LMFDB - Embedded newform 87.2.g.a.16.1

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			16.1
Root			$1.10857 + 1.39010i$ of defining polynomial
Character	$\chi$	$=$	87.16
Dual form			87.2.g.a.49.1

$q$-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 $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

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

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	−0.966466	−	0.256793i	$-0.917334\pi$
$2$	−2.50290	−	1.20533i	−1.76982	−	0.852299i	−0.803351	−	0.595506i	$-0.796952\pi$
$3$	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	0.868511	−	0.495670i	$-0.165077\pi$
$5$	2.28635	+	1.10105i	1.02249	+	0.492404i	0.153977	+	0.988074i	$0.450792\pi$
$6$	−2.50290	+	1.20533i	−1.02180	+	0.492075i
$7$	0.527912	−	0.661981i	0.199532	−	0.250205i	−0.671992	−	0.740559i	$-0.734561\pi$
$7$	0.527912	−	0.661981i	0.199532	−	0.250205i	0.871524	+	0.490353i	$0.163132\pi$
$8$	−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	−0.999436	−	0.0335941i	$-0.989305\pi$
$11$	−0.279921	+	1.22641i	−0.0843993	+	0.369778i	0.915036	+	0.403372i	$0.132162\pi$
$12$	5.71733			1.65045
$13$	0.494312	−	2.16572i	0.137098	−	0.600663i	−0.858967	−	0.512031i	$-0.828893\pi$
$13$	0.494312	−	2.16572i	0.137098	−	0.600663i	0.996064	−	0.0886323i	$-0.0282496\pi$
$14$	−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	0.524227	−	0.851579i	$-0.324354\pi$
$19$	−1.84230	−	2.31017i	−0.422652	−	0.529989i	−0.946879	+	0.321589i	$0.895783\pi$
$20$	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	−0.925310	−	0.379211i	$-0.876196\pi$
$23$	−5.78259	+	2.78475i	−1.20575	+	0.580660i	−0.280443	+	0.959871i	$0.590481\pi$
$24$	−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	0.386704	−	0.922204i	$-0.373613\pi$
$31$	−0.518900	−	0.249889i	−0.0931972	−	0.0448814i	−0.479902	+	0.877322i	$0.659328\pi$
$32$	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	0.993742	+	0.111698i	$0.0356288\pi$
$37$	0.893407	+	3.91427i	0.146875	+	0.643502i	−0.846867	+	0.531805i	$0.821514\pi$
$38$	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	−0.953410	−	0.301676i	$-0.902454\pi$
$43$	−8.60331	+	4.14313i	−1.31199	+	0.631822i	−0.358582	+	0.933498i	$0.616740\pi$
$44$	−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	−0.908450	−	0.417993i	$-0.862734\pi$
$47$	0.626576	−	2.74521i	0.0913956	−	0.400430i	0.999846	+	0.0175630i	$0.00559076\pi$
$48$	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	0.173336	−	0.984863i	$-0.444545\pi$
$53$	−3.55697	−	1.71295i	−0.488587	−	0.235291i	−0.661923	+	0.749571i	$0.730260\pi$
$54$	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	−0.934788	−	0.355207i	$-0.884410\pi$
$61$	−2.97162	+	3.72629i	−0.380477	+	0.477103i	0.554311	+	0.832310i	$0.312982\pi$
$62$	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	0.976847	−	0.213938i	$-0.0686290\pi$
$67$	0.0320387	+	0.140371i	0.00391415	+	0.0171490i	−0.972933	+	0.231087i	$0.925772\pi$
$68$	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	−0.861275	−	0.508139i	$-0.830334\pi$
$71$	1.13905	−	4.99050i	0.135180	−	0.592264i	0.996455	−	0.0841244i	$-0.0268093\pi$
$72$	−9.30411	+	4.48063i	−1.09650	+	0.528047i
$73$	−1.24324	+	0.598712i	−0.145510	+	0.0700739i	−0.505222	−	0.862990i	$-0.668589\pi$
$73$	−1.24324	+	0.598712i	−0.145510	+	0.0700739i	0.359712	+	0.933063i	$0.382875\pi$
$74$	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	0.971444	−	0.237268i	$-0.0762520\pi$
$79$	−0.0599388	−	0.262609i	−0.00674364	−	0.0295458i	−0.978188	+	0.207722i	$0.933395\pi$
$80$	−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	0.490869	−	0.871234i	$-0.336680\pi$
$83$	−4.26140	−	5.34363i	−0.467750	−	0.586540i	−0.958619	+	0.284694i	$0.908108\pi$
$84$	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	0.640875	−	0.767645i	$-0.278572\pi$
$89$	4.15363	+	2.00028i	0.440284	+	0.212030i	−0.200590	+	0.979675i	$0.564286\pi$
$90$	−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	0.613790	−	0.789469i	$-0.289644\pi$
$97$	−2.88047	−	3.61199i	−0.292467	−	0.366742i	−0.906257	+	0.422727i	$0.861073\pi$
$98$	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	0.0218131	−	0.999762i	$-0.493056\pi$
$101$	8.21134	−	3.95437i	0.817059	−	0.393475i	0.795246	+	0.606287i	$0.207342\pi$
$102$	−9.40056	+	4.52707i	−0.930794	+	0.448247i
$103$	3.20560	−	14.0446i	0.315857	−	1.38386i	−0.528889	−	0.848691i	$-0.677391\pi$
$103$	3.20560	−	14.0446i	0.315857	−	1.38386i	0.844745	−	0.535168i	$-0.179752\pi$
$104$	−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	0.990812	−	0.135244i	$-0.0431819\pi$
$107$	0.407981	+	1.78748i	0.0394410	+	0.172802i	−0.951371	+	0.308046i	$0.900325\pi$
$108$	−1.27223	−	5.57399i	−0.122420	−	0.536357i
