LMFDB - Embedded newform 87.2.g.a.52.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 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			52.3
Root			$-0.353498 - 1.54877i$ of defining polynomial
Character	$\chi$	$=$	87.52
Dual form			87.2.g.a.82.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61397 - 2.02385i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(-1.04604 - 4.58301i) q^{4} +(-0.716354 + 0.898279i) q^{5} +(1.61397 + 2.02385i) q^{6} +(-0.615328 + 2.69593i) q^{7} +(-6.29911 - 3.03349i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(1.61397 - 2.02385i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(-1.04604 - 4.58301i) q^{4} +(-0.716354 + 0.898279i) q^{5} +(1.61397 + 2.02385i) q^{6} +(-0.615328 + 2.69593i) q^{7} +(-6.29911 - 3.03349i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.661812 + 2.89959i) q^{10} +(3.92298 - 1.88921i) q^{11} +4.70087 q^{12} +(-5.07168 + 2.44239i) q^{13} +(4.46304 + 5.59648i) q^{14} +(-0.716354 - 0.898279i) q^{15} +(-7.83521 + 3.77324i) q^{16} +2.41516 q^{17} +(-2.33225 + 1.12315i) q^{18} +(-0.416772 - 1.82600i) q^{19} +(4.86616 + 2.34342i) q^{20} +(-2.49141 - 1.19980i) q^{21} +(2.50809 - 10.9886i) q^{22} +(-5.49948 - 6.89613i) q^{23} +(4.35912 - 5.46616i) q^{24} +(0.818862 + 3.58767i) q^{25} +(-3.24249 + 14.2063i) q^{26} +(0.623490 - 0.781831i) q^{27} +12.9991 q^{28} +(4.53581 + 2.90283i) q^{29} -2.97416 q^{30} +(0.972977 - 1.22007i) q^{31} +(-1.89780 + 8.31482i) q^{32} +(0.968895 + 4.24501i) q^{33} +(3.89799 - 4.88793i) q^{34} +(-1.98091 - 2.48398i) q^{35} +(-1.04604 + 4.58301i) q^{36} +(-6.99449 - 3.36837i) q^{37} +(-4.36821 - 2.10362i) q^{38} +(-1.25260 - 5.48800i) q^{39} +(7.23731 - 3.48530i) q^{40} +3.16072 q^{41} +(-6.44928 + 3.10581i) q^{42} +(-0.912772 - 1.14458i) q^{43} +(-12.7618 - 16.0028i) q^{44} +(1.03516 - 0.498507i) q^{45} -22.8327 q^{46} +(-0.321962 + 0.155049i) q^{47} +(-1.93514 - 8.47839i) q^{48} +(-0.582626 - 0.280578i) q^{49} +(8.58252 + 4.13313i) q^{50} +(-0.537424 + 2.35461i) q^{51} +(16.4987 + 20.6887i) q^{52} +(-1.01940 + 1.27828i) q^{53} +(-0.576019 - 2.52370i) q^{54} +(-1.11320 + 4.87727i) q^{55} +(12.0541 - 15.1154i) q^{56} +1.87296 q^{57} +(13.1955 - 4.49474i) q^{58} -4.85026 q^{59} +(-3.36749 + 4.22269i) q^{60} +(-0.346042 + 1.51611i) q^{61} +(-0.898897 - 3.93832i) q^{62} +(1.72411 - 2.16197i) q^{63} +(2.92070 + 3.66245i) q^{64} +(1.43917 - 6.30540i) q^{65} +(10.1550 + 4.89040i) q^{66} +(8.71192 + 4.19544i) q^{67} +(-2.52636 - 11.0687i) q^{68} +(7.94698 - 3.82706i) q^{69} -8.22432 q^{70} +(7.37090 - 3.54964i) q^{71} +(4.35912 + 5.46616i) q^{72} +(7.09446 + 8.89617i) q^{73} +(-18.1060 + 8.71937i) q^{74} -3.67993 q^{75} +(-7.93260 + 3.82014i) q^{76} +(2.67925 + 11.7386i) q^{77} +(-13.1286 - 6.32238i) q^{78} +(7.32556 + 3.52780i) q^{79} +(2.22336 - 9.74119i) q^{80} +(0.623490 + 0.781831i) q^{81} +(5.10130 - 6.39683i) q^{82} +(0.107218 + 0.469754i) q^{83} +(-2.89258 + 12.6732i) q^{84} +(-1.73011 + 2.16949i) q^{85} -3.78965 q^{86} +(-3.83936 + 3.77615i) q^{87} -30.4421 q^{88} +(-1.24461 + 1.56070i) q^{89} +(0.661812 - 2.89959i) q^{90} +(-3.46377 - 15.1758i) q^{91} +(-25.8523 + 32.4178i) q^{92} +(0.972977 + 1.22007i) q^{93} +(-0.205841 + 0.901847i) q^{94} +(1.93881 + 0.933683i) q^{95} +(-7.68405 - 3.70044i) q^{96} +(-1.03142 - 4.51895i) q^{97} +(-1.50819 + 0.726305i) q^{98} -4.35418 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 $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.61397	−	2.02385i	1.14125	−	1.43108i	0.255563	−	0.966792i	$-0.417739\pi$
$2$	1.61397	−	2.02385i	1.14125	−	1.43108i	0.885685	−	0.464287i	$-0.153689\pi$
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$4$	−1.04604	−	4.58301i	−0.523021	−	2.29150i
$5$	−0.716354	+	0.898279i	−0.320363	+	0.401723i	−0.915771	−	0.401701i	$-0.868419\pi$
$5$	−0.716354	+	0.898279i	−0.320363	+	0.401723i	0.595408	+	0.803424i	$0.296991\pi$
$6$	1.61397	+	2.02385i	0.658900	+	0.826234i
$7$	−0.615328	+	2.69593i	−0.232572	+	1.01897i	0.714925	+	0.699201i	$0.246461\pi$
$7$	−0.615328	+	2.69593i	−0.232572	+	1.01897i	−0.947497	+	0.319764i	$0.896396\pi$
$8$	−6.29911	−	3.03349i	−2.22707	−	1.07250i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	0.661812	+	2.89959i	0.209283	+	0.916930i
$11$	3.92298	−	1.88921i	1.18282	−	0.569617i	0.264090	−	0.964498i	$-0.414929\pi$
$11$	3.92298	−	1.88921i	1.18282	−	0.569617i	0.918732	+	0.394881i	$0.129214\pi$
$12$	4.70087			1.35702
$13$	−5.07168	+	2.44239i	−1.40663	+	0.677397i	−0.974494	−	0.224411i	$-0.927954\pi$
$13$	−5.07168	+	2.44239i	−1.40663	+	0.677397i	−0.432135	+	0.901809i	$0.642240\pi$
$14$	4.46304	+	5.59648i	1.19280	+	1.49572i
$15$	−0.716354	−	0.898279i	−0.184962	−	0.231935i
$16$	−7.83521	+	3.77324i	−1.95880	+	0.943310i
$17$	2.41516			0.585763			0.292881	−	0.956149i	$-0.405386\pi$
$17$	2.41516			0.585763			0.292881	+	0.956149i	$0.405386\pi$
$18$	−2.33225	+	1.12315i	−0.549717	+	0.264730i
$19$	−0.416772	−	1.82600i	−0.0956141	−	0.418913i	0.904355	−	0.426781i	$-0.140353\pi$
$19$	−0.416772	−	1.82600i	−0.0956141	−	0.418913i	−0.999969	+	0.00786845i	$0.997495\pi$
$20$	4.86616	+	2.34342i	1.08811	+	0.524004i
$21$	−2.49141	−	1.19980i	−0.543671	−	0.261818i
