0169i	0.392342	+	1.71896i
$99$	1.25795			0.126429
$100$	−1.83165	−	8.02500i	−0.183165	−	0.802500i
$101$	8.21134	+	3.95437i	0.817059	+	0.393475i	0.795246	−	0.606287i	$-0.207342\pi$
$101$	8.21134	+	3.95437i	0.817059	+	0.393475i	0.0218131	+	0.999762i	$0.493056\pi$
$102$	−9.40056	−	4.52707i	−0.930794	−	0.448247i
$103$	3.20560	+	14.0446i	0.315857	+	1.38386i	0.844745	+	0.535168i	$0.179752\pi$
$103$	3.20560	+	14.0446i	0.315857	+	1.38386i	−0.528889	+	0.848691i	$0.677391\pi$
$104$	−22.9401			−2.24946
$105$	0.478120	+	2.09478i	0.0466597	+	0.204430i
$106$	6.83807	−	8.57466i	0.664172	−	0.832845i
$107$	0.407981	−	1.78748i	0.0394410	−	0.172802i	−0.951371	−	0.308046i	$-0.900325\pi$
$107$	0.407981	−	1.78748i	0.0394410	−	0.172802i	0.990812	+	0.135244i	$0.0431819\pi$
$108$	−1.27223	+	5.57399i	−0.122420	+	0.536357i
$109$	8.94438	+	11.2159i	0.856716	+	1.07429i	0.996457	+	0.0840999i	$0.0268015\pi$
$109$	8.94438	+	11.2159i	0.856716	+	1.07429i	−0.139741	+	0.990188i	$0.544627\pi$
$110$	7.98990	+	3.84773i	0.761807	+	0.366867i
$111$	3.61733	−	1.74201i	0.343342	−	0.165345i
$112$	9.10820	−	11.4213i	0.860644	−	1.07921i
$113$	−7.34424	−	9.20939i	−0.690888	−	0.866346i	0.305418	−	0.952218i	$-0.401204\pi$
$113$	−7.34424	−	9.20939i	−0.690888	−	0.866346i	−0.996306	+	0.0858722i	$0.972632\pi$
$114$	7.39561	−	3.56154i	0.692663	−	0.333569i
$115$	−16.2872			−1.51879
$116$	0.298185	−	30.7873i	0.0276858	−	2.85853i
$117$	−2.22142			−0.205370
$118$	−5.62059	+	2.70673i	−0.517417	+	0.249175i
$119$	1.98277	+	2.48631i	0.181760	+	0.227920i
$120$	−16.3391	+	20.4886i	−1.49155	+	1.87034i
$121$	8.48492	−	4.08612i	0.771357	−	0.371466i
$122$	11.9291	+	5.74474i	1.08001	+	0.520104i
$123$	−5.79840	−	7.27096i	−0.522824	−	0.655601i
$124$	−0.732720	+	3.21026i	−0.0658002	+	0.288290i
$125$	−2.01043	+	8.80825i	−0.179818	+	0.787834i
$126$	1.46655	−	1.83899i	0.130650	−	0.163830i
$127$	−2.67677	−	11.7277i	−0.237524	−	1.04066i	−0.943226	−	0.332153i	$-0.892225\pi$
$127$	−2.67677	−	11.7277i	−0.237524	−	1.04066i	0.705701	−	0.708510i	$-0.250632\pi$
$128$	60.0872			5.31100
$129$	−2.12484	−	9.30954i	−0.187082	−	0.819659i
$130$	−14.1094	−	6.79471i	−1.23747	−	0.595936i
$131$	2.14780	+	1.03433i	0.187654	+	0.0903695i	0.525352	−	0.850885i	$-0.323934\pi$
$131$	2.14780	+	1.03433i	0.187654	+	0.0903695i	−0.337697	+	0.941255i	$0.609648\pi$
$132$	−1.60040	−	7.01181i	−0.139297	−	0.610300i
$133$	−2.50186			−0.216939
$134$	0.0890038	+	0.389951i	0.00768876	+	0.0336867i
$135$	−1.58221	+	1.98402i	−0.136175	+	0.170758i
$136$	−8.63071	+	37.8136i	−0.740077	+	3.24249i
$137$	3.01965	−	13.2299i	0.257986	−	1.13031i	−0.665416	−	0.746473i	$-0.731746\pi$
$137$	3.01965	−	13.2299i	0.257986	−	1.13031i	0.923401	−	0.383836i	$-0.125397\pi$
$138$	11.1167	+	13.9399i	0.946315	+	1.18664i
$139$	−18.0033	−	8.66991i	−1.52702	−	0.735373i	−0.533157	−	0.846017i	$-0.678994\pi$
$139$	−18.0033	−	8.66991i	−1.52702	−	0.735373i	−0.993860	+	0.110644i	$0.964709\pi$
$140$	11.0680	−	5.33007i	0.935418	−	0.450473i
$141$	−1.75563	+	2.20149i	−0.147851	+	0.185399i
$142$	−8.86614	−	11.1178i	−0.744030	−	0.932984i
$143$	2.51770	−	1.21246i	0.210541	−	0.101391i
$144$	17.2532			1.43777
$145$	6.04830	−	12.2544i	0.502284	−	1.01767i
$146$	3.83335			0.317250
$147$	5.66087	−	2.72613i	0.466901	−	0.224847i
$148$	−14.3120	−	17.9467i	−1.17644	−	1.47521i
$149$	−10.0592	+	12.6139i	−0.824085	+	1.03337i	0.174726	+	0.984617i	$0.444096\pi$
$149$	−10.0592	+	12.6139i	−0.824085	+	1.03337i	−0.998811	+	0.0487523i	$0.984476\pi$
$150$	−3.60348	+	1.73535i	−0.294223	+	0.141690i
$151$	−2.52401	−	1.21550i	−0.205401	−	0.0989158i	0.328355	−	0.944554i	$-0.393506\pi$
$151$	−2.52401	−	1.21550i	−0.205401	−	0.0989158i	−0.533756	+	0.845638i	$0.679220\pi$
$152$	−19.0250	−	23.8566i	−1.54313	−	1.93503i
$153$	−0.835759	+	3.66170i	−0.0675671	+	0.296031i
$154$	−0.658418	+	2.88472i	−0.0530568	+	0.232457i
$155$	−0.911248	+	1.14267i	−0.0731932	+	0.0917814i
$156$	2.82615	+	12.3822i	0.226273	+	0.991366i
$157$	8.49632			0.678080			0.339040	−	0.940772i	$-0.389898\pi$
$157$	8.49632			0.678080			0.339040	+	0.940772i	$0.389898\pi$
$158$	−0.166510	−	0.729530i	−0.0132469	−	0.0580383i
$159$	−3.55697	−	1.71295i	−0.282086	−	0.135845i
$160$	62.3628	+	30.0323i	4.93021	+	2.37426i
$161$	−1.20925	−	5.29807i	−0.0953022	−	0.417546i
$162$	2.77801			0.218261
$163$	4.61597	+	20.2239i	0.361550	+	1.58406i	0.749261	+	0.662275i	$0.230409\pi$
$163$	4.61597	+	20.2239i	0.361550	+	1.58406i	−0.387711	+	0.921781i	$0.626734\pi$
$164$	−33.1514	+	41.5705i	−2.58869	+	3.24611i
$165$	0.710344	−	3.11222i	0.0553002	−	0.242286i
$166$	4.22501	−	18.5110i	0.327924	−	1.43673i
$167$	6.10998	+	7.66168i	0.472805	+	0.592878i	0.959855	−	0.280495i	$-0.0904988\pi$
$167$	6.10998	+	7.66168i	0.472805	+	0.592878i	−0.487051	+	0.873374i	$0.661927\pi$
$168$	−7.87785	−	3.79377i	−0.607789	−	0.292696i
$169$	7.26658	−	3.49940i	0.558968	−	0.269185i
$170$	−16.5085	+	20.7010i	−1.26614	+	1.58769i
$171$	−1.84230	−	2.31017i	−0.140884	−	0.176663i
$172$	−49.1880	+	23.6877i	−3.75055	+	1.80617i
$173$	−20.1246			−1.53005			−0.765023	−	0.644003i	$-0.777272\pi$
$173$	−20.1246			−1.53005			−0.765023	+	0.644003i	$0.777272\pi$
$174$	−14.6165	+	3.18751i	−1.10808	+	0.241645i
$175$	1.21902			0.0921494
$176$	−19.5544	+	9.41691i	−1.47397	+	0.709826i
$177$	1.40013	+	1.75571i	0.105240	+	0.131967i
$178$	−7.98512	+	10.0130i	−0.598510	+	0.750508i
$179$	22.1567	−	10.6701i	1.65607	−	0.797521i	0.657023	−	0.753871i	$-0.271816\pi$
$179$	22.1567	−	10.6701i	1.65607	−	0.797521i	0.999047	−	0.0436504i	$-0.0138988\pi$
$180$	13.0718	+	6.29507i	0.974318	+	0.469207i
$181$	12.1022	+	15.1757i	0.899551	+	1.12800i	0.991221	+	0.132212i	$0.0422079\pi$
$181$	12.1022	+	15.1757i	0.899551	+	1.12800i	−0.0916705	+	0.995789i	$0.529221\pi$
$182$	1.16270	−	5.09412i	0.0861850	−	0.377601i