$109$	8.94438	−	11.2159i	0.856716	−	1.07429i	−0.139741	−	0.990188i	$-0.544627\pi$
$109$	8.94438	−	11.2159i	0.856716	−	1.07429i	0.996457	−	0.0840999i	$-0.0268015\pi$
$110$	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	−0.996306	−	0.0858722i	$-0.972632\pi$
$113$	−7.34424	+	9.20939i	−0.690888	+	0.866346i	0.305418	+	0.952218i	$0.401204\pi$
$114$	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	0.705701	+	0.708510i	$0.250632\pi$
$127$	−2.67677	+	11.7277i	−0.237524	+	1.04066i	−0.943226	+	0.332153i	$0.892225\pi$
$128$	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	−0.337697	−	0.941255i	$-0.609648\pi$
$131$	2.14780	−	1.03433i	0.187654	−	0.0903695i	0.525352	+	0.850885i	$0.323934\pi$
$132$	−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	0.923401	+	0.383836i	$0.125397\pi$
$137$	3.01965	+	13.2299i	0.257986	+	1.13031i	−0.665416	+	0.746473i	$0.731746\pi$
$138$	11.1167	−	13.9399i	0.946315	−	1.18664i
$139$	−18.0033	+	8.66991i	−1.52702	+	0.735373i	−0.993860	−	0.110644i	$-0.964709\pi$
$139$	−18.0033	+	8.66991i	−1.52702	+	0.735373i	−0.533157	+	0.846017i	$0.678994\pi$
$140$	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	−0.998811	−	0.0487523i	$-0.984476\pi$
$149$	−10.0592	−	12.6139i	−0.824085	−	1.03337i	0.174726	−	0.984617i	$-0.444096\pi$
$150$	−3.60348	−	1.73535i	−0.294223	−	0.141690i
$151$	−2.52401	+	1.21550i	−0.205401	+	0.0989158i	−0.533756	−	0.845638i	$-0.679220\pi$
$151$	−2.52401	+	1.21550i	−0.205401	+	0.0989158i	0.328355	+	0.944554i	$0.393506\pi$
$152$	−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	−0.387711	−	0.921781i	$-0.626734\pi$
$163$	4.61597	−	20.2239i	0.361550	−	1.58406i	0.749261	−	0.662275i	$-0.230409\pi$
$164$	−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	−0.487051	−	0.873374i	$-0.661927\pi$
$167$	6.10998	−	7.66168i	0.472805	−	0.592878i	0.959855	+	0.280495i	$0.0904988\pi$
$168$	−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	0.999047	+	0.0436504i	$0.0138988\pi$
$179$	22.1567	+	10.6701i	1.65607	+	0.797521i	0.657023	+	0.753871i	$0.271816\pi$
$180$	13.0718	−	6.29507i	0.974318	−	0.469207i
$181$	12.1022	−	15.1757i	0.899551	−	1.12800i	−0.0916705	−	0.995789i	$-0.529221\pi$
$181$	12.1022	−	15.1757i	0.899551	−	1.12800i	0.991221	−	0.132212i	$-0.0422079\pi$
$182$	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	0.950843	−	0.309673i	$-0.100220\pi$
$193$	6.07588	+	7.61891i	0.437351	+	0.548421i	−0.513492	+	0.858095i	$0.671648\pi$
$194$	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	−0.178480	−	0.983943i	$-0.557118\pi$
$197$	6.73034	−	3.24116i	0.479517	−	0.230923i	0.657997	+	0.753020i	$0.271404\pi$
$198$	−3.14853	−	1.51625i	−0.223756	−	0.107755i
$199$	16.1636	+	20.2685i	1.14581	+	1.43679i	0.881392	+	0.472385i	$0.156607\pi$
$199$	16.1636	+	20.2685i	1.14581	+	1.43679i	0.264413	+	0.964410i	$0.414822\pi$
$200$	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	−0.877384	−	0.479789i	$-0.840713\pi$
$211$	−4.28601	−	18.7782i	−0.295061	−	1.29275i	0.582323	−	0.812957i	$-0.302144\pi$
$212$	−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	0.980460	−	0.196717i	$-0.0630281\pi$
$223$	0.175370	+	0.768344i	0.0117436	+	0.0514521i	−0.968717	+	0.248170i	$0.920171\pi$
$224$	−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	0.901581	−	0.432609i	$-0.142407\pi$
$227$	16.9571	+	8.16610i	1.12548	+	0.542003i	0.223899	+	0.974612i	$0.428121\pi$
$228$	−10.5330	−	13.2080i	−0.697567	−	0.874722i
$229$	16.7757	−	21.0360i	1.10857	−	1.39010i	0.196281	−	0.980548i	$-0.437114\pi$
$229$	16.7757	−	21.0360i	1.10857	−	1.39010i	0.912287	−	0.409552i	$-0.134315\pi$
$230$	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	−0.693448	−	0.720507i	$-0.743909\pi$
$239$	2.52458	−	3.16572i	0.163302	−	0.204774i	0.856749	+	0.515733i	$0.172481\pi$
$240$	9.74261	+	42.6851i	0.628883	+	2.75531i
$241$	−0.896181	−	3.92643i	−0.0577281	−	0.252923i	0.937827	−	0.347103i	$-0.112834\pi$
$241$	−0.896181	−	3.92643i	−0.0577281	−	0.252923i	−0.995555	+	0.0941792i	$0.969977\pi$
$242$	−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	0.823443	+	0.567399i	$0.192050\pi$
$251$	18.9067	+	23.7083i	1.19338	+	1.49645i	0.369939	+	0.929056i	$0.379378\pi$
$252$	−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	0.597743	−	0.801688i	$-0.296064\pi$
$257$	−5.07958	−	6.36959i	−0.316855	−	0.397324i	−0.914598	+	0.404364i	$0.867493\pi$
$258$	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	0.584720	−	0.811235i	$-0.301204\pi$
$263$	5.10905	+	2.46039i	0.315038	+	0.151714i	−0.269682	+	0.962949i	$0.586919\pi$
$264$	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	−0.899252	−	0.437430i	$-0.855889\pi$