$22$	2.50809	−	10.9886i	0.534726	−	2.34279i
$23$	−5.49948	−	6.89613i	−1.14672	−	1.43794i	−0.880510	−	0.474027i	$-0.842800\pi$
$23$	−5.49948	−	6.89613i	−1.14672	−	1.43794i	−0.266210	−	0.963915i	$-0.585771\pi$
$24$	4.35912	−	5.46616i	0.889801	−	1.11577i
$25$	0.818862	+	3.58767i	0.163772	+	0.717534i
$26$	−3.24249	+	14.2063i	−0.635904	+	2.78608i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	12.9991			2.45660
$29$	4.53581	+	2.90283i	0.842279	+	0.539042i
$29$	4.53581	+	2.90283i	0.842279	+	0.539042i
$30$	−2.97416			−0.543004
$31$	0.972977	−	1.22007i	0.174752	−	0.219132i	−0.686740	−	0.726903i	$-0.740959\pi$
$31$	0.972977	−	1.22007i	0.174752	−	0.219132i	0.861492	+	0.507771i	$0.169530\pi$
$32$	−1.89780	+	8.31482i	−0.335488	+	1.46987i
$33$	0.968895	+	4.24501i	0.168663	+	0.738961i
$34$	3.89799	−	4.88793i	0.668500	−	0.838273i
$35$	−1.98091	−	2.48398i	−0.334834	−	0.419869i
$36$	−1.04604	+	4.58301i	−0.174340	+	0.763835i
$37$	−6.99449	−	3.36837i	−1.14989	−	0.553756i	−0.240887	−	0.970553i	$-0.577438\pi$
$37$	−6.99449	−	3.36837i	−1.14989	−	0.553756i	−0.909000	+	0.416797i	$0.863153\pi$
$38$	−4.36821	−	2.10362i	−0.708617	−	0.341252i
$39$	−1.25260	−	5.48800i	−0.200577	−	0.878784i
$40$	7.23731	−	3.48530i	1.14432	−	0.551075i
$41$	3.16072			0.493622			0.246811	−	0.969064i	$-0.420617\pi$
$41$	3.16072			0.493622			0.246811	+	0.969064i	$0.420617\pi$
$42$	−6.44928	+	3.10581i	−0.995146	+	0.479237i
$43$	−0.912772	−	1.14458i	−0.139196	−	0.174547i	0.707347	−	0.706867i	$-0.249892\pi$
$43$	−0.912772	−	1.14458i	−0.139196	−	0.174547i	−0.846543	+	0.532320i	$0.821320\pi$
$44$	−12.7618	−	16.0028i	−1.92392	−	2.41252i
$45$	1.03516	−	0.498507i	0.154313	−	0.0743131i
$46$	−22.8327			−3.36650
$47$	−0.321962	+	0.155049i	−0.0469630	+	0.0226162i	−0.457218	−	0.889355i	$-0.651154\pi$
$47$	−0.321962	+	0.155049i	−0.0469630	+	0.0226162i	0.410255	+	0.911971i	$0.365440\pi$
$48$	−1.93514	−	8.47839i	−0.279313	−	1.22375i
$49$	−0.582626	−	0.280578i	−0.0832323	−	0.0400826i
$50$	8.58252	+	4.13313i	1.21375	+	0.584512i
$51$	−0.537424	+	2.35461i	−0.0752544	+	0.329711i
$52$	16.4987	+	20.6887i	2.28796	+	2.86901i
$53$	−1.01940	+	1.27828i	−0.140025	+	0.175586i	−0.846899	−	0.531754i	$-0.821533\pi$
$53$	−1.01940	+	1.27828i	−0.140025	+	0.175586i	0.706874	+	0.707339i	$0.250105\pi$
$54$	−0.576019	−	2.52370i	−0.0783862	−	0.343432i
$55$	−1.11320	+	4.87727i	−0.150104	+	0.657651i
$56$	12.0541	−	15.1154i	1.61080	−	2.01987i
$57$	1.87296			0.248079
$58$	13.1955	−	4.49474i	1.73266	−	0.590188i
$59$	−4.85026			−0.631450			−0.315725	−	0.948851i	$-0.602248\pi$
$59$	−4.85026			−0.631450			−0.315725	+	0.948851i	$0.602248\pi$
$60$	−3.36749	+	4.22269i	−0.434741	+	0.545147i
$61$	−0.346042	+	1.51611i	−0.0443062	+	0.194118i	−0.992238	−	0.124356i	$-0.960313\pi$
$61$	−0.346042	+	1.51611i	−0.0443062	+	0.194118i	0.947931	+	0.318474i	$0.103171\pi$
$62$	−0.898897	−	3.93832i	−0.114160	−	0.500168i
$63$	1.72411	−	2.16197i	0.217218	−	0.272382i
$64$	2.92070	+	3.66245i	0.365088	+	0.457806i
$65$	1.43917	−	6.30540i	0.178507	−	0.782088i
$66$	10.1550	+	4.89040i	1.25000	+	0.601967i
$67$	8.71192	+	4.19544i	1.06433	+	0.512554i	0.882275	−	0.470734i	$-0.156011\pi$
$67$	8.71192	+	4.19544i	1.06433	+	0.512554i	0.182055	+	0.983288i	$0.441725\pi$
$68$	−2.52636	−	11.0687i	−0.306366	−	1.34228i
$69$	7.94698	−	3.82706i	0.956703	−	0.460724i
$70$	−8.22432			−0.982994
$71$	7.37090	−	3.54964i	0.874765	−	0.421264i	0.0580551	−	0.998313i	$-0.481510\pi$
$71$	7.37090	−	3.54964i	0.874765	−	0.421264i	0.816710	+	0.577049i	$0.195796\pi$
$72$	4.35912	+	5.46616i	0.513727	+	0.644193i
$73$	7.09446	+	8.89617i	0.830344	+	1.04122i	0.998461	+	0.0554515i	$0.0176598\pi$
$73$	7.09446	+	8.89617i	0.830344	+	1.04122i	−0.168117	+	0.985767i	$0.553769\pi$
$74$	−18.1060	+	8.71937i	−2.10477	+	1.01361i
$75$	−3.67993			−0.424922
$76$	−7.93260	+	3.82014i	−0.909932	+	0.438200i
$77$	2.67925	+	11.7386i	0.305329	+	1.33773i
$78$	−13.1286	−	6.32238i	−1.48652	−	0.715869i
$79$	7.32556	+	3.52780i	0.824189	+	0.396909i	0.797933	−	0.602747i	$-0.205927\pi$
$79$	7.32556	+	3.52780i	0.824189	+	0.396909i	0.0262567	+	0.999655i	$0.491641\pi$
$80$	2.22336	−	9.74119i	0.248579	−	1.08910i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	5.10130	−	6.39683i	0.563345	−	0.706412i
$83$	0.107218	+	0.469754i	0.0117687	+	0.0515622i	0.980471	−	0.196662i	$-0.0630102\pi$
$83$	0.107218	+	0.469754i	0.0117687	+	0.0515622i	−0.968703	+	0.248224i	$0.920153\pi$
$84$	−2.89258	+	12.6732i	−0.315606	+	1.38276i
$85$	−1.73011	+	2.16949i	−0.187657	+	0.235314i
$86$	−3.78965			−0.408648
$87$	−3.83936	+	3.77615i	−0.411623	+	0.404846i
$88$	−30.4421			−3.24514
$89$	−1.24461	+	1.56070i	−0.131929	+	0.165434i	−0.843408	−	0.537274i	$-0.819454\pi$
$89$	−1.24461	+	1.56070i	−0.131929	+	0.165434i	0.711479	+	0.702707i	$0.248026\pi$
$90$	0.661812	−	2.89959i	0.0697611	−	0.305643i
$91$	−3.46377	−	15.1758i	−0.363101	−	1.59085i
$92$	−25.8523	+	32.4178i	−2.69529	+	3.37979i
$93$	0.972977	+	1.22007i	0.100893	+	0.126516i
$94$	−0.205841	+	0.901847i	−0.0212309	+	0.0930184i
$95$	1.93881	+	0.933683i	0.198918	+	0.0957938i
$96$	−7.68405	−	3.70044i	−0.784250	−	0.377675i
$97$	−1.03142	−	4.51895i	−0.104725	−	0.458830i	−0.999914	−	0.0131424i	$-0.995817\pi$