$183$	1.06056	−	4.64661i	0.0783987	−	0.343487i
$184$	41.3244	−	51.8192i	3.04648	−	3.82016i
$185$	−2.26716	−	9.93310i	−0.166685	−	0.730296i
$186$	1.59995			0.117314
$187$	−1.05135	−	4.60625i	−0.0768820	−	0.336842i
$188$	14.5046	+	6.98506i	1.05786	+	0.509438i
$189$	−0.762856	−	0.367372i	−0.0554896	−	0.0267224i
$190$	−4.63520	−	20.3082i	−0.336273	−	1.47331i
$191$	−0.923161			−0.0667976			−0.0333988	−	0.999442i	$-0.510633\pi$
$191$	−0.923161			−0.0667976			−0.0333988	+	0.999442i	$0.510633\pi$
$192$	−9.18271	−	40.2321i	−0.662705	−	2.90350i
$193$	6.07588	−	7.61891i	0.437351	−	0.548421i	−0.513492	−	0.858095i	$-0.671648\pi$
$193$	6.07588	−	7.61891i	0.437351	−	0.548421i	0.950843	+	0.309673i	$0.100220\pi$
$194$	2.85587	−	12.5124i	0.205039	−	0.898336i
$195$	−1.25440	+	5.49587i	−0.0898292	+	0.393567i
$196$	−22.3973	−	28.0854i	−1.59981	−	2.00610i
$197$	6.73034	+	3.24116i	0.479517	+	0.230923i	0.657997	−	0.753020i	$-0.271404\pi$
$197$	6.73034	+	3.24116i	0.479517	+	0.230923i	−0.178480	+	0.983943i	$0.557118\pi$
$198$	−3.14853	+	1.51625i	−0.223756	+	0.107755i
$199$	16.1636	−	20.2685i	1.14581	−	1.43679i	0.264413	−	0.964410i	$-0.414822\pi$
$199$	16.1636	−	20.2685i	1.14581	−	1.43679i	0.881392	−	0.472385i	$-0.156607\pi$
$200$	9.26987	+	11.6241i	0.655479	+	0.821945i
$201$	0.129722	−	0.0624709i	0.00914989	−	0.00440636i
$202$	−25.3185			−1.78140
$203$	4.43530	+	1.05762i	0.311297	+	0.0742306i
$204$	21.4736			1.50345
$205$	−21.2629	+	10.2397i	−1.48506	+	0.715169i
$206$	−24.9518	−	31.2885i	−1.73847	−	2.17997i
$207$	4.00167	−	5.01794i	0.278136	−	0.348771i
$208$	34.5311	−	16.6293i	2.39430	−	1.15304i
$209$	3.34892	+	1.61276i	0.231650	+	0.111557i
$210$	−3.72160	−	4.66673i	−0.256814	−	0.322035i
$211$	−4.28601	+	18.7782i	−0.295061	+	1.29275i	0.582323	+	0.812957i	$0.302144\pi$
$211$	−4.28601	+	18.7782i	−0.295061	+	1.29275i	−0.877384	+	0.479789i	$0.840713\pi$
$212$	−5.02267	+	22.0058i	−0.344958	+	1.51136i
$213$	−3.19155	+	4.00207i	−0.218681	+	0.274217i
$214$	1.13337	+	4.96563i	0.0774758	+	0.339444i
$215$	−24.2320			−1.65261
$216$	−2.29793	−	10.0679i	−0.156354	−	0.685032i
$217$	−0.439356	−	0.211583i	−0.0298254	−	0.0143632i
$218$	−35.9058	−	17.2913i	−2.43185	−	1.17112i
$219$	−0.307054	−	1.34529i	−0.0207488	−	0.0909065i
$220$	−18.2512			−1.23050
$221$	1.85657	+	8.13417i	0.124886	+	0.547163i
$222$	−6.95411	+	8.72018i	−0.466729	+	0.585260i
$223$	0.175370	−	0.768344i	0.0117436	−	0.0514521i	−0.968717	−	0.248170i	$-0.920171\pi$
$223$	0.175370	−	0.768344i	0.0117436	−	0.0514521i	0.980460	+	0.196717i	$0.0630281\pi$
$224$	−5.13908	+	22.5158i	−0.343369	+	1.50440i
$225$	0.897653	+	1.12562i	0.0598435	+	0.0750414i
$226$	29.4823	+	14.1979i	1.96113	+	0.944431i
$227$	16.9571	−	8.16610i	1.12548	−	0.542003i	0.223899	−	0.974612i	$-0.428121\pi$
$227$	16.9571	−	8.16610i	1.12548	−	0.542003i	0.901581	+	0.432609i	$0.142407\pi$
$228$	−10.5330	+	13.2080i	−0.697567	+	0.874722i
$229$	16.7757	+	21.0360i	1.10857	+	1.39010i	0.912287	+	0.409552i	$0.134315\pi$
$229$	16.7757	+	21.0360i	1.10857	+	1.39010i	0.196281	+	0.980548i	$0.437114\pi$
$230$	40.7652	−	19.6315i	2.68798	−	1.29446i
$231$	1.06512			0.0700795
$232$	23.6425	+	50.3355i	1.55221	+	3.30469i
$233$	−13.1181			−0.859393			−0.429696	−	0.902973i	$-0.641379\pi$
$233$	−13.1181			−0.859393			−0.429696	+	0.902973i	$0.641379\pi$
$234$	5.55999	−	2.67755i	0.363468	−	0.175037i
$235$	4.45519	+	5.58663i	0.290624	+	0.364432i
$236$	8.00500	−	10.0380i	0.521081	−	0.653415i
$237$	−0.242687	+	0.116872i	−0.0157642	+	0.00759165i
$238$	−7.95951	−	3.83310i	−0.515938	−	0.248463i
$239$	2.52458	+	3.16572i	0.163302	+	0.204774i	0.856749	−	0.515733i	$-0.172481\pi$
$239$	2.52458	+	3.16572i	0.163302	+	0.204774i	−0.693448	+	0.720507i	$0.743909\pi$
$240$	9.74261	−	42.6851i	0.628883	−	2.75531i
$241$	−0.896181	+	3.92643i	−0.0577281	+	0.252923i	−0.995555	−	0.0941792i	$-0.969977\pi$
$241$	−0.896181	+	3.92643i	−0.0577281	+	0.252923i	0.937827	+	0.347103i	$0.112834\pi$
$242$	−16.3118	+	20.4543i	−1.04856	+	1.31485i
$243$	−0.222521	−	0.974928i	−0.0142747	−	0.0625417i
$244$	−27.2494			−1.74446
$245$	−3.54795	−	15.5446i	−0.226670	−	0.993108i
$246$	23.2767	+	11.2095i	1.48407	+	0.714691i
$247$	−5.91386	−	2.84796i	−0.376290	−	0.181212i
$248$	−1.32346	−	5.79845i	−0.0840396	−	0.368202i
$249$	−6.83476			−0.433135
$250$	−5.58498	−	24.4694i	−0.353225	−	1.54758i
$251$	18.9067	−	23.7083i	1.19338	−	1.49645i	0.369939	−	0.929056i	$-0.379378\pi$
$251$	18.9067	−	23.7083i	1.19338	−	1.49645i	0.823443	−	0.567399i	$-0.192050\pi$
$252$	−1.07720	+	4.71953i	−0.0678573	+	0.297302i
$253$	−1.79658	+	7.87135i	−0.112950	+	0.494868i
$254$	20.8354	+	26.1268i	1.30733	+	1.63934i
$255$	8.58724	+	4.13540i	0.537754	+	0.258969i
$256$	−76.0321	+	36.6151i	−4.75200	+	2.28844i
$257$	−5.07958	+	6.36959i	−0.316855	+	0.397324i	−0.914598	−	0.404364i	$-0.867493\pi$
$257$	−5.07958	+	6.36959i	−0.316855	+	0.397324i	0.597743	+	0.801688i	$0.296064\pi$
$258$	16.5394	+	20.7397i	1.02970	+	1.29120i
$259$	3.06282	−	1.47497i	0.190314	−	0.0916504i
$260$	32.2298			1.99881
$261$	2.28944	+	4.87427i	0.141713	+	0.301710i
$262$	−6.62243			−0.409135
$263$	5.10905	−	2.46039i	0.315038	−	0.151714i	−0.269682	−	0.962949i	$-0.586919\pi$
$263$	5.10905	−	2.46039i	0.315038	−	0.151714i	0.584720	+	0.811235i	$0.301204\pi$
$264$	8.09951	+	10.1565i	0.498491	+	0.625087i
$265$	−6.24645	+	7.83280i	−0.383716	+	0.481165i
$266$	6.26191	−	3.01558i	0.383942	−	0.184897i
$267$	4.15363	+	2.00028i	0.254198	+	0.122415i
$268$	−0.513248	−	0.643592i	−0.0313516	−	0.0393137i
$269$	−4.57344	+	20.0376i	−0.278848	+	1.22171i	0.620405	+	0.784282i	$0.286968\pi$
$269$	−4.57344	+	20.0376i	−0.278848	+	1.22171i	−0.899252	+	0.437430i	$0.855889\pi$
$270$	1.56869	−	6.87290i	0.0954677	−	0.418271i
$271$	5.98035	−	7.49912i	0.363280	−	0.455539i	−0.566278	−	0.824214i	$-0.691617\pi$