$269$	−4.57344	−	20.0376i	−0.278848	−	1.22171i	0.620405	−	0.784282i	$-0.286968\pi$
$270$	1.56869	+	6.87290i	0.0954677	+	0.418271i
$271$	5.98035	+	7.49912i	0.363280	+	0.455539i	0.929558	−	0.368675i	$-0.120189\pi$
$271$	5.98035	+	7.49912i	0.363280	+	0.455539i	−0.566278	+	0.824214i	$0.691617\pi$
$272$	−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	−0.441755	−	0.897136i	$-0.645644\pi$
$277$	5.75035	−	25.1939i	0.345505	−	1.51376i	0.787260	−	0.616621i	$-0.211499\pi$
$278$	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	0.938330	+	0.345740i	$0.112372\pi$
$281$	4.07233	+	17.8421i	0.242935	+	1.06437i	−0.695395	+	0.718627i	$0.744771\pi$
$282$	1.74063	+	7.62622i	0.103653	+	0.454135i
$283$	−8.60447	+	10.7897i	−0.511483	+	0.641379i	−0.968776	−	0.247937i	$-0.920247\pi$
$283$	−8.60447	+	10.7897i	−0.511483	+	0.641379i	0.457293	+	0.889316i	$0.348819\pi$
$284$	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	−0.961995	−	0.273069i	$-0.911961\pi$
$293$	−8.24552	+	10.3396i	−0.481708	+	0.604043i	0.480286	+	0.877112i	$0.340533\pi$
$294$	−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	0.998046	−	0.0624884i	$-0.0199036\pi$
$311$	1.26488	+	5.54181i	0.0717249	+	0.314247i	−0.926321	+	0.376736i	$0.877047\pi$
$312$	−14.3029	+	17.9353i	−0.809744	+	1.01539i
$313$	−3.59647	+	1.73197i	−0.203284	+	0.0978966i	−0.532756	−	0.846269i	$-0.678844\pi$
$313$	−3.59647	+	1.73197i	−0.203284	+	0.0978966i	0.329472	+	0.944165i	$0.393129\pi$
$314$	−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	0.0963994	−	0.995343i	$-0.469267\pi$
$317$	−11.0688	−	5.33046i	−0.621687	−	0.299389i	−0.718086	+	0.695954i	$0.754982\pi$
$318$	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	−0.974732	−	0.223377i	$-0.928292\pi$
$337$	0.00717696	−	0.0314443i	0.000390954	−	0.00171288i	0.975123	+	0.221664i	$0.0711489\pi$
$338$	−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	0.632045	−	0.774932i	$-0.282216\pi$
$353$	7.89583	+	3.80243i	0.420252	+	0.202383i	−0.211792	+	0.977315i	$0.567930\pi$
$354$	−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	−0.986431	−	0.164174i	$-0.947504\pi$
$359$	−0.501253	+	2.19613i	−0.0264551	+	0.115907i	0.959976	+	0.280081i	$0.0903614\pi$
$360$	−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	0.905694	−	0.423932i	$-0.139350\pi$
$367$	5.57199	+	6.98706i	0.290856	+	0.364721i	−0.614839	+	0.788653i	$0.710779\pi$
$368$	−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	0.698647	−	0.715467i	$-0.253786\pi$
$373$	−2.98091	−	3.73794i	−0.154346	−	0.193543i	−0.852992	+	0.521924i	$0.825215\pi$
$374$	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	−0.587931	−	0.808911i	$-0.700057\pi$
$379$	−30.8943	−	14.8779i	−1.58693	−	0.764226i	−0.999001	+	0.0446854i	$0.985771\pi$
$380$	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	−0.892309	−	0.451426i	$-0.850916\pi$
$383$	−21.4436	+	10.3267i	−1.09572	+	0.527669i	−0.203407	+	0.979094i	$0.565201\pi$
$384$	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	0.998683	+	0.0513005i	$0.0163366\pi$
$397$	2.41408	+	10.5768i	0.121159	+	0.530833i	−0.877524	+	0.479533i	$0.840806\pi$
$398$	−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	−0.343013	−	0.939331i	$-0.611447\pi$
$401$	−25.8578	−	12.4525i	−1.29128	−	0.621846i	−0.948263	+	0.317485i	$0.897162\pi$
$402$	−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	−1.00000		0.000741524i	$-0.999764\pi$
$409$	−15.7089	+	19.6984i	−0.776756	+	0.974021i	0.223244	+	0.974763i	$0.428335\pi$
$410$	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	0.854523	+	0.519413i	$0.173849\pi$
$419$	−2.88089	+	12.6220i	−0.140741	+	0.616625i	−0.995264	+	0.0972114i	$0.969008\pi$
$420$	11.0680	−	5.33007i	0.540064	−	0.260081i
$421$	−17.6399	+	8.49493i	−0.859716	+	0.414018i	−0.811175	−	0.584804i	$-0.801172\pi$
$421$	−17.6399	+	8.49493i	−0.859716	+	0.414018i	−0.0485414	+	0.998821i	$0.515457\pi$
$422$	−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	0.724738	−	0.689025i	$-0.241961\pi$
$431$	−2.24797	−	2.81887i	−0.108281	−	0.135780i	−0.833019	+	0.553245i	$0.813389\pi$
$432$	10.7572	−	13.4891i	0.517557	−	0.648996i
$433$	4.33066	+	2.08554i	0.208118	+	0.100225i	0.535039	−	0.844827i	$-0.320297\pi$
$433$	4.33066	+	2.08554i	0.208118	+	0.100225i	−0.326921	+	0.945052i	$0.606011\pi$
$434$	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	0.881332	−	0.472497i	$-0.156647\pi$
$439$	4.70521	+	5.90014i	0.224567	+	0.281599i	−0.656765	+	0.754095i	$0.728076\pi$
$440$	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	−0.939895	−	0.341465i	$-0.889077\pi$
$443$	−5.07740	−	22.2456i	−0.241235	−	1.05692i	0.698660	−	0.715454i	$-0.253780\pi$
$444$	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	−0.134489	−	0.990915i	$-0.542939\pi$