$97$	−1.03142	−	4.51895i	−0.104725	−	0.458830i	0.895189	−	0.445687i	$-0.147041\pi$
$98$	−1.50819	+	0.726305i	−0.152350	+	0.0733679i
$99$	−4.35418			−0.437611
$100$	15.5857	−	7.50570i	1.55857	−	0.750570i
$101$	−1.18405	−	1.48475i	−0.117817	−	0.147738i	0.719425	−	0.694570i	$-0.244405\pi$
$101$	−1.18405	−	1.48475i	−0.117817	−	0.147738i	−0.837243	+	0.546831i	$0.815834\pi$
$102$	3.89799	+	4.88793i	0.385959	+	0.483977i
$103$	7.40706	−	3.56705i	0.729840	−	0.351472i	−0.0317815	−	0.999495i	$-0.510118\pi$
$103$	7.40706	−	3.56705i	0.729840	−	0.351472i	0.761621	+	0.648023i	$0.224404\pi$
$104$	39.3560			3.85917
$105$	2.86249	−	1.37850i	0.279351	−	0.134528i
$106$	0.941781	+	4.12621i	0.0914739	+	0.400773i
$107$	−4.01632	−	1.93416i	−0.388273	−	0.186982i	0.229555	−	0.973296i	$-0.426273\pi$
$107$	−4.01632	−	1.93416i	−0.388273	−	0.186982i	−0.617828	+	0.786313i	$0.711987\pi$
$108$	−4.23534	−	2.03963i	−0.407545	−	0.196264i
$109$	−3.89981	+	17.0862i	−0.373534	+	1.63656i	0.343234	+	0.939250i	$0.388478\pi$
$109$	−3.89981	+	17.0862i	−0.373534	+	1.63656i	−0.716768	+	0.697311i	$0.754380\pi$
$110$	8.07419	+	10.1247i	0.769844	+	0.965354i
$111$	4.84034	−	6.06959i	0.459424	−	0.576100i
$112$	−5.35116	−	23.4450i	−0.505637	−	2.21534i
$113$	−1.76485	+	7.73232i	−0.166023	+	0.727395i	0.821537	+	0.570155i	$0.193117\pi$
$113$	−1.76485	+	7.73232i	−0.166023	+	0.727395i	−0.987560	+	0.157240i	$0.949740\pi$
$114$	3.02289	−	3.79059i	0.283120	−	0.355021i
$115$	10.1342			0.945021
$116$	8.55904	−	23.8241i	0.794687	−	2.21202i
$117$	5.62914			0.520414
$118$	−7.82817	+	9.81621i	−0.720641	+	0.903655i
$119$	−1.48612	+	6.51111i	−0.136232	+	0.596872i
$120$	1.78747	+	7.83141i	0.163173	+	0.714906i
$121$	4.96226	−	6.22247i	0.451114	−	0.565679i
$122$	2.50988	+	3.14729i	0.227234	+	0.284942i
$123$	−0.703327	+	3.08147i	−0.0634168	+	0.277847i
$124$	−6.60939	−	3.18291i	−0.593541	−	0.285834i
$125$	−8.98513	−	4.32701i	−0.803654	−	0.387020i
$126$	−1.59284	−	6.97869i	−0.141902	−	0.621711i
$127$	3.02313	−	1.45586i	0.268259	−	0.129187i	−0.294919	−	0.955522i	$-0.595293\pi$
$127$	3.02313	−	1.45586i	0.268259	−	0.129187i	0.563178	+	0.826335i	$0.309578\pi$
$128$	−4.93114			−0.435855
$129$	1.31899	−	0.635194i	0.116131	−	0.0559257i
$130$	−10.4384	−	13.0894i	−0.915510	−	1.14801i
$131$	−5.42012	−	6.79661i	−0.473558	−	0.593823i	0.486480	−	0.873692i	$-0.338281\pi$
$131$	−5.42012	−	6.79661i	−0.473558	−	0.593823i	−0.960038	+	0.279869i	$0.909709\pi$
$132$	18.4414	−	8.88091i	1.60512	−	0.772984i
$133$	5.17921			0.449095
$134$	22.5517	−	10.8603i	1.94817	−	0.938189i
$135$	0.255664	+	1.12014i	0.0220040	+	0.0964060i
$136$	−15.2134	−	7.32637i	−1.30453	−	0.628231i
$137$	−2.90456	−	1.39876i	−0.248153	−	0.119504i	0.305673	−	0.952137i	$-0.401119\pi$
$137$	−2.90456	−	1.39876i	−0.248153	−	0.119504i	−0.553826	+	0.832632i	$0.686833\pi$
$138$	5.08076	−	22.2603i	0.432503	−	1.89492i
$139$	−14.0213	−	17.5821i	−1.18927	−	1.49130i	−0.829726	−	0.558170i	$-0.811504\pi$
$139$	−14.0213	−	17.5821i	−1.18927	−	1.49130i	−0.359544	−	0.933128i	$-0.617068\pi$
$140$	−9.31198	+	11.6768i	−0.787006	+	0.986874i
$141$	−0.0795181	−	0.348391i	−0.00669663	−	0.0293398i
$142$	4.71245	−	20.6466i	0.395460	−	1.73262i
$143$	−15.2819	+	19.1629i	−1.27794	+	1.60248i
$144$	8.69643			0.724703
$145$	−5.85680	+	1.99497i	−0.486381	+	0.165674i
$146$	29.4548			2.43769
$147$	0.403190	−	0.505584i	0.0332545	−	0.0416999i
$148$	−8.12073	+	35.5792i	−0.667520	+	2.92460i
$149$	−0.286904	−	1.25701i	−0.0235041	−	0.102978i	0.961815	−	0.273700i	$-0.0882474\pi$
$149$	−0.286904	−	1.25701i	−0.0235041	−	0.102978i	−0.985319	+	0.170721i	$0.945390\pi$
$150$	−5.93929	+	7.44764i	−0.484941	+	0.608097i
$151$	4.08507	+	5.12252i	0.332439	+	0.416865i	0.919755	−	0.392492i	$-0.128387\pi$
$151$	4.08507	+	5.12252i	0.332439	+	0.416865i	−0.587317	+	0.809357i	$0.699816\pi$
$152$	−2.91385	+	12.7664i	−0.236345	+	1.03549i
$153$	−2.17599	−	1.04790i	−0.175918	−	0.0847176i
$154$	28.0813	+	13.5232i	2.26286	+	1.08973i
$155$	0.398972	+	1.74801i	0.0320462	+	0.140404i
$156$	−23.8413	+	11.4814i	−1.90883	+	0.919244i
$157$	−24.1178			−1.92481			−0.962407	−	0.271612i	$-0.912443\pi$
$157$	−24.1178			−1.92481			−0.962407	+	0.271612i	$0.912443\pi$
$158$	18.9630	−	9.13208i	1.50861	−	0.726509i
$159$	−1.01940	−	1.27828i	−0.0808434	−	0.101374i
$160$	−6.10953	−	7.66111i	−0.483001	−	0.605664i
$161$	21.9755	−	10.5828i	1.73191	−	0.834043i
$162$	2.58860			0.203380
$163$	−14.5447	+	7.00435i	−1.13923	+	0.548623i	−0.905781	−	0.423747i	$-0.860715\pi$
$163$	−14.5447	+	7.00435i	−1.13923	+	0.548623i	−0.233446	+	0.972370i	$0.575000\pi$
$164$	−3.30625	−	14.4856i	−0.258174	−	1.13114i
$165$	−4.50727	−	2.17059i	−0.350891	−	0.168980i
$166$	1.12376	+	0.541174i	0.0872206	+	0.0420032i
$167$	1.20616	−	5.28454i	0.0933357	−	0.408930i	−0.906578	−	0.422037i	$-0.861315\pi$
$167$	1.20616	−	5.28454i	0.0933357	−	0.408930i	0.999914	+	0.0131071i	$0.00417224\pi$
$168$	12.0541	+	15.1154i	0.929993	+	1.16617i
$169$	11.6513	−	14.6102i	0.896251	−	1.12386i
$170$	1.59838	+	7.00297i	0.122590	+	0.537104i
$171$	−0.416772	+	1.82600i	−0.0318714	+	0.139638i
$172$	−4.29082	+	5.38052i	−0.327172	+	0.410261i