$271$	5.98035	−	7.49912i	0.363280	−	0.455539i	0.929558	+	0.368675i	$0.120189\pi$
$272$	−14.4196	−	63.1762i	−0.874314	−	3.83062i
$273$	−1.88089			−0.113837
$274$	8.38860	+	36.7529i	0.506774	+	2.22032i
$275$	−1.63175	−	0.785809i	−0.0983982	−	0.0473861i
$276$	−33.0610	−	15.9213i	−1.99004	−	0.958352i
$277$	5.75035	+	25.1939i	0.345505	+	1.51376i	0.787260	+	0.616621i	$0.211499\pi$
$277$	5.75035	+	25.1939i	0.345505	+	1.51376i	−0.441755	+	0.897136i	$0.645644\pi$
$278$	55.5105			3.32930
$279$	−0.128158	−	0.561496i	−0.00767260	−	0.0336159i
$280$	−13.8344	+	17.3478i	−0.826764	+	1.03673i
$281$	4.07233	−	17.8421i	0.242935	−	1.06437i	−0.695395	−	0.718627i	$-0.744771\pi$
$281$	4.07233	−	17.8421i	0.242935	−	1.06437i	0.938330	−	0.345740i	$-0.112372\pi$
$282$	1.74063	−	7.62622i	0.103653	−	0.454135i
$283$	−8.60447	−	10.7897i	−0.511483	−	0.641379i	0.457293	−	0.889316i	$-0.348819\pi$
$283$	−8.60447	−	10.7897i	−0.511483	−	0.641379i	−0.968776	+	0.247937i	$0.920247\pi$
$284$	26.3679	+	12.6981i	1.56465	+	0.753494i
$285$	−6.75576	+	3.25340i	−0.400177	+	0.192715i
$286$	−4.84014	+	6.06934i	−0.286203	+	0.358888i
$287$	−4.90954	−	6.15637i	−0.289801	−	0.363399i
$288$	−24.5749	+	11.8346i	−1.44809	+	0.697363i
$289$	−2.89345			−0.170203
$290$	−0.367672	+	37.9617i	−0.0215904	+	2.22919i
$291$	−4.61991			−0.270824
$292$	−7.10800	+	3.42303i	−0.415964	+	0.200318i
$293$	−8.24552	−	10.3396i	−0.481708	−	0.604043i	0.480286	−	0.877112i	$-0.340533\pi$
$293$	−8.24552	−	10.3396i	−0.481708	−	0.604043i	−0.961995	+	0.273069i	$0.911961\pi$
$294$	−10.8827	+	13.6465i	−0.634691	+	0.795878i
$295$	5.13431	−	2.47255i	0.298931	−	0.143958i
$296$	37.3554	+	17.9894i	2.17124	+	1.04561i
$297$	0.784321	+	0.983507i	0.0455109	+	0.0570689i
$298$	9.97333	−	43.6960i	0.577739	−	2.53124i
$299$	3.17259	−	13.9000i	0.183476	−	0.803859i
$300$	5.13218	−	6.43555i	0.296307	−	0.371557i
$301$	−1.79912	−	7.88244i	−0.103699	−	0.454336i
$302$	7.78241			0.447828
$303$	2.02803	+	8.88540i	0.116507	+	0.510453i
$304$	45.9316	+	22.1195i	2.63436	+	1.26864i
$305$	−10.8970	−	5.24772i	−0.623960	−	0.300483i
$306$	−2.32175	−	10.1722i	−0.132725	−	0.581508i
$307$	23.3280			1.33140			0.665698	−	0.746221i	$-0.268134\pi$
$307$	23.3280			1.33140			0.665698	+	0.746221i	$0.268134\pi$
$308$	−1.35507	−	5.93694i	−0.0772122	−	0.338289i
$309$	−8.98189	+	11.2629i	−0.510962	+	0.640726i
$310$	0.903466	−	3.95834i	0.0513134	−	0.224819i
$311$	1.26488	−	5.54181i	0.0717249	−	0.314247i	−0.926321	−	0.376736i	$-0.877047\pi$
$311$	1.26488	−	5.54181i	0.0717249	−	0.314247i	0.998046	+	0.0624884i	$0.0199036\pi$
$312$	−14.3029	−	17.9353i	−0.809744	−	1.01539i
$313$	−3.59647	−	1.73197i	−0.203284	−	0.0978966i	0.329472	−	0.944165i	$-0.393129\pi$
$313$	−3.59647	−	1.73197i	−0.203284	−	0.0978966i	−0.532756	+	0.846269i	$0.678844\pi$
$314$	−21.2654	+	10.2409i	−1.20008	+	0.577927i
$315$	−1.33966	+	1.67988i	−0.0754815	+	0.0946507i
$316$	0.960196	+	1.20405i	0.0540153	+	0.0677330i
$317$	−11.0688	+	5.33046i	−0.621687	+	0.299389i	−0.718086	−	0.695954i	$-0.754982\pi$
$317$	−11.0688	+	5.33046i	−0.621687	+	0.299389i	0.0963994	+	0.995343i	$0.469267\pi$
$318$	10.9674			0.615022
$319$	−5.25519	−	4.27479i	−0.294234	−	0.239342i
$320$	−104.721			−5.85408
$321$	1.65188	−	0.795503i	0.0921989	−	0.0444007i
$322$	9.41257	+	11.8030i	0.524542	+	0.657755i
$323$	−6.91943	+	8.67669i	−0.385007	+	0.482784i
$324$	−5.15114	+	2.48066i	−0.286174	+	0.137814i
$325$	2.88150	+	1.38766i	0.159837	+	0.0769735i
$326$	−35.9298	−	45.0545i	−1.98997	−	2.49534i
$327$	−3.19221	+	13.9860i	−0.176530	+	0.773427i
$328$	21.3705	−	93.6303i	1.17999	−	5.16987i
$329$	−1.48650	+	1.86401i	−0.0819534	+	0.102766i
$330$	1.97334	+	8.64578i	0.108629	+	0.475934i
$331$	−15.4931			−0.851579			−0.425790	−	0.904822i	$-0.640004\pi$
$331$	−15.4931			−0.851579			−0.425790	+	0.904822i	$0.640004\pi$
$332$	8.69537	+	38.0969i	0.477220	+	2.09084i
$333$	3.61733	+	1.74201i	0.198229	+	0.0954618i
$334$	−24.5275	−	11.8118i	−1.34209	−	0.646315i
$335$	−0.0813034	−	0.356213i	−0.00444208	−	0.0194620i
$336$	14.6084			0.796955
$337$	0.00717696	+	0.0314443i	0.000390954	+	0.00171288i	0.975123	−	0.221664i	$-0.0711489\pi$
$337$	0.00717696	+	0.0314443i	0.000390954	+	0.00171288i	−0.974732	+	0.223377i	$0.928292\pi$
$338$	−13.9696	+	17.5173i	−0.759845	+	0.952816i
$339$	2.62113	−	11.4839i	0.142360	−	0.623721i
$340$	12.1257	−	53.1264i	0.657611	−	2.88118i
$341$	0.451718	+	0.566437i	0.0244619	+	0.0306743i
$342$	7.39561	+	3.56154i	0.399909	+	0.192586i
$343$	10.1331	−	4.87983i	0.547135	−	0.263486i
$344$	61.4823	−	77.0964i	3.31490	−	4.15676i
$345$	−10.1549	−	12.7338i	−0.546721	−	0.685567i
$346$	50.3699	−	24.2568i	2.70790	−	1.30406i
$347$	−4.44819			−0.238791			−0.119396	−	0.992847i	$-0.538096\pi$
$347$	−4.44819			−0.238791			−0.119396	+	0.992847i	$0.538096\pi$
$348$	24.2564	−	18.9625i	1.30028	−	1.01649i
$349$	−17.0567			−0.913024			−0.456512	−	0.889717i	$-0.650901\pi$
$349$	−17.0567			−0.913024			−0.456512	+	0.889717i	$0.650901\pi$
$350$	−3.05109	+	1.46933i	−0.163088	+	0.0785389i
$351$	−1.38503	−	1.73677i	−0.0739275	−	0.0927022i
$352$	21.3932	−	26.8262i	1.14026	−	1.42984i
$353$	7.89583	−	3.80243i	0.420252	−	0.202383i	−0.211792	−	0.977315i	$-0.567930\pi$
$353$	7.89583	−	3.80243i	0.420252	−	0.202383i	0.632045	+	0.774932i	$0.282216\pi$
$354$	−5.62059	−	2.70673i	−0.298731	−	0.143861i
$355$	8.09906	+	10.1559i	0.429854	+	0.539019i
$356$	5.86520	−	25.6971i	0.310855	−	1.36194i
$357$	−0.707642	+	3.10038i	−0.0374524	+	0.164090i
$358$	−42.5950	+	53.4124i	−2.25121	+	2.82293i
$359$	−0.501253	−	2.19613i	−0.0264551	−	0.115907i	0.959976	−	0.280081i	$-0.0903614\pi$
$359$	−0.501253	−	2.19613i	−0.0264551	−	0.115907i	−0.986431	+	0.164174i	$0.947504\pi$
$360$	−26.2059			−1.38117
$361$	2.28508	+	10.0116i	0.120267	+	0.526925i