$449$	11.7896	−	5.67759i	0.556388	−	0.267942i	0.690876	+	0.722973i	$0.257225\pi$
$450$	−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	0.0747922	+	0.997199i	$0.476171\pi$
$457$	−19.5401	+	24.5025i	−0.914048	+	1.14618i	−0.988840	+	0.148981i	$0.952401\pi$
$458$	−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	0.193584	−	0.981084i	$-0.437989\pi$
$461$	23.7681	−	29.8043i	1.10699	−	1.38813i	0.913410	−	0.407042i	$-0.133440\pi$
$462$	−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	−0.537249	−	0.843423i	$-0.680537\pi$
$467$	8.74298	−	10.9633i	0.404577	−	0.507323i	0.941826	+	0.336100i	$0.109108\pi$
$468$	−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	0.732408	−	0.680866i	$-0.238396\pi$
$479$	37.6742	−	18.1430i	1.72138	−	0.828973i	0.988971	−	0.148107i	$-0.0473180\pi$
$480$	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	−0.699106	−	0.715018i	$-0.746419\pi$
$487$	−12.7105	+	6.12107i	−0.575969	+	0.277372i	0.123138	+	0.992390i	$0.460704\pi$
$488$	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	−0.193041	−	0.981191i	$-0.561835\pi$
$491$	−23.9429	−	11.5303i	−1.08053	−	0.520354i	−0.887485	+	0.460837i	$0.847549\pi$
$492$	−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	−0.777641	−	0.628709i	$-0.783584\pi$
$499$	−17.2217	+	8.29352i	−0.770948	+	0.371269i	0.00669320	+	0.999978i	$0.497869\pi$
$500$	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	0.953944	−	0.299986i	$-0.0969821\pi$
$503$	10.0746	+	12.6332i	0.449206	+	0.563287i	−0.504737	+	0.863273i	$0.668411\pi$
$504$	−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	−0.686276	−	0.727341i	$-0.740756\pi$
$509$	5.58653	−	24.4762i	0.247619	−	1.08489i	0.933895	−	0.357548i	$-0.116387\pi$
$510$	−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	0.928995	−	0.370094i	$-0.120674\pi$
$541$	8.40733	+	10.5425i	0.361459	+	0.453256i	−0.567535	+	0.823349i	$0.692103\pi$
$542$	−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	0.988655	−	0.150206i	$-0.0479935\pi$
$547$	14.5525	+	18.2482i	0.622219	+	0.780238i	−0.366436	+	0.930443i	$0.619422\pi$
$548$	−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	−0.496469	−	0.868054i	$-0.665370\pi$
$557$	−3.00534	+	1.44729i	−0.127340	+	0.0613238i	0.369129	+	0.929378i	$0.379656\pi$
$558$	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	−0.975719	−	0.219028i	$-0.929711\pi$
$569$	−0.0380192	+	0.166573i	−0.00159385	+	0.00698310i	0.974125	+	0.226011i	$0.0725685\pi$
$570$	12.9876	+	16.2859i	0.543989	+	0.682140i
$571$	−5.95314	−	26.0824i	−0.249131	−	1.09152i	−0.932423	−	0.361370i	$-0.882309\pi$
$571$	−5.95314	−	26.0824i	−0.249131	−	1.09152i	0.683291	−	0.730146i	$-0.260548\pi$
$572$	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	−0.0557170	+	0.998447i	$0.517744\pi$
$577$	−24.4227	+	30.6252i	−1.01673	+	1.27494i	−0.961015	+	0.276495i	$0.910827\pi$
$578$	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	−0.808017	−	0.589159i	$-0.799459\pi$
$587$	−1.30417	+	1.63538i	−0.0538290	+	0.0674994i	0.754188	+	0.656658i	$0.228031\pi$
$588$	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	0.774963	+	0.632007i	$0.217768\pi$
$593$	−4.80876	+	21.0685i	−0.197472	+	0.865181i	−0.972435	+	0.233174i	$0.925089\pi$
$594$	−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	0.639064	−	0.769154i	$-0.279322\pi$
$599$	−6.19230	−	7.76490i	−0.253011	−	0.317265i	−0.892074	+	0.451888i	$0.850751\pi$
$600$	−3.30838	−	14.4950i	−0.135064	−	0.591754i
$601$	−3.45048	−	15.1175i	−0.140748	−	0.616657i	−0.995262	−	0.0972287i	$-0.969002\pi$
$601$	−3.45048	−	15.1175i	−0.140748	−	0.616657i	0.854514	−	0.519428i	$-0.173855\pi$
$602$	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	0.426497	−	0.904489i	$-0.359747\pi$
$607$	−0.363257	−	0.174936i	−0.0147442	−	0.00710042i	−0.441241	+	0.897388i	$0.645462\pi$
$608$	−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	0.559843	−	0.828598i	$-0.310861\pi$
$613$	−9.22408	−	11.5666i	−0.372557	−	0.467172i	−0.932401	+	0.361426i	$0.882290\pi$
$614$	−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	0.972179	−	0.234239i	$-0.0752599\pi$
$617$	−0.133056	−	0.582958i	−0.00535665	−	0.0234690i	−0.977536	+	0.210770i	$0.932403\pi$
$618$	8.90518	+	39.0161i	0.358219	+	1.56946i
$619$	3.30388	+	4.14293i	0.132794	+	0.166518i	0.843783	−	0.536685i	$-0.180324\pi$
$619$	3.30388	+	4.14293i	0.132794	+	0.166518i	−0.710989	+	0.703204i	$0.751752\pi$
$620$	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	−0.993229	−	0.116177i	$-0.962936\pi$
$631$	−16.5526	+	20.7564i	−0.658950	+	0.826298i	0.334278	+	0.942474i	$0.391508\pi$
$632$	−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	−0.712971	−	0.701194i	$-0.752651\pi$