$173$	−11.2923			−0.858537			−0.429268	−	0.903177i	$-0.641229\pi$
$173$	−11.2923			−0.858537			−0.429268	+	0.903177i	$0.641229\pi$
$174$	1.44576	+	13.8649i	0.109603	+	1.05109i
$175$	−10.1760			−0.769231
$176$	−23.6089	+	29.6047i	−1.77959	+	2.23154i
$177$	1.07928	−	4.72866i	0.0811240	−	0.355428i
$178$	1.14985	+	5.03783i	0.0861851	+	0.377601i
$179$	−6.64270	+	8.32969i	−0.496499	+	0.622590i	−0.965436	−	0.260642i	$-0.916066\pi$
$179$	−6.64270	+	8.32969i	−0.496499	+	0.622590i	0.468937	+	0.883232i	$0.344637\pi$
$180$	−3.36749	−	4.22269i	−0.250998	−	0.314741i
$181$	2.73554	−	11.9852i	0.203331	−	0.890853i	−0.765559	−	0.643365i	$-0.777538\pi$
$181$	2.73554	−	11.9852i	0.203331	−	0.890853i	0.968891	−	0.247488i	$-0.0796051\pi$
$182$	−36.3039	−	17.4830i	−2.69102	−	1.29593i
$183$	−1.40110	−	0.674732i	−0.103572	−	0.0498777i
$184$	13.7225	+	60.1220i	1.01163	+	4.43226i
$185$	8.03626	−	3.87006i	0.590838	−	0.284533i
$186$	4.03961			0.296198
$187$	9.47462	−	4.56274i	0.692853	−	0.333660i
$188$	1.04738	+	1.31337i	0.0763877	+	0.0957872i
$189$	1.72411	+	2.16197i	0.125411	+	0.157260i
$190$	5.01882	−	2.41693i	0.364103	−	0.175343i
$191$	−1.68311			−0.121786			−0.0608929	−	0.998144i	$-0.519395\pi$
$191$	−1.68311			−0.121786			−0.0608929	+	0.998144i	$0.519395\pi$
$192$	−4.22054	+	2.03250i	−0.304591	+	0.146683i
$193$	−2.35340	−	10.3109i	−0.169402	−	0.742197i	−0.986239	−	0.165328i	$-0.947132\pi$
$193$	−2.35340	−	10.3109i	−0.169402	−	0.742197i	0.816837	−	0.576869i	$-0.195726\pi$
$194$	−10.8104	−	5.20599i	−0.776138	−	0.373769i
$195$	5.82706	+	2.80617i	0.417285	+	0.200954i
$196$	−0.676440	+	2.96368i	−0.0483171	+	0.211691i
$197$	−7.55361	−	9.47193i	−0.538172	−	0.674847i	0.436184	−	0.899858i	$-0.356330\pi$
$197$	−7.55361	−	9.47193i	−0.538172	−	0.674847i	−0.974356	+	0.225011i	$0.927758\pi$
$198$	−7.02750	+	8.81221i	−0.499423	+	0.626256i
$199$	−1.11170	−	4.87066i	−0.0788060	−	0.345272i	0.920118	−	0.391640i	$-0.128092\pi$
$199$	−1.11170	−	4.87066i	−0.0788060	−	0.345272i	−0.998924	+	0.0463686i	$0.985235\pi$
$200$	5.72505	−	25.0831i	0.404823	−	1.77364i
$201$	−6.02883	+	7.55992i	−0.425241	+	0.533235i
$202$	−4.91594			−0.345884
$203$	−10.6168	+	10.4420i	−0.745156	+	0.732887i
$204$	11.3534			0.794894
$205$	−2.26419	+	2.83921i	−0.158138	+	0.198299i
$206$	4.73557	−	20.7479i	0.329943	−	1.44558i
$207$	1.96274	+	8.59933i	0.136420	+	0.597695i
$208$	30.5219	−	38.2733i	2.11632	−	2.65378i
$209$	−5.08467	−	6.37598i	−0.351714	−	0.441036i
$210$	1.83008	−	8.01812i	0.126288	−	0.553303i
$211$	17.3083	+	8.33526i	1.19156	+	0.573823i	0.921257	−	0.388954i	$-0.127163\pi$
$211$	17.3083	+	8.33526i	1.19156	+	0.573823i	0.270298	+	0.962777i	$0.412878\pi$
$212$	6.92471	+	3.33476i	0.475591	+	0.229033i
$213$	1.82046	+	7.97596i	0.124736	+	0.546504i
$214$	−10.3967	+	5.00677i	−0.710701	+	0.342256i
$215$	1.68202			0.114713
$216$	−6.29911	+	3.03349i	−0.428600	+	0.206403i
$217$	2.69054	+	3.37383i	0.182645	+	0.229030i
$218$	28.2858	+	35.4692i	1.91575	+	2.40228i
$219$	−10.2518	+	4.93700i	−0.692752	+	0.333612i
$220$	23.5170			1.58552
$221$	−12.2489	+	5.89877i	−0.823951	+	0.396794i
$222$	−4.47180	−	19.5922i	−0.300128	−	1.31495i
$223$	19.1403	+	9.21751i	1.28173	+	0.617250i	0.945835	−	0.324649i	$-0.105246\pi$
$223$	19.1403	+	9.21751i	1.28173	+	0.617250i	0.335898	+	0.941898i	$0.390960\pi$
$224$	−21.2484	−	10.2327i	−1.41972	−	0.683701i
$225$	0.818862	−	3.58767i	0.0545908	−	0.239178i
$226$	12.8007	+	16.0515i	0.851487	+	1.06773i
$227$	12.3176	−	15.4458i	0.817549	−	1.02517i	−0.181577	−	0.983377i	$-0.558120\pi$
$227$	12.3176	−	15.4458i	0.817549	−	1.02517i	0.999126	−	0.0417977i	$-0.0133085\pi$
$228$	−1.95919	−	8.58378i	−0.129751	−	0.568474i
$229$	−4.60927	+	20.1945i	−0.304589	+	1.33449i	0.558528	+	0.829486i	$0.311366\pi$
$229$	−4.60927	+	20.1945i	−0.304589	+	1.33449i	−0.863116	+	0.505005i	$0.831491\pi$
$230$	16.3563	−	20.5102i	1.07850	−	1.35240i
$231$	−12.0404			−0.792202
$232$	−19.7659	−	32.0446i	−1.29769	−	2.10383i
$233$	20.7745			1.36098			0.680492	−	0.732756i	$-0.261766\pi$
$233$	20.7745			1.36098			0.680492	+	0.732756i	$0.261766\pi$
$234$	9.08525	−	11.3925i	0.593921	−	0.744753i
$235$	0.0913617	−	0.400282i	0.00595978	−	0.0261115i
$236$	5.07358	+	22.2288i	0.330262	+	1.44697i
$237$	−5.06944	+	6.35688i	−0.329296	+	0.412924i
$238$	10.7790	+	13.5164i	0.698697	+	0.876138i
$239$	0.506194	−	2.21778i	0.0327430	−	0.143456i	−0.955914	−	0.293646i	$-0.905131\pi$
$239$	0.506194	−	2.21778i	0.0327430	−	0.143456i	0.988657	+	0.150190i	$0.0479885\pi$
$240$	9.00221	+	4.33524i	0.581090	+	0.279838i
$241$	−10.6119	−	5.11041i	−0.683571	−	0.329190i	0.0596665	−	0.998218i	$-0.480996\pi$
$241$	−10.6119	−	5.11041i	−0.683571	−	0.329190i	−0.743237	+	0.669028i	$0.766711\pi$
$242$	−4.58444	−	20.0857i	−0.294699	−	1.29116i
$243$	−0.900969	+	0.433884i	−0.0577972	+	0.0278337i
$244$	7.31032			0.467995
$245$	0.669404	−	0.322368i	0.0427666	−	0.0205953i
$246$	5.10130	+	6.39683i	0.325247	+	0.407847i
$247$	6.57353	+	8.24295i	0.418264	+	0.524486i
$248$	−9.82997	+	4.73386i	−0.624204	+	0.300601i
$249$	−0.481835			−0.0305350
$250$	−23.2589	+	11.2009i	−1.47102	+	0.708408i
$251$	0.317569	+	1.39136i	0.0200448	+	0.0878219i	0.983961	−	0.178384i	$-0.0570870\pi$