$362$	−48.5824	−	23.3961i	−2.55344	−	1.22967i
$363$	8.48492	+	4.08612i	0.445343	+	0.214466i
$364$	2.39292	+	10.4840i	0.125423	+	0.549513i
$365$	−3.50169			−0.183287
$366$	2.94624	+	12.9083i	0.154002	+	0.674729i
$367$	5.57199	−	6.98706i	0.290856	−	0.364721i	−0.614839	−	0.788653i	$-0.710779\pi$
$367$	5.57199	−	6.98706i	0.290856	−	0.364721i	0.905694	+	0.423932i	$0.139350\pi$
$368$	−24.6408	+	107.958i	−1.28449	+	5.62771i
$369$	2.06943	−	9.06674i	0.107730	−	0.471996i
$370$	17.6472	+	22.1289i	0.917433	+	1.15042i
$371$	−3.01171	−	1.45036i	−0.156360	−	0.0752990i
$372$	−2.96672	+	1.42870i	−0.153817	+	0.0740746i
$373$	−2.98091	+	3.73794i	−0.154346	+	0.193543i	−0.852992	−	0.521924i	$-0.825215\pi$
$373$	−2.98091	+	3.73794i	−0.154346	+	0.193543i	0.698647	+	0.715467i	$0.253786\pi$
$374$	8.18347	+	10.2618i	0.423157	+	0.530623i
$375$	−8.14005	+	3.92004i	−0.420350	+	0.202430i
$376$	−29.0783			−1.49960
$377$	9.28014	+	7.54886i	0.477952	+	0.388786i
$378$	2.35216			0.120982
$379$	−30.8943	+	14.8779i	−1.58693	+	0.764226i	−0.999001	−	0.0446854i	$-0.985771\pi$
$379$	−30.8943	+	14.8779i	−1.58693	+	0.764226i	−0.587931	+	0.808911i	$0.700057\pi$
$380$	26.7293	+	33.5175i	1.37118	+	1.71941i
$381$	7.50013	−	9.40486i	0.384243	−	0.481826i
$382$	2.31058	−	1.11272i	0.118220	−	0.0569315i
$383$	−21.4436	−	10.3267i	−1.09572	−	0.527669i	−0.203407	−	0.979094i	$-0.565201\pi$
$383$	−21.4436	−	10.3267i	−1.09572	−	0.527669i	−0.892309	+	0.451426i	$0.850916\pi$
$384$	37.4637	+	46.9780i	1.91181	+	2.39734i
$385$	0.601453	−	2.63514i	0.0306529	−	0.134299i
$386$	−6.02399	+	26.3928i	−0.306613	+	1.34336i
$387$	5.95367	−	7.46567i	0.302642	−	0.379501i
$388$	5.87757	+	25.7513i	0.298388	+	1.30733i
$389$	18.5239			0.939198			0.469599	−	0.882880i	$-0.344399\pi$
$389$	18.5239			0.939198			0.469599	+	0.882880i	$0.344399\pi$
$390$	−3.48472	−	15.2676i	−0.176456	−	0.773104i
$391$	−21.7186	−	10.4591i	−1.09836	−	0.528942i
$392$	58.4586	+	28.1522i	2.95260	+	1.42190i
$393$	0.530463	+	2.32411i	0.0267583	+	0.117236i
$394$	−20.7521			−1.04547
$395$	0.152104	+	0.666413i	0.00765320	+	0.0335309i
$396$	4.48422	−	5.62304i	0.225341	−	0.282568i
$397$	2.41408	−	10.5768i	0.121159	−	0.530833i	−0.877524	−	0.479533i	$-0.840806\pi$
$397$	2.41408	−	10.5768i	0.121159	−	0.530833i	0.998683	−	0.0513005i	$-0.0163366\pi$
$398$	−16.0255	+	70.2125i	−0.803287	+	3.51943i
$399$	−1.55989	−	1.95603i	−0.0780919	−	0.0979242i
$400$	−22.3800	−	10.7776i	−1.11900	−	0.538881i
$401$	−25.8578	+	12.4525i	−1.29128	+	0.621846i	−0.948263	−	0.317485i	$-0.897162\pi$
$401$	−25.8578	+	12.4525i	−1.29128	+	0.621846i	−0.343013	+	0.939331i	$0.611447\pi$
$402$	−0.249383	+	0.312717i	−0.0124381	+	0.0155969i
$403$	−0.797689	−	1.00027i	−0.0397357	−	0.0498270i
$404$	46.9470	−	22.6085i	2.33570	−	1.12481i
$405$	−2.53766			−0.126097
$406$	−12.3759	+	2.69888i	−0.614205	+	0.133943i
$407$	−5.05060			−0.250349
$408$	−34.9450	+	16.8286i	−1.73004	+	0.833142i
$409$	−15.7089	−	19.6984i	−0.776756	−	0.974021i	0.223244	−	0.974763i	$-0.428335\pi$
$409$	−15.7089	−	19.6984i	−0.776756	−	0.974021i	−1.00000		0.000741524i	$0.999764\pi$
$410$	40.8767	−	51.2577i	2.01875	−	2.53144i
$411$	12.2263	−	5.88787i	0.603079	−	0.290427i
$412$	74.2064	+	35.7359i	3.65589	+	1.76058i
$413$	1.18550	+	1.48657i	0.0583345	+	0.0731491i
$414$	−3.96750	+	17.3828i	−0.194992	+	0.854316i
$415$	−3.85947	+	16.9095i	−0.189454	+	0.830052i
$416$	−37.7782	+	47.3724i	−1.85223	+	2.32262i
$417$	−4.44644	−	19.4811i	−0.217743	−	0.953995i
$418$	−10.3259			−0.505057
$419$	−2.88089	−	12.6220i	−0.140741	−	0.616625i	−0.995264	−	0.0972114i	$-0.969008\pi$
$419$	−2.88089	−	12.6220i	−0.140741	−	0.616625i	0.854523	−	0.519413i	$-0.173849\pi$
$420$	11.0680	+	5.33007i	0.540064	+	0.260081i
$421$	−17.6399	−	8.49493i	−0.859716	−	0.414018i	−0.0485414	−	0.998821i	$-0.515457\pi$
$421$	−17.6399	−	8.49493i	−0.859716	−	0.414018i	−0.811175	+	0.584804i	$0.801172\pi$
$422$	−11.9066	−	52.1661i	−0.579602	−	2.53940i
$423$	−2.81581			−0.136909
$424$	−9.07207	−	39.7473i	−0.440579	−	1.93030i
$425$	3.37147	−	4.22769i	0.163540	−	0.205073i
$426$	3.16429	−	13.8637i	0.153310	−	0.671697i
$427$	0.897981	−	3.93431i	0.0434563	−	0.190395i
$428$	−6.53569	−	8.19550i	−0.315915	−	0.396144i
$429$	2.51770	+	1.21246i	0.121556	+	0.0585382i
$430$	60.6503	−	29.2076i	2.92482	−	1.40852i
$431$	−2.24797	+	2.81887i	−0.108281	+	0.135780i	−0.833019	−	0.553245i	$-0.813389\pi$
$431$	−2.24797	+	2.81887i	−0.108281	+	0.135780i	0.724738	+	0.689025i	$0.241961\pi$
$432$	10.7572	+	13.4891i	0.517557	+	0.648996i
$433$	4.33066	−	2.08554i	0.208118	−	0.100225i	−0.326921	−	0.945052i	$-0.606011\pi$
$433$	4.33066	−	2.08554i	0.208118	−	0.100225i	0.535039	+	0.844827i	$0.320297\pi$
$434$	1.35469			0.0650272
$435$	13.3519	−	2.91173i	0.640176	−	0.139607i
$436$	82.0190			3.92800
$437$	17.0865	−	8.22842i	0.817358	−	0.393619i
$438$	2.39005	+	2.99703i	0.114201	+	0.143204i
$439$	4.70521	−	5.90014i	0.224567	−	0.281599i	−0.656765	−	0.754095i	$-0.728076\pi$
$439$	4.70521	−	5.90014i	0.224567	−	0.281599i	0.881332	+	0.472497i	$0.156647\pi$
$440$	29.7011	−	14.3033i	1.41595	−	0.681884i
$441$	5.66087	+	2.72613i	0.269565	+	0.129816i
$442$	−14.4512	−	18.1212i	−0.687373	−	0.861939i
$443$	−5.07740	+	22.2456i	−0.241235	+	1.05692i	0.698660	+	0.715454i	$0.253780\pi$
$443$	−5.07740	+	22.2456i	−0.241235	+	1.05692i	−0.939895	+	0.341465i	$0.889077\pi$
$444$	5.10791	−	22.3792i	0.242411	−	1.06207i
$445$	7.29426	−	9.14672i	0.345781	−	0.433596i
$446$	0.487178	+	2.13447i	0.0230686	+	0.101070i
$447$	−16.1338			−0.763101
$448$	−7.77505	−	34.0647i	−0.367337	−	1.60941i
$449$	11.7896	+	5.67759i	0.556388	+	0.267942i	0.690876	−	0.722973i	$-0.257225\pi$
$449$	11.7896	+	5.67759i	0.556388	+	0.267942i	−0.134489	+	0.990915i	$0.542939\pi$
$450$	−3.60348	−	1.73535i	−0.169870	−	0.0818050i