$641$	3.27345	−	4.10477i	0.129293	−	0.162129i	0.842264	+	0.539065i	$0.181222\pi$
$642$	−3.17564	−	3.98213i	−0.125333	−	0.157162i
$643$	−16.1356	−	7.77051i	−0.636327	−	0.306439i	0.0877660	−	0.996141i	$-0.472027\pi$
$643$	−16.1356	−	7.77051i	−0.636327	−	0.306439i	−0.724093	+	0.689702i	$0.757742\pi$
$644$	−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	0.860439	+	0.509554i	$0.170190\pi$
$647$	7.79104	+	34.1348i	0.306297	+	1.34198i	−0.554141	+	0.832423i	$0.686953\pi$
$648$	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	−0.731113	−	0.682256i	$-0.760999\pi$
$653$	−16.7006	+	8.04260i	−0.653546	+	0.314731i	0.0775675	+	0.996987i	$0.475285\pi$
$654$	−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	0.980277	−	0.197630i	$-0.0633246\pi$
$659$	0.290833	+	1.27422i	0.0113293	+	0.0496367i	−0.968947	+	0.247267i	$0.920467\pi$
$660$	−11.3794	+	14.2694i	−0.442944	+	0.555434i
$661$	−30.7540	+	14.8103i	−1.19619	+	0.576055i	−0.922588	−	0.385788i	$-0.873930\pi$
$661$	−30.7540	+	14.8103i	−1.19619	+	0.576055i	−0.273603	+	0.961843i	$0.588215\pi$
$662$	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	−0.0736527	−	0.997284i	$-0.523466\pi$
$673$	17.1253	−	8.24713i	0.660134	−	0.317904i	0.733786	+	0.679380i	$0.237751\pi$
$674$	−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	0.979968	−	0.199153i	$-0.0638189\pi$
$677$	14.7723	+	18.5239i	0.567746	+	0.711930i	−0.412223	+	0.911083i	$0.635248\pi$
$678$	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	0.874734	+	0.484603i	$0.161036\pi$
$683$	−3.23113	+	14.1565i	−0.123636	+	0.541683i	−0.998370	+	0.0570798i	$0.981821\pi$
$684$	−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	0.637166	−	0.770727i	$-0.280107\pi$
$691$	11.3521	+	5.46688i	0.431854	+	0.207970i	−0.205312	+	0.978697i	$0.565821\pi$
$692$	−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	−0.302721	−	0.953079i	$-0.597895\pi$
$701$	−32.7410	−	15.7672i	−1.23661	−	0.595521i	−0.933891	+	0.357559i	$0.883609\pi$
$702$	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	−0.818294	−	0.574800i	$-0.805080\pi$
$709$	4.48293	−	19.6410i	0.168360	−	0.737633i	0.986654	−	0.162833i	$-0.0520630\pi$
$710$	−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	−0.0762449	−	0.997089i	$-0.524293\pi$
$719$	17.5840	−	8.46801i	0.655773	−	0.315804i	0.732018	+	0.681286i	$0.238579\pi$
$720$	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	0.450258	−	0.892899i	$-0.351332\pi$
$727$	0.886876	+	0.427097i	0.0328924	+	0.0158401i	−0.417365	+	0.908739i	$0.637046\pi$
$728$	−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	0.908620	+	0.417624i	$0.137137\pi$
$733$	7.34197	+	32.1673i	0.271182	+	1.18812i	−0.637438	+	0.770501i	$0.720006\pi$
$734$	−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	−0.758248	−	0.651967i	$-0.773944\pi$
$739$	−19.6077	+	9.44255i	−0.721279	+	0.347350i	0.0369684	+	0.999316i	$0.488230\pi$
$740$	−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	−0.855416	−	0.517942i	$-0.826698\pi$
$743$	3.81650	−	16.7212i	0.140014	−	0.613440i	0.995430	−	0.0954983i	$-0.0304445\pi$
$744$	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	−0.140949	−	0.990017i	$-0.545015\pi$
$751$	23.4475	−	29.4022i	0.855610	−	1.07290i	0.996559	−	0.0828839i	$-0.0264131\pi$
$752$	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	−0.418017	−	0.908439i	$-0.637275\pi$
$757$	15.4259	−	19.3435i	0.560664	−	0.703050i	0.978680	+	0.205389i	$0.0658460\pi$
$758$	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	−0.973570	−	0.228391i	$-0.926654\pi$
$761$	−14.7384	+	18.4813i	−0.534266	+	0.669948i	0.439304	+	0.898338i	$0.355225\pi$
$762$	−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
$766$	66.1182			2.38895
$767$	1.11004	−	4.86341i	0.0400813	−	0.175608i
$768$	−76.0321	+	36.6151i	−2.74357	+	1.32123i
$769$	1.87153	−	0.901284i	0.0674893	−	0.0325011i	−0.399835	−	0.916587i	$-0.630932\pi$
$769$	1.87153	−	0.901284i	0.0674893	−	0.0325011i	0.467324	+	0.884086i	$0.345218\pi$
$770$	1.67084	−	7.32043i	0.0602129	−	0.263810i
$771$	−8.14701			−0.293407
$772$	−12.3978	+	54.3183i	−0.446206	+	1.95496i
$773$	8.08528	+	10.1386i	0.290807	+	0.364661i	0.905677	−	0.423968i	$-0.139363\pi$
$773$	8.08528	+	10.1386i	0.290807	+	0.364661i	−0.614870	+	0.788628i	$0.710792\pi$
$774$	−5.90283	−	25.8620i	−0.212173	−	0.929590i
$775$	−0.184512	−	0.808398i	−0.00662786	−	0.0290385i
$776$	−29.7460	+	37.3003i	−1.06782	+	1.33900i
$777$	3.06282	−	1.47497i	0.109878	−	0.0529144i
$778$	−46.3634	−	22.3274i	−1.66221	−	0.800478i
$779$	17.1332	+	21.4844i	0.613861	+	0.769758i
$780$	20.0949	−	25.1983i	0.719515	−	0.902243i
$781$	5.80158	+	2.79389i	0.207597	+	0.0999733i
$782$	66.9663			2.39471