$251$	0.317569	+	1.39136i	0.0200448	+	0.0878219i	−0.963916	+	0.266206i	$0.914230\pi$
$252$	−11.7118	−	5.64011i	−0.737775	−	0.355294i
$253$	−34.6025	−	16.6637i	−2.17544	−	1.04764i
$254$	1.93278	−	8.46808i	0.121274	−	0.531334i
$255$	−1.73011	−	2.16949i	−0.108344	−	0.135859i
$256$	−13.8001	+	17.3048i	−0.862507	+	1.08155i
$257$	6.37412	+	27.9268i	0.397607	+	1.74203i	0.636774	+	0.771051i	$0.280268\pi$
$257$	6.37412	+	27.9268i	0.397607	+	1.74203i	−0.239167	+	0.970978i	$0.576874\pi$
$258$	0.843276	−	3.69463i	0.0525001	−	0.230018i
$259$	13.3848	−	16.7840i	0.831690	−	1.04291i
$260$	−30.4031			−1.88552
$261$	−2.82714	−	4.58337i	−0.174995	−	0.283704i
$262$	−22.5032			−1.39025
$263$	11.5360	−	14.4657i	0.711340	−	0.891993i	−0.286473	−	0.958088i	$-0.592483\pi$
$263$	11.5360	−	14.4657i	0.711340	−	0.891993i	0.997813	+	0.0660957i	$0.0210543\pi$
$264$	6.77401	−	29.6789i	0.416911	−	1.82661i
$265$	−0.418006	−	1.83140i	−0.0256779	−	0.112502i
$266$	8.35908	−	10.4820i	0.512528	−	0.642690i
$267$	−1.24461	−	1.56070i	−0.0761692	−	0.0955131i
$268$	10.1147	−	44.3154i	0.617853	−	2.70699i
$269$	25.8645	+	12.4557i	1.57698	+	0.759435i	0.998419	−	0.0562017i	$-0.0178990\pi$
$269$	25.8645	+	12.4557i	1.57698	+	0.759435i	0.578564	+	0.815637i	$0.303613\pi$
$270$	2.67962	+	1.29044i	0.163077	+	0.0785336i
$271$	−0.401519	−	1.75917i	−0.0243905	−	0.106862i	0.961267	−	0.275617i	$-0.0888823\pi$
$271$	−0.401519	−	1.75917i	−0.0243905	−	0.106862i	−0.985658	+	0.168756i	$0.946025\pi$
$272$	−18.9233	+	9.11298i	−1.14739	+	0.552556i
$273$	15.5660			0.942099
$274$	−7.51875	+	3.62084i	−0.454224	+	0.218743i
$275$	9.99022	+	12.5273i	0.602433	+	0.755427i
$276$	−25.8523	−	32.4178i	−1.55613	−	1.95132i
$277$	12.7892	−	6.15895i	0.768428	−	0.370055i	−0.00823988	−	0.999966i	$-0.502623\pi$
$277$	12.7892	−	6.15895i	0.768428	−	0.370055i	0.776667	+	0.629911i	$0.216909\pi$
$278$	−58.2136			−3.49142
$279$	−1.40599	+	0.677091i	−0.0841746	+	0.0405363i
$280$	4.94281	+	21.6559i	0.295390	+	1.29419i
$281$	−16.9576	−	8.16637i	−1.01161	−	0.487165i	−0.146746	−	0.989174i	$-0.546880\pi$
$281$	−16.9576	−	8.16637i	−1.01161	−	0.487165i	−0.864862	+	0.502010i	$0.832594\pi$
$282$	−0.833432	−	0.401360i	−0.0496302	−	0.0239006i
$283$	−4.86946	+	21.3345i	−0.289460	+	1.26821i	0.595809	+	0.803126i	$0.296831\pi$
$283$	−4.86946	+	21.3345i	−0.289460	+	1.26821i	−0.885269	+	0.465079i	$0.846026\pi$
$284$	−23.9783	−	30.0678i	−1.42285	−	1.78420i
$285$	−1.34170	+	1.68244i	−0.0794754	+	0.0996590i
$286$	14.1184	+	61.8566i	0.834836	+	3.65765i
$287$	−1.94488	+	8.52108i	−0.114803	+	0.502983i
$288$	5.31753	−	6.66797i	0.313338	−	0.392914i
$289$	−11.1670			−0.656882
$290$	−5.41515	+	15.0731i	−0.317989	+	0.885124i
$291$	4.63516			0.271718
$292$	33.3501	−	41.8198i	1.95167	−	2.44732i
$293$	−0.00172808	+	0.00757121i	−0.000100955	+	0.000442315i	−0.974978	−	0.222300i	$-0.928644\pi$
$293$	−0.00172808	+	0.00757121i	−0.000100955	+	0.000442315i	0.974877	+	0.222742i	$0.0715008\pi$
$294$	−0.372492	−	1.63199i	−0.0217242	−	0.0951797i
$295$	3.47450	−	4.35689i	0.202293	−	0.253668i
$296$	33.8411	+	42.4354i	1.96697	+	2.46651i
$297$	0.968895	−	4.24501i	0.0562210	−	0.246320i
$298$	−3.00706	−	1.44812i	−0.174194	−	0.0838875i
$299$	44.7346	+	21.5431i	2.58707	+	1.24587i
$300$	3.84936	+	16.8652i	0.222243	+	0.973710i
$301$	3.64736	−	1.75648i	0.210231	−	0.101242i
$302$	16.9604			0.975961
$303$	1.71100	−	0.823975i	0.0982945	−	0.0473361i
$304$	10.1554	+	12.7345i	0.582454	+	0.730374i
$305$	−1.11400	−	1.39691i	−0.0637876	−	0.0799871i
$306$	−5.63276	+	2.71260i	−0.322004	+	0.155069i
$307$	0.214941			0.0122673			0.00613367	−	0.999981i	$-0.498048\pi$
$307$	0.214941			0.0122673			0.00613367	+	0.999981i	$0.498048\pi$
$308$	50.9953	−	24.5580i	2.90573	−	1.39932i
$309$	1.82939	+	8.01510i	0.104071	+	0.455963i
$310$	4.18164	+	2.01377i	0.237501	+	0.114375i
$311$	−25.4313	−	12.2471i	−1.44207	−	0.694467i	−0.460876	−	0.887465i	$-0.652465\pi$
$311$	−25.4313	−	12.2471i	−1.44207	−	0.694467i	−0.981199	+	0.192998i	$0.938179\pi$
$312$	−8.75753	+	38.3693i	−0.495798	+	2.17223i
$313$	−6.37841	−	7.99827i	−0.360529	−	0.452089i	0.568177	−	0.822907i	$-0.307649\pi$
$313$	−6.37841	−	7.99827i	−0.360529	−	0.452089i	−0.928706	+	0.370817i	$0.879078\pi$
$314$	−38.9254	+	48.8110i	−2.19669	+	2.75456i
$315$	0.706977	+	3.09747i	0.0398336	+	0.174523i
$316$	8.50511	−	37.2633i	0.478450	−	2.09622i
$317$	14.8259	−	18.5911i	0.832704	−	1.04418i	−0.165613	−	0.986191i	$-0.552960\pi$
$317$	14.8259	−	18.5911i	0.832704	−	1.04418i	0.998317	−	0.0579872i	$-0.0184683\pi$
$318$	−4.23233			−0.237337
$319$	23.2779	+	2.81864i	1.30331	+	0.157814i
$320$	−5.38216			−0.300872
$321$	2.77938	−	3.48523i	0.155130	−	0.194527i
$322$	14.0496	−	61.5554i	0.782955	−	3.43035i
$323$	−1.00657	−	4.41008i	−0.0560072	−	0.245383i
$324$	2.93094	−	3.67529i	0.162830	−	0.204183i
$325$	−12.9155	−	16.1955i	−0.716422	−	0.898365i
$326$	−9.29888	+	40.7411i	−0.515017	+	2.25644i
$327$	−15.7900	−	7.60407i	−0.873190	−	0.420506i
$328$	−19.9097	−	9.58801i	−1.09933	−	0.529409i
$329$	−0.219888	−	0.963393i	−0.0121228	−	0.0531136i
$330$	−11.6675	+	5.61879i	−0.642277	+	0.309304i
$331$	−7.07856			−0.389073			−0.194536	−	0.980895i	$-0.562320\pi$