$451$	2.60324	+	11.4055i	0.122582	+	0.537066i
$452$	−67.3459			−3.16768
$453$	−0.623378	−	2.73120i	−0.0292889	−	0.128323i
$454$	−32.5990	+	40.8778i	−1.52995	+	1.91849i
$455$	−1.06210	+	4.65339i	−0.0497922	+	0.218154i
$456$	6.78995	−	29.7487i	0.317969	−	1.39311i
$457$	−19.5401	−	24.5025i	−0.914048	−	1.14618i	−0.988840	−	0.148981i	$-0.952401\pi$
$457$	−19.5401	−	24.5025i	−0.914048	−	1.14618i	0.0747922	−	0.997199i	$-0.476171\pi$
$458$	−67.3432	−	32.4308i	−3.14674	−	1.51539i
$459$	−3.38392	+	1.62961i	−0.157948	+	0.0760637i
$460$	−58.0589	+	72.8036i	−2.70701	+	3.39448i
$461$	23.7681	+	29.8043i	1.10699	+	1.38813i	0.913410	+	0.407042i	$0.133440\pi$
$461$	23.7681	+	29.8043i	1.10699	+	1.38813i	0.193584	+	0.981084i	$0.437989\pi$
$462$	−2.66588	+	1.28382i	−0.124028	+	0.0597287i
$463$	39.1593			1.81989			0.909944	−	0.414732i	$-0.136125\pi$
$463$	39.1593			1.81989			0.909944	+	0.414732i	$0.136125\pi$
$464$	−72.0767	−	58.6302i	−3.34608	−	2.72184i
$465$	−1.46153			−0.0677768
$466$	32.8332	−	15.8116i	1.52097	−	0.732460i
$467$	8.74298	+	10.9633i	0.404577	+	0.507323i	0.941826	−	0.336100i	$-0.109108\pi$
$467$	8.74298	+	10.9633i	0.404577	+	0.507323i	−0.537249	+	0.843423i	$0.680537\pi$
$468$	−7.91869	+	9.92972i	−0.366042	+	0.459002i
$469$	0.109836	−	0.0528945i	0.00507178	−	0.00244244i
$470$	−17.8846	−	8.61279i	−0.824957	−	0.397278i
$471$	5.29737	+	6.64269i	0.244090	+	0.306079i
$472$	−5.16029	+	22.6087i	−0.237522	+	1.04065i
$473$	−2.67295	+	11.7110i	−0.122902	+	0.538471i
$474$	0.466552	−	0.585038i	0.0214294	−	0.0268717i
$475$	0.946631	+	4.14746i	0.0434344	+	0.190299i
$476$	18.1818			0.833361
$477$	−0.878499	−	3.84895i	−0.0402237	−	0.176232i
$478$	−10.1345	−	4.88053i	−0.463542	−	0.223230i
$479$	37.6742	+	18.1430i	1.72138	+	0.828973i	0.988971	+	0.148107i	$0.0473180\pi$
$479$	37.6742	+	18.1430i	1.72138	+	0.828973i	0.732408	+	0.680866i	$0.238396\pi$
$480$	15.4023	+	67.4820i	0.703017	+	3.08012i
$481$	8.91885			0.406665
$482$	−2.48960	−	10.9077i	−0.113398	−	0.496830i
$483$	3.38824	−	4.24872i	0.154170	−	0.193323i
$484$	11.9813	−	52.4933i	0.544603	−	2.38606i
$485$	−2.60878	+	11.4298i	−0.118459	+	0.519002i
$486$	1.73206	+	2.17193i	0.0785679	+	0.0985210i
$487$	−12.7105	−	6.12107i	−0.575969	−	0.277372i	0.123138	−	0.992390i	$-0.460704\pi$
$487$	−12.7105	−	6.12107i	−0.575969	−	0.277372i	−0.699106	+	0.715018i	$0.746419\pi$
$488$	44.3444	−	21.3551i	2.00738	−	0.966701i
$489$	−12.9337	+	16.2183i	−0.584880	+	0.733416i
$490$	27.6166	+	34.6301i	1.24759	+	1.56443i
$491$	−23.9429	+	11.5303i	−1.08053	+	0.520354i	−0.887485	−	0.460837i	$-0.847549\pi$
$491$	−23.9429	+	11.5303i	−1.08053	+	0.520354i	−0.193041	+	0.981191i	$0.561835\pi$
$492$	−53.1707			−2.39712
$493$	15.9347	−	12.4569i	0.717662	−	0.561033i
$494$	18.2345			0.820411
$495$	2.87613	−	1.38507i	0.129272	−	0.0622542i
$496$	6.19546	+	7.76887i	0.278185	+	0.348832i
$497$	−2.70230	+	3.38858i	−0.121215	+	0.151998i
$498$	17.1067	−	8.23816i	0.766571	−	0.369161i
$499$	−17.2217	−	8.29352i	−0.770948	−	0.371269i	0.00669320	−	0.999978i	$-0.497869\pi$
$499$	−17.2217	−	8.29352i	−0.770948	−	0.371269i	−0.777641	+	0.628709i	$0.783584\pi$
$500$	32.2063	+	40.3854i	1.44031	+	1.80609i
$501$	−2.18063	+	9.55395i	−0.0974232	+	0.426839i
$502$	−18.7453	+	82.1284i	−0.836642	+	3.66557i
$503$	10.0746	−	12.6332i	0.449206	−	0.563287i	−0.504737	−	0.863273i	$-0.668411\pi$
$503$	10.0746	−	12.6332i	0.449206	−	0.563287i	0.953944	+	0.299986i	$0.0969821\pi$
$504$	−1.94567	−	8.52453i	−0.0866669	−	0.379713i
$505$	23.1280			1.02918
$506$	−4.99093	−	21.8667i	−0.221874	−	0.972093i
$507$	7.26658	+	3.49940i	0.322720	+	0.155414i
$508$	−61.9645	−	29.8405i	−2.74923	−	1.32396i
$509$	5.58653	+	24.4762i	0.247619	+	1.08489i	0.933895	+	0.357548i	$0.116387\pi$
$509$	5.58653	+	24.4762i	0.247619	+	1.08489i	−0.686276	+	0.727341i	$0.740756\pi$
$510$	−26.4775			−1.17245
$511$	−0.259985	−	1.13907i	−0.0115010	−	0.0503894i
$512$	71.2398	−	89.3318i	3.14838	−	3.94795i
$513$	0.657509	−	2.88073i	0.0290297	−	0.127188i
$514$	5.03620	−	22.0650i	0.222137	−	0.973246i
$515$	22.7930	+	28.5815i	1.00438	+	1.25945i
$516$	−49.1880	−	23.6877i	−2.16538	−	1.04279i
$517$	3.19137	−	1.53688i	0.140356	−	0.0675921i
$518$	−5.88808	+	7.38342i	−0.258708	+	0.324409i
$519$	−12.5475	−	15.7340i	−0.550773	−	0.690648i
$520$	−52.4492	+	25.2582i	−2.30005	+	1.10765i
$521$	2.82291			0.123674			0.0618370	−	0.998086i	$-0.480304\pi$
$521$	2.82291			0.123674			0.0618370	+	0.998086i	$0.480304\pi$
$522$	−11.6053	−	9.44027i	−0.507952	−	0.413189i
$523$	30.2113			1.32105			0.660523	−	0.750805i	$-0.270334\pi$
$523$	30.2113			1.32105			0.660523	+	0.750805i	$0.270334\pi$
$524$	12.2797	−	5.91359i	0.536441	−	0.258336i
$525$	0.760048	+	0.953070i	0.0331712	+	0.0415954i
$526$	−9.82186	+	12.3162i	−0.428253	+	0.537013i
$527$	−1.94892	+	0.938550i	−0.0848963	+	0.0408839i
$528$	−19.5544	−	9.41691i	−0.850997	−	0.409818i
$529$	11.3432	+	14.2240i	0.493184	+	0.618433i
$530$	6.19311	−	27.1338i	0.269011	−	1.17862i
$531$	−0.499700	+	2.18933i	−0.0216851	+	0.0950088i
$532$	−8.91839	+	11.1833i	−0.386661	+	0.484858i
$533$	−4.59706	−	20.1410i	−0.199121	−	0.872405i
$534$	−12.8071			−0.554219
$535$	−1.03532	−	4.53602i	−0.0447606	−	0.196109i
$536$	1.33961	+	0.645123i	0.0578625	+	0.0278651i
$537$	22.1567	+	10.6701i	0.956132	+	0.460449i
$538$	−12.7051	−	55.6645i	−0.547754	−	2.39987i
$539$	−7.90383			−0.340442
$540$	3.22848	+	14.1449i	0.138932	+	0.608699i
$541$	8.40733	−	10.5425i	0.361459	−	0.453256i	−0.567535	−	0.823349i	$-0.692103\pi$
$541$	8.40733	−	10.5425i	0.361459	−	0.453256i	0.928995	+	0.370094i	$0.120674\pi$
$542$	−5.92928	+	25.9779i	−0.254684	+	1.11584i
$543$	−4.31923	+	18.9238i	−0.185356	+	0.812098i
$544$	63.8736	+	80.0950i	2.73856	+	3.43405i
$545$	32.7993	+	15.7953i	1.40497	+	0.676596i
$546$	4.70767	−	2.26710i	0.201470	−	0.0970228i