$783$	−2.38342	−	4.82901i	−0.0851763	−	0.172575i
$784$	−108.404			−3.87156
$785$	19.4256	+	9.35487i	0.693329	+	0.333890i
$786$	−4.12902	+	5.17763i	−0.147277	+	0.184680i
$787$	−4.28528	−	5.37357i	−0.152754	−	0.191547i	0.699566	−	0.714568i	$-0.253377\pi$
$787$	−4.28528	−	5.37357i	−0.152754	−	0.191547i	−0.852320	+	0.523020i	$0.824805\pi$
$788$	38.4796	+	18.5308i	1.37078	+	0.660133i
$789$	5.10905	−	2.46039i	0.181887	−	0.0875922i
$790$	−1.18395	+	1.48463i	−0.0421231	+	0.0528207i
$791$	2.21933	+	9.72350i	0.0789101	+	0.345728i
$792$	−2.89068	−	12.6649i	−0.102716	−	0.450028i
$793$	6.60120	+	8.27765i	0.234416	+	0.293948i
$794$	6.70634	−	29.3824i	0.237999	−	1.04274i
$795$	−10.0185			−0.355321
$796$	−32.9817	+	144.502i	−1.16900	+	5.12174i
$797$	12.1118	−	5.83274i	0.429023	−	0.206606i	−0.206895	−	0.978363i	$-0.566336\pi$
$797$	12.1118	−	5.83274i	0.429023	−	0.206606i	0.635918	+	0.771757i	$0.280622\pi$
$798$	6.26191	−	3.01558i	0.221669	−	0.106750i
$799$	2.35334	−	10.3106i	0.0832551	−	0.364765i
$800$	39.2700			1.38840
$801$	1.02586	−	4.49460i	0.0362471	−	0.158809i
$802$	49.7101	+	62.3345i	1.75532	+	2.20111i
$803$	−0.386260	−	1.69232i	−0.0136308	−	0.0597205i
$804$	0.183176	+	0.802547i	0.00646012	+	0.0283036i
$805$	−8.59821	+	10.7818i	−0.303047	+	0.380009i
$806$	3.20219	−	1.54210i	0.112792	−	0.0543180i
$807$	−18.5175	−	8.91755i	−0.651847	−	0.313913i
$808$	−58.6812	−	73.5839i	−2.06440	−	2.58867i
$809$	22.3326	−	28.0043i	0.785174	−	0.984577i	−0.214795	−	0.976659i	$-0.568908\pi$
$809$	22.3326	−	28.0043i	0.785174	−	0.984577i	0.999969	−	0.00791779i	$-0.00252034\pi$
$810$	6.35151	+	3.05873i	0.223169	+	0.107473i
$811$	−42.0554			−1.47677			−0.738383	−	0.674382i	$-0.764410\pi$
$811$	−42.0554			−1.47677			−0.738383	+	0.674382i	$0.764410\pi$
$812$	20.5381	+	16.0556i	0.720745	+	0.563442i
$813$	9.59174			0.336397
$814$	12.6411	+	6.08765i	0.443072	+	0.213372i
$815$	32.8212	−	41.1565i	1.14968	−	1.44165i
$816$	40.4027	+	50.6634i	1.41438	+	1.77357i
$817$	25.4212	+	12.2422i	0.889376	+	0.428301i
$818$	63.0609	−	30.3685i	2.20487	−	1.06181i
$819$	−1.17271	+	1.47054i	−0.0409780	+	0.0513847i
$820$	−30.0246	−	131.546i	−1.04850	−	4.59380i
$821$	4.17288	+	18.2826i	0.145635	+	0.638067i	0.994068	+	0.108764i	$0.0346894\pi$
$821$	4.17288	+	18.2826i	0.145635	+	0.638067i	−0.848433	+	0.529303i	$0.822454\pi$
$822$	−23.5043	−	29.4735i	−0.819808	−	1.02801i
$823$	4.43930	−	19.4498i	0.154744	−	0.677978i	−0.836724	−	0.547626i	$-0.815532\pi$
$823$	4.43930	−	19.4498i	0.154744	−	0.677978i	0.991468	−	0.130353i	$-0.0416110\pi$
$824$	−148.766			−5.18251
$825$	−0.403009	+	1.76570i	−0.0140310	+	0.0614737i
$826$	−4.75899	+	2.29181i	−0.165586	+	0.0797422i
$827$	−13.3371	+	6.42279i	−0.463775	+	0.223342i	−0.651154	−	0.758945i	$-0.725715\pi$
$827$	−13.3371	+	6.42279i	−0.463775	+	0.223342i	0.187379	+	0.982288i	$0.440001\pi$
$828$	−8.16539	+	35.7749i	−0.283767	+	1.24326i
$829$	−33.7345			−1.17165			−0.585824	−	0.810438i	$-0.699229\pi$
$829$	−33.7345			−1.17165			−0.585824	+	0.810438i	$0.699229\pi$
$830$	−10.7216	+	46.9746i	−0.372154	+	1.63051i
$831$	−16.1121	−	20.2040i	−0.558924	−	0.700868i
$832$	20.3986	+	89.3723i	0.707196	+	3.09843i
$833$	5.25115	+	23.0068i	0.181942	+	0.797138i
$834$	34.6102	−	43.3998i	1.19845	−	1.50281i
$835$	22.4055	−	10.7899i	0.775373	−	0.373400i
$836$	19.1469	+	9.22066i	0.662209	+	0.318903i
$837$	0.359090	+	0.450284i	0.0124120	+	0.0155641i
$838$	22.4243	−	28.1191i	0.774634	−	0.971360i
$839$	−16.9843	−	8.17920i	−0.586363	−	0.282377i	0.117088	−	0.993122i	$-0.462644\pi$
$839$	−16.9843	−	8.17920i	−0.586363	−	0.282377i	−0.703451	+	0.710744i	$0.748358\pi$
$840$	−22.1887			−0.765582
$841$	6.99951	+	28.1426i	0.241362	+	0.970435i
$842$	54.3901			1.87441
$843$	16.4885	+	7.94046i	0.567895	+	0.273484i
$844$	68.6602	−	86.0971i	2.36338	−	2.96358i
$845$	12.7610	+	16.0017i	0.438991	+	0.550477i
$846$	7.04769	+	3.39399i	0.242304	+	0.116688i
$847$	7.18423	−	3.45974i	0.246853	−	0.118878i
$848$	42.4688	−	53.2542i	1.45839	−	1.82876i
$849$	3.07090	+	13.4545i	0.105393	+	0.461757i
$850$	−3.34267	−	14.6452i	−0.114653	−	0.502327i
$851$	−16.0665	−	20.1467i	−0.550751	−	0.690620i
$852$	6.51233	−	28.5324i	0.223109	−	0.977503i
$853$	50.4469			1.72727			0.863634	−	0.504119i	$-0.168183\pi$
$853$	50.4469			1.72727			0.863634	+	0.504119i	$0.168183\pi$
$854$	2.49460	−	10.9295i	0.0853634	−	0.374001i
$855$	−6.75576	+	3.25340i	−0.231042	+	0.111264i
$856$	17.0586	−	8.21499i	0.583051	−	0.280783i
$857$	−12.6515	+	55.4299i	−0.432168	+	1.89345i	0.0167160	+	0.999860i	$0.494679\pi$
$857$	−12.6515	+	55.4299i	−0.432168	+	1.89345i	−0.448884	+	0.893590i	$0.648178\pi$
$858$	−7.76298			−0.265024