$331$	−7.07856			−0.389073			−0.194536	+	0.980895i	$0.562320\pi$
$332$	2.04073	−	0.982764i	0.112000	−	0.0539362i
$333$	4.84034	+	6.06959i	0.265249	+	0.332611i
$334$	−8.74843	−	10.9702i	−0.478693	−	0.600261i
$335$	−10.0095	+	4.82032i	−0.546877	+	0.263362i
$336$	24.0479			1.31192
$337$	6.32843	−	3.04761i	0.344731	−	0.166014i	−0.253504	−	0.967334i	$-0.581583\pi$
$337$	6.32843	−	3.04761i	0.344731	−	0.166014i	0.598235	+	0.801320i	$0.295869\pi$
$338$	−10.7642	−	47.1609i	−0.585493	−	2.56521i
$339$	−7.14574	−	3.44121i	−0.388103	−	0.186901i
$340$	11.7526	+	5.65973i	0.637372	+	0.306942i
$341$	1.51199	−	6.62448i	0.0818791	−	0.358736i
$342$	3.02289	+	3.79059i	0.163459	+	0.204971i
$343$	−10.9539	+	13.7357i	−0.591453	+	0.741658i
$344$	2.27758	+	9.97872i	0.122799	+	0.538016i
$345$	−2.25508	+	9.88013i	−0.121409	+	0.531929i
$346$	−18.2254	+	22.8539i	−0.979803	+	1.22863i
$347$	10.0795			0.541094			0.270547	−	0.962707i	$-0.412795\pi$
$347$	10.0795			0.541094			0.270547	+	0.962707i	$0.412795\pi$
$348$	21.3223	+	13.6458i	1.14299	+	0.731492i
$349$	−1.64246			−0.0879187			−0.0439593	−	0.999033i	$-0.513997\pi$
$349$	−1.64246			−0.0879187			−0.0439593	+	0.999033i	$0.513997\pi$
$350$	−16.4237	+	20.5947i	−0.877883	+	1.10083i
$351$	−1.25260	+	5.48800i	−0.0668589	+	0.292928i
$352$	8.26337	+	36.2042i	0.440439	+	1.92969i
$353$	15.0406	−	18.8603i	0.800530	−	1.00383i	−0.199185	−	0.979962i	$-0.563830\pi$
$353$	15.0406	−	18.8603i	0.800530	−	1.00383i	0.999715	−	0.0238707i	$-0.00759901\pi$
$354$	−7.82817	−	9.81621i	−0.416062	−	0.521726i
$355$	−2.09161	+	9.16392i	−0.111011	+	0.486370i
$356$	8.45461	+	4.07153i	0.448093	+	0.215790i
$357$	−6.01717	−	2.89771i	−0.318462	−	0.153363i
$358$	6.13694	+	26.8877i	0.324347	+	1.42106i
$359$	11.6187	−	5.59526i	0.613210	−	0.295307i	−0.101382	−	0.994848i	$-0.532326\pi$
$359$	11.6187	−	5.59526i	0.613210	−	0.295307i	0.714592	+	0.699541i	$0.246612\pi$
$360$	−8.03281			−0.423366
$361$	13.9578	−	6.72174i	0.734623	−	0.353776i
$362$	−19.8412	−	24.8801i	−1.04283	−	1.30767i
$363$	4.96226	+	6.22247i	0.260451	+	0.326595i
$364$	−65.9274	+	31.7489i	−3.45553	+	1.66410i
$365$	−13.0734			−0.684293
$366$	−3.62688	+	1.74661i	−0.189580	+	0.0912970i
$367$	7.06325	+	30.9461i	0.368699	+	1.61537i	0.730358	+	0.683064i	$0.239353\pi$
$367$	7.06325	+	30.9461i	0.368699	+	1.61537i	−0.361659	+	0.932310i	$0.617790\pi$
$368$	69.1103	+	33.2818i	3.60262	+	1.73493i
$369$	−2.84771	−	1.37139i	−0.148246	−	0.0713915i
$370$	5.13784	−	22.5104i	0.267104	−	1.17026i
$371$	−2.81890	−	3.53478i	−0.146350	−	0.183517i
$372$	4.57384	−	5.73541i	0.237142	−	0.297367i
$373$	−1.05811	−	4.63589i	−0.0547869	−	0.240037i	0.940119	−	0.340847i	$-0.110714\pi$
$373$	−1.05811	−	4.63589i	−0.0547869	−	0.240037i	−0.994906	+	0.100810i	$0.967857\pi$
$374$	6.05743	−	26.5393i	0.313222	−	1.37232i
$375$	6.21790	−	7.79700i	0.321091	−	0.402636i
$376$	2.49841			0.128846
$377$	−30.0940	−	3.64398i	−1.54992	−	0.187675i
$378$	7.15816			0.368176
$379$	1.32155	−	1.65717i	0.0678834	−	0.0851231i	−0.746730	−	0.665127i	$-0.768377\pi$
$379$	1.32155	−	1.65717i	0.0678834	−	0.0851231i	0.814614	+	0.580004i	$0.196949\pi$
$380$	2.25100	−	9.86226i	0.115474	−	0.505924i
$381$	0.746651	+	3.27129i	0.0382521	+	0.167593i
$382$	−2.71649	+	3.40637i	−0.138988	+	0.174285i
$383$	9.12830	+	11.4465i	0.466434	+	0.584890i	0.958294	−	0.285784i	$-0.0922541\pi$
$383$	9.12830	+	11.4465i	0.466434	+	0.584890i	−0.491860	+	0.870675i	$0.663683\pi$
$384$	1.09728	−	4.80751i	0.0559954	−	0.245332i
$385$	−12.4638	−	6.00224i	−0.635213	−	0.305903i
$386$	−24.6661	−	11.8786i	−1.25547	−	0.604604i
$387$	0.325765	+	1.42727i	0.0165596	+	0.0725521i
$388$	−19.6315	+	9.45401i	−0.996636	+	0.479955i
$389$	1.93401			0.0980583			0.0490292	−	0.998797i	$-0.484387\pi$
$389$	1.93401			0.0980583			0.0490292	+	0.998797i	$0.484387\pi$
$390$	15.0840	−	7.26405i	0.763806	−	0.367830i
$391$	−13.2821	−	16.6553i	−0.671706	−	0.842293i
$392$	2.81889	+	3.53478i	0.142376	+	0.178533i
$393$	7.83230	−	3.77184i	0.395087	−	0.190264i
$394$	−31.3611			−1.57995
$395$	−8.41664	+	4.05324i	−0.423487	+	0.203941i
$396$	4.55465	+	19.9552i	0.228880	+	1.00279i
$397$	27.0463	+	13.0248i	1.35742	+	0.653697i	0.964059	−	0.265689i	$-0.0855995\pi$
$397$	27.0463	+	13.0248i	1.35742	+	0.653697i	0.393357	+	0.919386i	$0.371314\pi$
$398$	−11.6517	−	5.61118i	−0.584048	−	0.281263i
$399$	−1.15248	+	5.04936i	−0.0576963	+	0.252784i
$400$	−19.9531	−	25.0204i	−0.997654	−	1.25102i
$401$	9.79407	−	12.2814i	0.489093	−	0.613303i	−0.474638	−	0.880181i	$-0.657421\pi$
$401$	9.79407	−	12.2814i	0.489093	−	0.613303i	0.963730	+	0.266879i	$0.0859923\pi$
$402$	5.56981	+	24.4029i	0.277797	+	1.21711i
$403$	−1.95473	+	8.56422i	−0.0973719	+	0.426614i
$404$	−5.56607	+	6.97963i	−0.276922	+	0.347249i
$405$	−1.14894			−0.0570914
$406$	3.99791	+	38.3400i	0.198413	+	1.90278i
$407$	−33.8027			−1.67554
$408$	10.5280	−	13.2017i	0.521212	−	0.653579i
$409$	1.08416	−	4.75001i	0.0536081	−	0.234873i	−0.941025	−	0.338337i	$-0.890136\pi$
$409$	1.08416	−	4.75001i	0.0536081	−	0.234873i	0.994633	+	0.103464i	$0.0329928\pi$
$410$	2.09180	+	9.16479i	0.103307	+	0.452617i
$411$	2.01002	−	2.52048i	0.0991468	−	0.124326i
$412$	−24.0959	−	30.2153i	−1.18712	−	1.48860i