$547$	14.5525	−	18.2482i	0.622219	−	0.780238i	−0.366436	−	0.930443i	$-0.619422\pi$
$547$	14.5525	−	18.2482i	0.622219	−	0.780238i	0.988655	+	0.150206i	$0.0479935\pi$
$548$	−48.3736	−	60.6585i	−2.06642	−	2.59120i
$549$	4.29411	−	2.06793i	0.183268	−	0.0882573i
$550$	5.03126			0.214534
$551$	−0.154107	+	15.9114i	−0.00656520	+	0.677850i
$552$	66.2793			2.82103
$553$	−0.205485	+	0.0989562i	−0.00873810	+	0.00420805i
$554$	−44.7596	−	56.1268i	−1.90165	−	2.38460i
$555$	6.35245	−	7.96572i	0.269647	−	0.338126i
$556$	−102.931	+	49.5688i	−4.36523	+	2.10219i
$557$	−3.00534	−	1.44729i	−0.127340	−	0.0613238i	0.369129	−	0.929378i	$-0.379656\pi$
$557$	−3.00534	−	1.44729i	−0.127340	−	0.0613238i	−0.496469	+	0.868054i	$0.665370\pi$
$558$	0.997555	+	1.25089i	0.0422299	+	0.0529546i
$559$	4.72016	−	20.6804i	0.199642	−	0.874687i
$560$	8.24912	−	36.1418i	0.348589	−	1.52727i
$561$	2.94581	−	3.69392i	0.124372	−	0.155958i
$562$	11.3130	+	49.5654i	0.477209	+	2.09079i
$563$	7.82895			0.329951			0.164976	−	0.986298i	$-0.447245\pi$
$563$	7.82895			0.329951			0.164976	+	0.986298i	$0.447245\pi$
$564$	3.58235	+	15.6953i	0.150844	+	0.660891i
$565$	−26.9315	−	12.9695i	−1.13302	−	0.545633i
$566$	34.5413	+	16.6342i	1.45188	+	0.699188i
$567$	−0.188410	−	0.825477i	−0.00791247	−	0.0346668i
$568$	−52.8612			−2.21801
$569$	−0.0380192	−	0.166573i	−0.00159385	−	0.00698310i	0.974125	−	0.226011i	$-0.0725685\pi$
$569$	−0.0380192	−	0.166573i	−0.00159385	−	0.00698310i	−0.975719	+	0.219028i	$0.929711\pi$
$570$	12.9876	−	16.2859i	0.543989	−	0.682140i
$571$	−5.95314	+	26.0824i	−0.249131	+	1.09152i	0.683291	+	0.730146i	$0.260548\pi$
$571$	−5.95314	+	26.0824i	−0.249131	+	1.09152i	−0.932423	+	0.361370i	$0.882309\pi$
$572$	3.55516	−	15.5762i	0.148649	−	0.651273i
$573$	−0.575582	−	0.721757i	−0.0240453	−	0.0301518i
$574$	19.7086	+	9.49114i	0.822619	+	0.396153i
$575$	−8.32533	+	4.00927i	−0.347190	+	0.167198i
$576$	25.7294	−	32.2636i	1.07206	−	1.34432i
$577$	−24.4227	−	30.6252i	−1.01673	−	1.27494i	−0.961015	−	0.276495i	$-0.910827\pi$
$577$	−24.4227	−	30.6252i	−1.01673	−	1.27494i	−0.0557170	−	0.998447i	$-0.517744\pi$
$578$	7.24202	−	3.48757i	0.301228	−	0.145064i
$579$	9.74495			0.404986
$580$	−33.2166	−	70.7191i	−1.37925	−	2.93645i
$581$	−5.78703			−0.240087
$582$	11.5632	−	5.56853i	0.479309	−	0.230823i
$583$	3.09645	+	3.88283i	0.128242	+	0.160810i
$584$	8.88462	−	11.1410i	0.367648	−	0.461016i
$585$	−5.07895	+	2.44589i	−0.209989	+	0.101125i
$586$	33.1003	+	15.9403i	1.36736	+	0.658486i
$587$	−1.30417	−	1.63538i	−0.0538290	−	0.0674994i	0.754188	−	0.656658i	$-0.228031\pi$
$587$	−1.30417	−	1.63538i	−0.0538290	−	0.0674994i	−0.808017	+	0.589159i	$0.799459\pi$
$588$	7.99351	−	35.0219i	0.329647	−	1.44428i
$589$	0.378683	−	1.65912i	0.0156033	−	0.0683627i
$590$	−9.87041	+	12.3771i	−0.406358	+	0.509557i
$591$	1.66226	+	7.28283i	0.0683761	+	0.299575i
$592$	−69.2706			−2.84701
$593$	−4.80876	−	21.0685i	−0.197472	−	0.865181i	−0.972435	−	0.233174i	$-0.925089\pi$
$593$	−4.80876	−	21.0685i	−0.197472	−	0.865181i	0.774963	−	0.632007i	$-0.217768\pi$
$594$	−3.14853	−	1.51625i	−0.129186	−	0.0622126i
$595$	7.27087	+	3.50147i	0.298077	+	0.143546i
$596$	20.5258	+	89.9294i	0.840769	+	3.68365i
$597$	25.9244			1.06101
$598$	8.81348	+	38.6144i	0.360410	+	1.57906i
$599$	−6.19230	+	7.76490i	−0.253011	+	0.317265i	−0.892074	−	0.451888i	$-0.850751\pi$
$599$	−6.19230	+	7.76490i	−0.253011	+	0.317265i	0.639064	+	0.769154i	$0.279322\pi$
$600$	−3.30838	+	14.4950i	−0.135064	+	0.591754i
$601$	−3.45048	+	15.1175i	−0.140748	+	0.616657i	0.854514	+	0.519428i	$0.173855\pi$
$601$	−3.45048	+	15.1175i	−0.140748	+	0.616657i	−0.995262	+	0.0972287i	$0.969002\pi$
$602$	14.0040	+	17.5604i	0.570759	+	0.715710i
$603$	0.129722	+	0.0624709i	0.00528269	+	0.00254401i
$604$	−14.4306	+	6.94941i	−0.587172	+	0.282767i
$605$	14.9005	−	18.6846i	0.605792	−	0.759639i
$606$	−15.7858	−	19.7948i	−0.641255	−	0.804109i
$607$	−0.363257	+	0.174936i	−0.0147442	+	0.00710042i	−0.441241	−	0.897388i	$-0.645462\pi$
$607$	−0.363257	+	0.174936i	−0.0147442	+	0.00710042i	0.426497	+	0.904489i	$0.359747\pi$
$608$	−80.5959			−3.26859
$609$	1.93848	+	4.12707i	0.0785511	+	0.167237i
$610$	33.5993			1.36040
$611$	−5.63564	+	2.71398i	−0.227994	+	0.109796i
$612$	13.3885	+	16.7887i	0.541200	+	0.678643i
$613$	−9.22408	+	11.5666i	−0.372557	+	0.467172i	−0.932401	−	0.361426i	$-0.882290\pi$
$613$	−9.22408	+	11.5666i	−0.372557	+	0.467172i	0.559843	+	0.828598i	$0.310861\pi$
$614$	−58.3875	+	28.1180i	−2.35633	+	1.13475i
$615$	−21.2629	−	10.2397i	−0.857402	−	0.412903i
$616$	6.85791	+	8.59954i	0.276313	+	0.346485i
$617$	−0.133056	+	0.582958i	−0.00535665	+	0.0234690i	−0.977536	−	0.210770i	$-0.932403\pi$
$617$	−0.133056	+	0.582958i	−0.00535665	+	0.0234690i	0.972179	+	0.234239i	$0.0752599\pi$
$618$	8.90518	−	39.0161i	0.358219	−	1.56946i
$619$	3.30388	−	4.14293i	0.132794	−	0.166518i	−0.710989	−	0.703204i	$-0.751752\pi$
$619$	3.30388	−	4.14293i	0.132794	−	0.166518i	0.843783	+	0.536685i	$0.180324\pi$
$620$	1.85940	+	8.14655i	0.0746751	+	0.327173i
$621$	6.41819			0.257553
$622$	3.51385	+	15.3952i	0.140893	+	0.617291i
$623$	3.51691	+	1.69365i	0.140902	+	0.0678548i
$624$	34.5311	+	16.6293i	1.38235	+	0.665705i
$625$	6.70362	+	29.3705i	0.268145	+	1.17482i
$626$	11.0892			0.443214
$627$	0.827115	+	3.62383i	0.0330318	+	0.144722i
$628$	30.2868	−	37.9785i	1.20858	−	1.51551i
$629$	3.35552	−	14.7015i	0.133793	−	0.586187i
$630$	1.32822	−	5.81932i	0.0529176	−	0.231847i
$631$	−16.5526	−	20.7564i	−0.658950	−	0.826298i	0.334278	−	0.942474i	$-0.391508\pi$
$631$	−16.5526	−	20.7564i	−0.658950	−	0.826298i	−0.993229	+	0.116177i	$0.962936\pi$
$632$	−2.50618	−	1.20691i	−0.0996904	−	0.0480084i
$633$	−17.3537	+	8.35709i	−0.689747	+	0.332165i
$634$	21.2792	−	26.6832i	0.845104	−	1.05973i