$859$	3.91095	−	17.1350i	0.133440	−	0.584638i	−0.863352	−	0.504602i	$-0.831639\pi$
$859$	3.91095	−	17.1350i	0.133440	−	0.584638i	0.996792	−	0.0800362i	$-0.0255036\pi$
$860$	−86.3798	−	108.317i	−2.94553	−	3.69357i
$861$	1.75219	+	7.67687i	0.0597146	+	0.261627i
$862$	2.22877	+	9.76490i	0.0759123	+	0.332594i
$863$	−19.5746	+	24.5458i	−0.666329	+	0.835550i	−0.994016	−	0.109237i	$-0.965159\pi$
$863$	−19.5746	+	24.5458i	−0.666329	+	0.835550i	0.327687	+	0.944786i	$0.393731\pi$
$864$	−24.5749	+	11.8346i	−0.836055	+	0.402623i
$865$	−46.0120	−	22.1582i	−1.56445	−	0.753401i
$866$	−8.32545	−	10.4398i	−0.282910	−	0.354758i
$867$	−1.80404	+	2.26219i	−0.0612684	+	0.0768281i
$868$	−2.51194	−	1.20969i	−0.0852609	−	0.0410595i
$869$	0.338845			0.0114945
$870$	−29.9089	−	23.3813i	−1.01401	−	0.792700i
$871$	0.319841			0.0108374
$872$	−133.474	−	64.2776i	−4.51999	−	2.17671i
$873$	−2.88047	+	3.61199i	−0.0974890	+	0.122247i
$874$	−32.8478	−	41.1898i	−1.11109	−	1.39327i
$875$	−6.89223	−	3.31912i	−0.233000	−	0.112207i
$876$	−7.10800	+	3.42303i	−0.240157	+	0.115654i
$877$	18.1826	−	22.8002i	0.613981	−	0.769908i	−0.373502	−	0.927629i	$-0.621843\pi$
$877$	18.1826	−	22.8002i	0.613981	−	0.769908i	0.987484	+	0.157721i	$0.0504146\pi$
$878$	−4.66502	−	20.4388i	−0.157437	−	0.689776i
$879$	2.94279	+	12.8932i	0.0992579	+	0.434877i
$880$	−34.3398	−	43.0608i	−1.15760	−	1.45158i
$881$	1.37959	−	6.04439i	0.0464796	−	0.203641i	−0.946357	−	0.323124i	$-0.895267\pi$
$881$	1.37959	−	6.04439i	0.0464796	−	0.203641i	0.992836	+	0.119484i	$0.0381239\pi$
$882$	−17.4545			−0.587723
$883$	11.6283	−	50.9468i	0.391322	−	1.71450i	−0.268678	−	0.963230i	$-0.586587\pi$
$883$	11.6283	−	50.9468i	0.391322	−	1.71450i	0.660000	−	0.751265i	$-0.270556\pi$
$884$	42.9778	−	20.6970i	1.44550	−	0.696116i
$885$	5.13431	−	2.47255i	0.172588	−	0.0831139i
$886$	−14.1051	+	61.7984i	−0.473869	+	2.07616i
$887$	−26.4724			−0.888855			−0.444428	−	0.895815i	$-0.646593\pi$
$887$	−26.4724			−0.888855			−0.444428	+	0.895815i	$0.646593\pi$
$888$	9.22602	−	40.4219i	0.309605	−	1.35647i
$889$	6.35040	+	7.96315i	0.212986	+	0.267076i
$890$	−7.23197	−	31.6853i	−0.242416	−	1.06209i
$891$	−0.279921	−	1.22641i	−0.00937770	−	0.0410864i
$892$	−2.80935	+	3.52282i	−0.0940641	+	0.117953i
$893$	−7.49624	+	3.61000i	−0.250852	+	0.120804i
$894$	40.3812	+	19.4465i	1.35055	+	0.650390i
$895$	38.9097	+	48.7913i	1.30061	+	1.63091i
$896$	31.7208	−	39.7766i	1.05972	−	1.32884i
$897$	12.8455	+	6.18609i	0.428900	+	0.206548i
$898$	−36.3517			−1.21307
$899$	−1.37269	−	2.78120i	−0.0457819	−	0.0927581i
$900$	8.23138			0.274379
$901$	−13.3595	−	6.43360i	−0.445070	−	0.214334i
$902$	−20.2631	+	25.4091i	−0.674688	+	0.846032i
$903$	5.04101	+	6.32123i	0.167754	+	0.210357i
$904$	109.595	+	52.7784i	3.64509	+	1.75538i
$905$	44.3792	−	21.3719i	1.47521	−	0.710425i
$906$	4.85226	−	6.08454i	0.161205	−	0.202145i
$907$	4.33990	+	19.0144i	0.144104	+	0.631362i	0.994457	+	0.105148i	$0.0335316\pi$
$907$	4.33990	+	19.0144i	0.144104	+	0.631362i	−0.850352	+	0.526214i	$0.823611\pi$
$908$	23.9445	+	104.908i	0.794626	+	3.48148i
$909$	−5.68242	−	7.12553i	−0.188474	−	0.236339i
$910$	−2.95054	+	12.9271i	−0.0978093	+	0.428531i
$911$	26.8766			0.890461			0.445231	−	0.895416i	$-0.353122\pi$
$911$	26.8766			0.890461			0.445231	+	0.895416i	$0.353122\pi$
$912$	11.3442	−	49.7020i	0.375643	−	1.64580i
$913$	7.74636	−	3.73045i	0.256367	−	0.123460i
$914$	78.4406	−	37.7750i	2.59459	−	1.24949i
$915$	−2.69134	+	11.7915i	−0.0889728	+	0.389815i
$916$	153.831			5.08272
$917$	0.449146	−	1.96784i	0.0148321	−	0.0649837i
$918$	6.50539	+	8.15750i	0.214710	+	0.269238i
$919$	5.24040	+	22.9597i	0.172865	+	0.757370i	0.984810	+	0.173636i	$0.0555517\pi$
$919$	5.24040	+	22.9597i	0.172865	+	0.757370i	−0.811945	+	0.583734i	$0.801591\pi$
$920$	37.4268	+	163.977i	1.23392	+	5.40617i
$921$	14.5447	−	18.2385i	0.479266	−	0.600980i
$922$	−95.4134	+	45.9487i	−3.14227	+	1.51324i
$923$	−10.2450	−	4.93373i	−0.337218	−	0.162396i
$924$	3.79682	+	4.76106i	0.124906	+	0.156627i
$925$	−3.60402	+	4.51930i	−0.118499	+	0.148594i
$926$	−98.0118	−	47.2000i	−3.22087	−	1.55109i
$927$	−14.4058			−0.473149
$928$	142.880	−	34.0706i	4.69027	−	1.11842i
$929$	−26.2377			−0.860831			−0.430416	−	0.902631i	$-0.641633\pi$
$929$	−26.2377			−0.860831			−0.430416	+	0.902631i	$0.641633\pi$
$930$	3.65806	+	1.76163i	0.119953	+	0.0577661i
$931$	11.5753	−	14.5150i	0.379366	−	0.475710i
$932$	−46.7619	−	58.6376i	−1.53174	−	1.92074i
$933$	5.12140	+	2.46634i	0.167667	+	0.0807443i
$934$	−35.0973	+	16.9020i	−1.14842	+	0.553049i
$935$	−7.47546	+	9.37393i	−0.244474	+	0.306560i
$936$	5.10466	+	22.3650i	0.166851	+	0.731022i
$937$	−9.73863	−	42.6677i	−0.318147	−	1.39389i	−0.840799	−	0.541348i	$-0.817914\pi$