$413$	2.98450	−	13.0760i	0.146858	−	0.643426i
$414$	20.5716	+	9.90675i	1.01104	+	0.486890i
$415$	−0.498776	−	0.240198i	−0.0244840	−	0.0117909i
$416$	−10.6830	−	46.8053i	−0.523777	−	2.29482i
$417$	20.2614	−	9.75736i	0.992203	−	0.477820i
$418$	−21.1105			−1.03255
$419$	−17.1303	+	8.24949i	−0.836867	+	0.403014i	−0.802686	−	0.596402i	$-0.796597\pi$
$419$	−17.1303	+	8.24949i	−0.836867	+	0.403014i	−0.0341812	+	0.999416i	$0.510882\pi$
$420$	−9.31198	−	11.6768i	−0.454378	−	0.569772i
$421$	7.80429	+	9.78627i	0.380358	+	0.476954i	0.934752	−	0.355300i	$-0.115621\pi$
$421$	7.80429	+	9.78627i	0.380358	+	0.476954i	−0.554394	+	0.832254i	$0.687050\pi$
$422$	44.8044	−	21.5767i	2.18105	−	1.05034i
$423$	0.357351			0.0173750
$424$	10.2989	−	4.95971i	0.500161	−	0.240865i
$425$	1.97768	+	8.66480i	0.0959317	+	0.420304i
$426$	19.0803	+	9.18860i	0.924445	+	0.445189i
$427$	−3.87440	−	1.86581i	−0.187495	−	0.0902929i
$428$	−4.66303	+	20.4300i	−0.225396	+	0.987524i
$429$	−15.2819	−	19.1629i	−0.737816	−	0.925193i
$430$	2.71473	−	3.40416i	0.130916	−	0.164163i
$431$	−7.87657	−	34.5095i	−0.379401	−	1.66227i	−0.699311	−	0.714817i	$-0.746510\pi$
$431$	−7.87657	−	34.5095i	−0.379401	−	1.66227i	0.319910	−	0.947448i	$-0.396347\pi$
$432$	−1.93514	+	8.47839i	−0.0931044	+	0.407917i
$433$	3.65050	−	4.57758i	0.175432	−	0.219984i	−0.686340	−	0.727281i	$-0.740784\pi$
$433$	3.65050	−	4.57758i	0.175432	−	0.219984i	0.861772	+	0.507297i	$0.169355\pi$
$434$	11.1706			0.536204
$435$	−0.641696	−	6.15388i	−0.0307670	−	0.295056i
$436$	82.3856			3.94555
$437$	−10.3003	+	12.9161i	−0.492729	+	0.617863i
$438$	−6.55430	+	28.7163i	−0.313177	+	1.37212i
$439$	−5.52514	−	24.2072i	−0.263700	−	1.15535i	−0.917202	−	0.398422i	$-0.869558\pi$
$439$	−5.52514	−	24.2072i	−0.263700	−	1.15535i	0.653502	−	0.756925i	$-0.273299\pi$
$440$	21.8073	−	27.3455i	1.03962	−	1.30365i
$441$	0.403190	+	0.505584i	0.0191995	+	0.0240754i
$442$	−7.83113	+	34.3104i	−0.372489	+	1.63198i
$443$	−21.3969	−	10.3042i	−1.01660	−	0.489568i	−0.150060	−	0.988677i	$-0.547947\pi$
$443$	−21.3969	−	10.3042i	−1.01660	−	0.489568i	−0.866539	+	0.499109i	$0.833661\pi$
$444$	−32.8802	−	15.8343i	−1.56042	−	0.751460i
$445$	−0.510358	−	2.23602i	−0.0241933	−	0.105998i
$446$	49.5468	−	23.8605i	2.34611	−	1.12983i
$447$	1.28934			0.0609835
$448$	−11.6709	+	5.62040i	−0.551398	+	0.265539i
$449$	4.02060	+	5.04167i	0.189744	+	0.237931i	0.867599	−	0.497264i	$-0.165662\pi$
$449$	4.02060	+	5.04167i	0.189744	+	0.237931i	−0.677856	+	0.735195i	$0.737091\pi$
$450$	−5.93929	−	7.44764i	−0.279981	−	0.351085i
$451$	12.3994	−	5.97125i	0.583866	−	0.281175i
$452$	37.2834			1.75366
$453$	−5.90310	+	2.84278i	−0.277352	+	0.133566i
$454$	−11.3798	−	49.8581i	−0.534080	−	2.33996i
$455$	16.1134	+	7.75978i	0.755406	+	0.363784i
$456$	−11.7980	−	5.68159i	−0.552490	−	0.266065i
$457$	0.584270	−	2.55985i	0.0273310	−	0.119745i	−0.959422	−	0.281973i	$-0.909011\pi$
$457$	0.584270	−	2.55985i	0.0273310	−	0.119745i	0.986753	+	0.162228i	$0.0518682\pi$
$458$	33.4315	+	41.9218i	1.56215	+	1.95888i
$459$	1.50583	−	1.88825i	0.0702861	−	0.0881359i
$460$	−10.6008	−	46.4452i	−0.494266	−	2.16552i
$461$	1.59279	−	6.97847i	0.0741837	−	0.325020i	−0.924196	−	0.381918i	$-0.875264\pi$
$461$	1.59279	−	6.97847i	0.0741837	−	0.325020i	0.998380	+	0.0568978i	$0.0181209\pi$
$462$	−19.4329	+	24.3680i	−0.904099	+	1.13370i
$463$	−18.2411			−0.847737			−0.423868	−	0.905724i	$-0.639328\pi$
$463$	−18.2411			−0.847737			−0.423868	+	0.905724i	$0.639328\pi$
$464$	−46.4921	−	5.62957i	−2.15834	−	0.261346i
$465$	−1.79296			−0.0831467
$466$	33.5294	−	42.0445i	1.55322	−	1.94768i
$467$	−7.89230	+	34.5784i	−0.365212	+	1.60010i	0.374534	+	0.927213i	$0.377803\pi$
$467$	−7.89230	+	34.5784i	−0.365212	+	1.60010i	−0.739746	+	0.672886i	$0.765054\pi$
$468$	−5.88831	−	25.7984i	−0.272187	−	1.19253i
$469$	−16.6713	+	20.9051i	−0.769809	+	0.965310i
$470$	−0.662656	−	0.830944i	−0.0305660	−	0.0383286i
$471$	5.36673	−	23.5132i	0.247286	−	1.08343i
$472$	30.5523	+	14.7132i	1.40628	+	0.677231i
$473$	−5.74313	−	2.76575i	−0.264070	−	0.127169i
$474$	4.68346	+	20.5196i	0.215119	+	0.942496i
$475$	6.20979	−	2.99048i	0.284925	−	0.137213i
$476$	31.3950			1.43899
$477$	1.47307	−	0.709393i	0.0674472	−	0.0324809i
$478$	−3.67148	−	4.60389i	−0.167929	−	0.210577i
$479$	16.2734	+	20.4061i	0.743548	+	0.932380i	0.999410	−	0.0343330i	$-0.0109307\pi$
$479$	16.2734	+	20.4061i	0.743548	+	0.932380i	−0.255862	+	0.966713i	$0.582359\pi$
$480$	8.82853	−	4.25160i	0.402966	−	0.194058i
$481$	43.7006			1.99258
$482$	−27.4699	+	13.2288i	−1.25122	+	0.602556i
$483$	5.42749	+	23.7794i	0.246959	+	1.08200i
$484$	−33.7084	−	16.2331i	−1.53220	−	0.737868i
$485$	4.79814	+	2.31066i	0.217872	+	0.104922i
$486$	−0.576019	+	2.52370i	−0.0261287	+	0.114477i
$487$	13.8098	+	17.3170i	0.625783	+	0.784708i	0.989145	−	0.146940i	$-0.0469426\pi$
$487$	13.8098	+	17.3170i	0.625783	+	0.784708i	−0.363362	+	0.931648i	$0.618371\pi$
$488$	6.77886	−	8.50042i	0.306865	−	0.384796i
$489$	−3.59224	−	15.7386i	−0.162447	−	0.711725i
$490$	0.427971	−	1.87507i	0.0193338	−	0.0847068i
$491$	−7.32494	+	9.18518i	−0.330570	+	0.414521i	−0.919144	−	0.393922i	$-0.871118\pi$