$635$	−19.0328	−	23.8664i	−0.755293	−	0.947108i
$636$	−20.3364	+	9.79348i	−0.806390	+	0.388337i
$637$	13.9574			0.553011
$638$	18.3058	+	4.36512i	0.724732	+	0.172817i
$639$	−5.11884			−0.202498
$640$	137.381	−	66.1590i	5.43044	−	2.61516i
$641$	3.27345	+	4.10477i	0.129293	+	0.162129i	0.842264	−	0.539065i	$-0.181222\pi$
$641$	3.27345	+	4.10477i	0.129293	+	0.162129i	−0.712971	+	0.701194i	$0.752651\pi$
$642$	−3.17564	+	3.98213i	−0.125333	+	0.157162i
$643$	−16.1356	+	7.77051i	−0.636327	+	0.306439i	−0.724093	−	0.689702i	$-0.757742\pi$
$643$	−16.1356	+	7.77051i	−0.636327	+	0.306439i	0.0877660	+	0.996141i	$0.472027\pi$
$644$	−27.9929	−	13.4807i	−1.10308	−	0.531213i
$645$	−15.1084	−	18.9453i	−0.594893	−	0.745972i
$646$	6.86034	−	30.0571i	0.269916	−	1.18258i
$647$	7.79104	−	34.1348i	0.306297	−	1.34198i	−0.554141	−	0.832423i	$-0.686953\pi$
$647$	7.79104	−	34.1348i	0.306297	−	1.34198i	0.860439	−	0.509554i	$-0.170190\pi$
$648$	6.43865	−	8.07381i	0.252934	−	0.317169i
$649$	−0.628599	−	2.75407i	−0.0246747	−	0.108107i
$650$	−8.88471			−0.348487
$651$	−0.108512	−	0.475422i	−0.00425292	−	0.0186332i
$652$	106.855	+	51.4587i	4.18477	+	2.01528i
$653$	−16.7006	−	8.04260i	−0.653546	−	0.314731i	0.0775675	−	0.996987i	$-0.475285\pi$
$653$	−16.7006	−	8.04260i	−0.653546	−	0.314731i	−0.731113	+	0.682256i	$0.760999\pi$
$654$	−8.86799	−	38.8532i	−0.346766	−	1.51928i
$655$	6.04947			0.236372
$656$	35.7043	+	156.431i	1.39402	+	6.10759i
$657$	0.860347	−	1.07884i	0.0335653	−	0.0420896i
$658$	1.47381	−	6.45717i	0.0574549	−	0.251727i
$659$	0.290833	−	1.27422i	0.0113293	−	0.0496367i	−0.968947	−	0.247267i	$-0.920467\pi$
$659$	0.290833	−	1.27422i	0.0113293	−	0.0496367i	0.980277	+	0.197630i	$0.0633246\pi$
$660$	−11.3794	−	14.2694i	−0.442944	−	0.555434i
$661$	−30.7540	−	14.8103i	−1.19619	−	0.576055i	−0.273603	−	0.961843i	$-0.588215\pi$
$661$	−30.7540	−	14.8103i	−1.19619	−	0.576055i	−0.922588	+	0.385788i	$0.873930\pi$
$662$	38.7777	−	18.6744i	1.50714	−	0.725800i
$663$	−5.20200	+	6.52310i	−0.202029	+	0.253336i
$664$	−44.0066	−	55.1826i	−1.70779	−	2.14150i
$665$	−5.72014	+	2.75467i	−0.221818	+	0.106822i
$666$	−11.1535			−0.432190
$667$	−33.7693	+	7.36429i	−1.30755	+	0.285146i
$668$	56.0279			2.16778
$669$	0.710057	−	0.341945i	0.0274524	−	0.0132204i
$670$	0.632850	+	0.793569i	0.0244491	+	0.0306582i
$671$	−3.73815	+	4.68750i	−0.144310	+	0.180959i
$672$	−20.8077	+	10.0205i	−0.802675	+	0.386548i
$673$	17.1253	+	8.24713i	0.660134	+	0.317904i	0.733786	−	0.679380i	$-0.237751\pi$
$673$	17.1253	+	8.24713i	0.660134	+	0.317904i	−0.0736527	+	0.997284i	$0.523466\pi$
$674$	−0.0558641	−	0.0700513i	−0.00215180	−	0.00269828i
$675$	−0.320369	+	1.40363i	−0.0123310	+	0.0540256i
$676$	10.2609	−	44.9559i	0.394650	−	1.72907i
$677$	14.7723	−	18.5239i	0.567746	−	0.711930i	−0.412223	−	0.911083i	$-0.635248\pi$
$677$	14.7723	−	18.5239i	0.567746	−	0.711930i	0.979968	+	0.199153i	$0.0638189\pi$
$678$	7.28152	+	31.9024i	0.279645	+	1.22521i
$679$	−3.91170			−0.150117
$680$	21.9018	+	95.9581i	0.839896	+	3.67983i
$681$	16.9571	+	8.16610i	0.649796	+	0.312926i
$682$	−1.81335	−	0.873263i	−0.0694368	−	0.0334390i
$683$	−3.23113	−	14.1565i	−0.123636	−	0.541683i	−0.998370	−	0.0570798i	$-0.981821\pi$
$683$	−3.23113	−	14.1565i	−0.123636	−	0.541683i	0.874734	−	0.484603i	$-0.161036\pi$
$684$	−16.8937			−0.645946
$685$	−7.66284	−	33.5731i	−0.292782	−	1.28276i
$686$	−19.4803	+	24.4275i	−0.743760	+	0.932645i
$687$	−5.98717	+	26.2315i	−0.228425	+	1.00079i
$688$	−36.6604	+	160.620i	−1.39766	+	6.12357i
$689$	−5.46802	−	6.85668i	−0.208315	−	0.261219i
$690$	40.7652	+	19.6315i	1.55190	+	0.747358i
$691$	11.3521	−	5.46688i	0.431854	−	0.207970i	−0.205312	−	0.978697i	$-0.565821\pi$
$691$	11.3521	−	5.46688i	0.431854	−	0.207970i	0.637166	+	0.770727i	$0.280107\pi$
$692$	−71.7382	+	89.9568i	−2.72708	+	3.41964i
$693$	0.664089	+	0.832741i	0.0252267	+	0.0316332i
$694$	11.1334	−	5.36155i	0.422617	−	0.203522i
$695$	−50.7078			−1.92346
$696$	−24.6130	+	49.8682i	−0.932954	+	1.89025i
$697$	−34.9292			−1.32304
$698$	42.6912	−	20.5590i	1.61588	−	0.778169i
$699$	−8.17898	−	10.2561i	−0.309357	−	0.387922i
$700$	4.34545	−	5.44902i	0.164243	−	0.205954i
$701$	−32.7410	+	15.7672i	−1.23661	+	0.595521i	−0.933891	−	0.357559i	$-0.883609\pi$
$701$	−32.7410	+	15.7672i	−1.23661	+	0.595521i	−0.302721	+	0.953079i	$0.597895\pi$
$702$	5.55999	+	2.67755i	0.209848	+	0.101058i
$703$	7.39671	+	9.27518i	0.278972	+	0.349820i
$704$	−11.5514	+	50.6101i	−0.435360	+	1.90744i
$705$	−1.59004	+	6.96641i	−0.0598843	+	0.262370i
$706$	−15.1793	+	19.0342i	−0.571279	+	0.716362i
$707$	1.71715	+	7.52332i	0.0645800	+	0.282943i
$708$	12.8390			0.482520
$709$	4.48293	+	19.6410i	0.168360	+	0.737633i	0.986654	+	0.162833i	$0.0520630\pi$
$709$	4.48293	+	19.6410i	0.168360	+	0.737633i	−0.818294	+	0.574800i	$0.805080\pi$
$710$	−32.5124	−	15.6571i	−1.22017	−	0.587602i
$711$	−0.242687	−	0.116872i	−0.00910148	−	0.00438304i
$712$	10.5939	+	46.4148i	0.397022	+	1.73947i
$713$	3.69646			0.138434
$714$	−1.96584	−	8.61289i	−0.0735696	−	0.322329i
$715$	4.42138	−	5.54423i	0.165350	−	0.207343i
$716$	31.2867	−	137.076i	1.16924	−	5.12277i
$717$	−0.901012	+	3.94759i	−0.0336489	+	0.147426i
$718$	3.90165	+	4.89252i	0.145608	+	0.182587i
$719$	17.5840	+	8.46801i	0.655773	+	0.315804i	0.732018	−	0.681286i	$-0.238579\pi$
$719$	17.5840	+	8.46801i	0.655773	+	0.315804i	−0.0762449	+	0.997089i	$0.524293\pi$
$720$	39.4470	−	18.9967i	1.47010	−	0.707964i
$721$	−7.60501	+	9.53639i	−0.283226	+	0.355154i
$722$	−17.7866	−	22.3037i	−0.661949	−	0.830058i
$723$	−3.62856	+	1.74742i	−0.134948	+	0.0649874i
$724$	110.976			4.12439
$725$	0.0750882	−	7.75279i	0.00278871	−	0.287931i
$726$	−26.1621			−0.970965
$727$	0.886876	−	0.427097i	0.0328924	−	0.0158401i	−0.417365	−	0.908739i	$-0.637046\pi$