$937$	−9.73863	−	42.6677i	−0.318147	−	1.39389i	0.522651	−	0.852546i	$-0.324943\pi$
$938$	−0.211154	−	0.264779i	−0.00689443	−	0.00864534i
$939$	−0.888255	+	3.89170i	−0.0289871	+	0.127001i
$940$	40.8536			1.33250
$941$	−3.40693	+	14.9267i	−0.111063	+	0.486597i	0.888550	+	0.458779i	$0.151713\pi$
$941$	−3.40693	+	14.9267i	−0.111063	+	0.486597i	−0.999613	+	0.0278180i	$0.991144\pi$
$942$	−21.2654	+	10.2409i	−0.692865	+	0.333666i
$943$	53.7776	−	25.8979i	1.75124	−	0.843352i
$944$	−8.62144	+	37.7730i	−0.280604	+	1.22941i
$945$	−2.14865			−0.0698957
$946$	−7.42548	+	32.5332i	−0.241423	+	1.05774i
$947$	−7.57022	−	9.49275i	−0.245999	−	0.308473i	0.643467	−	0.765474i	$-0.277495\pi$
$947$	−7.57022	−	9.49275i	−0.245999	−	0.308473i	−0.889466	+	0.457000i	$0.848924\pi$
$948$	−0.342690	−	1.50142i	−0.0111301	−	0.0487640i
$949$	0.682096	+	2.98846i	0.0221418	+	0.0970095i
$950$	−7.36839	+	9.23967i	−0.239062	+	0.299775i
$951$	−11.0688	+	5.33046i	−0.358931	+	0.172852i
$952$	−29.5882	−	14.2489i	−0.958958	−	0.461810i
$953$	−8.91546	−	11.1796i	−0.288800	−	0.362144i	0.616174	−	0.787610i	$-0.288682\pi$
$953$	−8.91546	−	11.1796i	−0.288800	−	0.362144i	−0.904974	+	0.425466i	$0.860110\pi$
$954$	6.83807	−	8.57466i	0.221391	−	0.277615i
$955$	−2.11067	−	1.01645i	−0.0682998	−	0.0328914i
$956$	23.1501			0.748729
$957$	0.0656080	+	6.77397i	0.00212081	+	0.218971i
$958$	−116.163			−3.75306
$959$	10.3521	+	4.98530i	0.334286	+	0.160984i
$960$	−65.2924	+	81.8741i	−2.10730	+	2.64248i
$961$	−19.1214	−	23.9774i	−0.616818	−	0.773466i
$962$	−22.3230	−	10.7502i	−0.719722	−	0.346600i
$963$	1.65188	−	0.795503i	0.0532311	−	0.0256347i
$964$	14.3565	−	18.0025i	0.462391	−	0.579820i
$965$	5.50281	+	24.1094i	0.177142	+	0.776108i
$966$	−3.35931	−	14.7181i	−0.108084	−	0.473546i
$967$	−7.56263	−	9.48324i	−0.243198	−	0.304960i	0.645219	−	0.763997i	$-0.276766\pi$
$967$	−7.56263	−	9.48324i	−0.243198	−	0.304960i	−0.888417	+	0.459037i	$0.848195\pi$
$968$	21.6408	−	94.8147i	0.695563	−	3.04746i
$969$	−11.0979			−0.356516
$970$	−7.24722	+	31.7521i	−0.232694	+	1.01950i
$971$	47.0955	−	22.6800i	1.51137	−	0.727836i	0.519423	−	0.854517i	$-0.326147\pi$
$971$	47.0955	−	22.6800i	1.51137	−	0.727836i	0.991943	+	0.126681i	$0.0404325\pi$
$972$	−5.15114	+	2.48066i	−0.165223	+	0.0795672i
$973$	−3.76483	+	16.4948i	−0.120695	+	0.528798i
$974$	39.1911			1.25576
$975$	0.711673	−	3.11804i	0.0227918	−	0.0998573i
$976$	−51.2700	−	64.2906i	−1.64111	−	2.05789i
$977$	−9.93012	−	43.5067i	−0.317693	−	1.39190i	−0.841588	−	0.540120i	$-0.818379\pi$
$977$	−9.93012	−	43.5067i	−0.317693	−	1.39190i	0.523896	−	0.851782i	$-0.324478\pi$
$978$	12.8232	+	56.1821i	0.410041	+	1.79651i
$979$	−3.61586	+	4.53415i	−0.115564	+	0.144912i
$980$	−82.1316	+	39.5525i	−2.62360	+	1.26346i
$981$	−12.9250	−	6.22435i	−0.412664	−	0.198728i
$982$	46.0288	+	57.7182i	1.46884	+	1.84186i
$983$	3.24886	−	4.07394i	0.103622	−	0.129938i	−0.727316	−	0.686303i	$-0.759233\pi$
$983$	3.24886	−	4.07394i	0.103622	−	0.129938i	0.830939	+	0.556364i	$0.187804\pi$
$984$	86.5274	+	41.6694i	2.75839	+	1.32837i
$985$	18.9566			0.604008
$986$	−24.8682	−	50.3851i	−0.791964	−	1.60459i
$987$	−2.38416			−0.0758887
$988$	−33.8115	−	16.2828i	−1.07569	−	0.518024i
$989$	38.2118	−	47.9161i	1.21506	−	1.52364i
$990$	−5.52918	−	6.93338i	−0.175729	−	0.220357i
$991$	−34.5135	−	16.6208i	−1.09636	−	0.527978i	−0.203846	−	0.979003i	$-0.565344\pi$
$991$	−34.5135	−	16.6208i	−1.09636	−	0.527978i	−0.892511	+	0.451025i	$0.851059\pi$
$992$	−14.1536	+	6.81599i	−0.449376	+	0.216408i
$993$	−9.65981	+	12.1130i	−0.306545	+	0.384395i
$994$	2.67922	+	11.7384i	0.0849798	+	0.372321i
$995$	14.6390	+	64.1378i	0.464089	+	2.03331i
$996$	−24.3639	−	30.5513i	−0.771999	−	0.968056i
$997$	−2.54648	+	11.1568i	−0.0806477	+	0.353341i	−0.999111	−	0.0421665i	$-0.986574\pi$
$997$	−2.54648	+	11.1568i	−0.0806477	+	0.353341i	0.918463	+	0.395507i	$0.129431\pi$
$998$	53.1005			1.68087
$999$	0.893407	−	3.91427i	0.0282661	−	0.123842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.g.a.16.1	✓	18
3.2	odd	2		261.2.k.c.190.3		18
29.7	even	7		2523.2.a.r.1.9		9
29.20	even	7	inner	87.2.g.a.49.1	yes	18
29.22	even	14		2523.2.a.o.1.1		9
87.20	odd	14		261.2.k.c.136.3		18
87.65	odd	14		7569.2.a.bj.1.1		9
87.80	odd	14		7569.2.a.bm.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.16.1	✓	18	1.1	even	1	trivial
87.2.g.a.49.1	yes	18	29.20	even	7	inner
261.2.k.c.136.3		18	87.20	odd	14
261.2.k.c.190.3		18	3.2	odd	2
2523.2.a.o.1.1		9	29.22	even	14
2523.2.a.r.1.9		9	29.7	even	7
7569.2.a.bj.1.1		9	87.65	odd	14
7569.2.a.bm.1.9		9	87.80	odd	14

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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