$727$	0.886876	−	0.427097i	0.0328924	−	0.0158401i	0.450258	+	0.892899i	$0.351332\pi$
$728$	−12.1104	−	15.1859i	−0.448840	−	0.562828i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	8.76438	−	4.22070i	0.324384	−	0.156215i
$731$	−32.3129	−	15.5611i	−1.19514	−	0.575547i
$732$	−16.9897	−	21.3044i	−0.627958	−	0.787435i
$733$	7.34197	−	32.1673i	0.271182	−	1.18812i	−0.637438	−	0.770501i	$-0.720006\pi$
$733$	7.34197	−	32.1673i	0.271182	−	1.18812i	0.908620	−	0.417624i	$-0.137137\pi$
$734$	−5.52441	+	24.2040i	−0.203910	+	0.893386i
$735$	9.94114	−	12.4658i	0.366684	−	0.459808i
$736$	−38.9552	−	170.674i	−1.43591	−	6.29112i
$737$	−0.181121			−0.00667167
$738$	5.74888	+	25.1875i	0.211619	+	0.927165i
$739$	−19.6077	−	9.44255i	−0.721279	−	0.347350i	0.0369684	−	0.999316i	$-0.488230\pi$
$739$	−19.6077	−	9.44255i	−0.721279	−	0.347350i	−0.758248	+	0.651967i	$0.773944\pi$
$740$	−52.4826	−	25.2743i	−1.92930	−	0.929102i
$741$	−1.46060	−	6.39932i	−0.0536566	−	0.235085i
$742$	9.28617			0.340906
$743$	3.81650	+	16.7212i	0.140014	+	0.613440i	0.995430	+	0.0954983i	$0.0304445\pi$
$743$	3.81650	+	16.7212i	0.140014	+	0.613440i	−0.855416	+	0.517942i	$0.826698\pi$
$744$	3.70825	−	4.64999i	0.135951	−	0.170477i
$745$	−9.11045	+	39.9155i	−0.333781	+	1.46239i
$746$	2.95545	−	12.9487i	0.108207	−	0.474085i
$747$	−4.26140	−	5.34363i	−0.155917	−	0.195513i
$748$	−24.3376	−	11.7204i	−0.889871	−	0.428540i
$749$	1.39866	−	0.673557i	0.0511058	−	0.0246112i
$750$	15.6488	−	19.6229i	0.571412	−	0.716529i
$751$	23.4475	+	29.4022i	0.855610	+	1.07290i	0.996559	+	0.0828839i	$0.0264131\pi$
$751$	23.4475	+	29.4022i	0.855610	+	1.07290i	−0.140949	+	0.990017i	$0.545015\pi$
$752$	43.7707	−	21.0789i	1.59615	−	0.768667i
$753$	30.3241			1.10507
$754$	−32.3262	−	7.70836i	−1.17725	−	0.280722i
$755$	−7.10910			−0.258726
$756$	−4.36150	+	2.10039i	−0.158626	+	0.0763904i
$757$	15.4259	+	19.3435i	0.560664	+	0.703050i	0.978680	−	0.205389i	$-0.0658460\pi$
$757$	15.4259	+	19.3435i	0.560664	+	0.703050i	−0.418017	+	0.908439i	$0.637275\pi$
$758$	59.3924	−	74.4757i	2.15723	−	2.70508i
$759$	−7.27422	+	3.50308i	−0.264038	+	0.127154i
$760$	−69.7653	−	33.5972i	−2.53065	−	1.21870i
$761$	−14.7384	−	18.4813i	−0.534266	−	0.669948i	0.439304	−	0.898338i	$-0.355225\pi$
$761$	−14.7384	−	18.4813i	−0.534266	−	0.669948i	−0.973570	+	0.228391i	$0.926654\pi$
$762$	−7.43608	+	32.5796i	−0.269381	+	1.18023i
$763$	−2.70286	+	11.8420i	−0.0978503	+	0.428710i
$764$	−3.29079	+	4.12652i	−0.119057	+	0.149292i
$765$	2.12087	+	9.29216i	0.0766804	+	0.335959i</

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)

\(f(q)\)	\(=\)	\(q+(-2.50290 + 1.20533i) q^{2} +(0.623490 + 0.781831i) q^{3} +(3.56470 - 4.46999i) q^{4} +(2.28635 - 1.10105i) q^{5} +(-2.50290 - 1.20533i) q^{6} +(0.527912 + 0.661981i) q^{7} +(-2.29793 + 10.0679i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})\)	\(q+(-2.50290 + 1.20533i) q^{2} +(0.623490 + 0.781831i) q^{3} +(3.56470 - 4.46999i) q^{4} +(2.28635 - 1.10105i) q^{5} +(-2.50290 - 1.20533i) q^{6} +(0.527912 + 0.661981i) q^{7} +(-2.29793 + 10.0679i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(-4.39538 + 5.51163i) q^{10} +(-0.279921 - 1.22641i) q^{11} +5.71733 q^{12} +(0.494312 + 2.16572i) q^{13} +(-2.11922 - 1.02056i) q^{14} +(2.28635 + 1.10105i) q^{15} +(-3.83921 - 16.8207i) q^{16} +3.75587 q^{17} +(-0.618165 - 2.70836i) q^{18} +(-1.84230 + 2.31017i) q^{19} +(3.22848 - 14.1449i) q^{20} +(-0.188410 + 0.825477i) q^{21} +(2.17885 + 2.73219i) q^{22} +(-5.78259 - 2.78475i) q^{23} +(-9.30411 + 4.48063i) q^{24} +(0.897653 - 1.12562i) q^{25} +(-3.84763 - 4.82478i) q^{26} +(-0.900969 + 0.433884i) q^{27} +4.84090 q^{28} +(4.24261 - 3.31666i) q^{29} -7.04965 q^{30} +(-0.518900 + 0.249889i) q^{31} +(17.0064 + 21.3253i) q^{32} +(0.784321 - 0.983507i) q^{33} +(-9.40056 + 4.52707i) q^{34} +(1.93587 + 0.932265i) q^{35} +(3.56470 + 4.46999i) q^{36} +(0.893407 - 3.91427i) q^{37} +(1.82657 - 8.00271i) q^{38} +(-1.38503 + 1.73677i) q^{39} +(5.83136 + 25.5489i) q^{40} -9.29991 q^{41} +(-0.523404 - 2.29318i) q^{42} +(-8.60331 - 4.14313i) q^{43} +(-6.47989 - 3.12055i) q^{44} +(0.564683 + 2.47404i) q^{45} +17.8298 q^{46} +(0.626576 + 2.74521i) q^{47} +(10.7572 - 13.4891i) q^{48} +(1.39812 - 6.12556i) q^{49} +(-0.889987 + 3.89929i) q^{50} +(2.34175 + 2.93646i) q^{51} +(11.4428 + 5.51058i) q^{52} +(-3.55697 + 1.71295i) q^{53} +(1.73206 - 2.17193i) q^{54} +(-1.99034 - 2.49581i) q^{55} +(-7.87785 + 3.79377i) q^{56} -2.95482 q^{57} +(-6.62115 + 13.4150i) q^{58} +2.24563 q^{59} +(13.0718 - 6.29507i) q^{60} +(-2.97162 - 3.72629i) q^{61} +(0.997555 - 1.25089i) q^{62} +(-0.762856 + 0.367372i) q^{63} +(-37.1800 - 17.9050i) q^{64} +(3.51474 + 4.40735i) q^{65} +(-0.777623 + 3.40699i) q^{66} +(0.0320387 - 0.140371i) q^{67} +(13.3885 - 16.7887i) q^{68} +(-1.42818 - 6.25727i) q^{69} -5.96898 q^{70} +(1.13905 + 4.99050i) q^{71} +(-9.30411 - 4.48063i) q^{72} +(-1.24324 - 0.598712i) q^{73} +(2.48189 + 10.8739i) q^{74} +1.43972 q^{75} +(3.75920 + 16.4701i) q^{76} +(0.664089 - 0.832741i) q^{77} +(1.37320 - 6.01640i) q^{78} +(-0.0599388 + 0.262609i) q^{79} +(-27.2982 - 34.2308i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(23.2767 - 11.2095i) q^{82} +(-4.26140 + 5.34363i) q^{83} +(3.01825 + 3.78477i) q^{84} +(8.58724 - 4.13540i) q^{85} +26.5271 q^{86} +(5.23830 + 1.24910i) q^{87} +12.9906 q^{88} +(4.15363 - 2.00028i) q^{89} +(-4.39538 - 5.51163i) q^{90} +(-1.17271 + 1.47054i) q^{91} +(-33.0610 + 15.9213i) q^{92} +(-0.518900 - 0.249889i) q^{93} +(-4.87715 - 6.11575i) q^{94} +(-1.66853 + 7.31033i) q^{95} +(-6.06950 + 26.5922i) q^{96} +(-2.88047 + 3.61199i) q^{97} +(3.88399 + 17.0169i) q^{98} +1.25795 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

Introduction

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