$491$	−7.32494	+	9.18518i	−0.330570	+	0.414521i	0.588574	+	0.808443i	$0.299690\pi$
$492$	14.8581			0.669856
$493$	10.9547	+	7.01080i	0.493376	+	0.315750i
$494$	27.2920			1.22792
$495$	3.11913	−	3.91127i	0.140194	−	0.175798i
$496$	−3.01985	+	13.2308i	−0.135595	+	0.594082i
$497$	5.03405	+	22.0556i	0.225808	+	0.989330i
$498$	−0.777666	+	0.975162i	−0.0348480	+	0.0436980i
$499$	−10.2098	−	12.8027i	−0.457056	−	0.573130i	0.498893	−	0.866664i	$-0.333740\pi$
$499$	−10.2098	−	12.8027i	−0.457056	−	0.573130i	−0.955949	+	0.293534i	$0.905169\pi$
$500$	−10.4319	+	45.7052i	−0.466529	+	2.04400i
$501$	4.88365	+	2.35184i	0.218186	+	0.105073i
$502$	3.32846	+	1.60290i	0.148556	+	0.0715409i
$503$	−3.30118	−	14.4634i	−0.147192	−	0.644892i	−0.993658	−	0.112448i	$-0.964131\pi$
$503$	−3.30118	−	14.4634i	−0.147192	−	0.644892i	0.846465	−	0.532444i	$-0.178726\pi$
$504$	−17.4187	+	8.38839i	−0.775889	+	0.373648i
$505$	2.18192			0.0970942
$506$	−89.5722	+	43.1357i	−3.98197	+	1.91762i
$507$	11.6513	+	14.6102i	0.517451	+	0.648863i
$508$	−9.83454	−	12.3321i	−0.436337	−	0.547150i
$509$	−28.4466	+	13.6992i	−1.26087	+	0.607204i	−0.940405	−	0.340055i	$-0.889554\pi$
$509$	−28.4466	+	13.6992i	−1.26087	+	0.607204i	−0.320467	+	0.947260i	$0.603840\pi$
$510$	−7.18307			−0.318072
$511$	−28.3489	+	13.6521i	−1.25408	+	0.603934i
$512$	10.5548	+	46.2437i	0.466462	+	2.04370i
$513$	−1.68748	−	0.812645i	−0.0745039	−	0.0358792i
$514$	66.8074	+	32.1728i	2.94675	+	1.41908i
$515$	−2.10187	+	9.20888i	−0.0926193	+	0.405792i
$516$	−4.29082	−	5.38052i	−0.188893	−	0.236864i
$517$	−0.970130	+	1.21651i	−0.0426663	+	0.0535018i
$518$	−12.3657	−	54.1777i	−0.543318	−	2.38043i
$519$	2.51277	−	11.0092i	0.110298	−	0.483249i
$520$	−28.1928	+	35.3527i	−1.23634	+	1.55032i
$521$	−8.03875			−0.352184			−0.176092	−	0.984374i	$-0.556346\pi$
$521$	−8.03875			−0.352184			−0.176092	+	0.984374i	$0.556346\pi$
$522$	−13.8390	−	1.67571i	−0.605715	−	0.0733440i
$523$	−1.48633			−0.0649927			−0.0324963	−	0.999472i	$-0.510346\pi$
$523$	−1.48633			−0.0649927			−0.0324963	+	0.999472i	$0.510346\pi$
$524$	−25.4793	+	31.9500i	−1.11307	+	1.39574i
$525$	2.26437	−	9.92084i	0.0988250	−	0.432981i
$526$	−10.6577	−	46.6943i	−0.464697	−	2.03597i
$527$	2.34990	−	2.94668i	0.102363	−	0.128359i
$528$	−23.6089	−	29.6047i	−1.02745	−	1.28838i
$529$	−12.1943	+	53.4268i	−0.530188	+	2.32291i
$530$	−4.38114	−	2.10985i	−0.190305	−	0.0916459i
$531$	4.36993	+	2.10445i	0.189639	+	0.0913253i
$532$	−5.41767	−	23.7364i	−0.234886	−	1.02910i
$533$	−16.0302	+	7.71971i	−0.694343	+	0.334378i
$534$	−5.16739			−0.223615
$535$	4.61452	−	2.22224i	0.199503	−	0.0960757i
$536$	−42.1505	−	52.8550i	−1.82062	−	2.28299i
$537$	−6.64270	−	8.32969i	−0.286654	−	0.359453i
$538$	66.9528	−	32.2428i	2.88654	−	1.39008i
$539$	−2.81570			−0.121281
$540$	4.86616	−	2.34342i	0.209406	−	0.100845i
$541$	−8.64061	−	37.8570i	−0.371489	−	1.62760i	−0.722601	−	0.691266i	$-0.757053\pi$
$541$	−8.64061	−	37.8570i	−0.371489	−	1.62760i	0.351112	−	0.936334i	$-0.385804\pi$
$542$	−4.20834	−	2.02663i	−0.180764	−	0.0870511i
$543$	11.0760	+	5.33392i	0.475316	+	0.228900i
$544$	−4.58350	+	20.0816i	−0.196516	+	0.860993i
$545$	−12.5545	−	15.7429i	−0.537777	−	0.674351i
$546$	25.1231	−	31.5033i	1.07517	−	1.34822i
$547$	3.86062	+	16.9145i	0.165068	+	0.723210i	0.987921	+	0.154956i	$0.0495237\pi$
$547$	3.86062	+	16.9145i	0.165068	+	0.723210i	−0.822853	+	0.568254i	$0.807619\pi$
$548$	−3.37225	+	14.7748i	−0.144055	+	0.631147i
$549$	0.969589	−	1.21583i	0.0413810	−	0.0518902i
$550$	41.4774			1.76860
$551$	3.41016	−	9.49220i	0.145278	−	0.404381i
$552$	−61.6682			−2.62477
$553$	−14.0183	+	17.5784i	−0.596120	+	0.747511i
$554$	8.17654	−	35.8238i	0.347388	−	1.52201i
$555$	1.98479	+	8.69595i	0.0842498	+	0.369122i
$556$	−65.9123	+	82.6514i	−2.79530	+	3.50520i
$557$	18.9702	+	23.7879i	0.803794	+	1.00793i	0.999628	+	0.0272889i	$0.00868740\pi$
$557$	18.9702	+	23.7879i	0.803794	+	1.00793i	−0.195833	+	0.980637i	$0.562741\pi$
$558$	−0.898897	+	3.93832i	−0.0380533	+	0.166723i
$559$	7.42480	+	3.57559i	0.314036	+	0.151232i
$560$	24.8935	+	11.9881i	1.05194	+	0.506588i
$561$	2.34004	+	10.2524i	0.0987965	+	0.432856i
$562$	−43.8966	+	21.1395i	−1.85167	+	0.891715i
$563$	−12.1911			−0.513793			−0.256897	−	0.966439i	$-0.582700\pi$
$563$	−12.1911			−0.513793			−0.256897	+	0.966439i	$0.582700\pi$
$564$	−1.51350	+	0.728864i	−0.0637299	+	0.0306907i
$565$	−5.68152	−	7.12441i	−0.239024	−	0.299726i
$566$	35.3187	+	44.2883i	1.48456	+	1.86158i
$567$	−2.49141	+	1.19980i	−0.104630	+	0.0503869i
$568$	−57.1978			−2.39997
$569$	2.84513	−	1.37014i	0.119274	−	0.0574393i	−0.373295	−	0.927713i	$-0.621772\pi$
$569$	2.84513	−	1.37014i	0.119274	−	0.0574393i	0.492569	+	0.870273i	$0.336058\pi$
$570$	1.23955	+	5.43080i	0.0519188	+	0.227471i
$571$	−21.9308	−	10.5613i	−0.917776	−	0.441977i	−0.0854992	−	0.996338i	$-0.527249\pi$
$571$	−21.9308	−	10.5613i	−0.917776	−	0.441977i	−0.832276	+	0.554361i	$0.812963\pi$
$572$	103.809	+	49.9918i	4.34048	+	2.09026i
$573$	0.374528	−	1.64091i	0.0156461	−	0.0685501i
$574$	14.1064	+	17.6889i	0.588791	+	0.738321i
$575$	20.2377	−	25.3773i	0.843970	−	1.05831i
$576$	−1.04239	−	4.56700i	−0.0434328	−	0.190291i
$577$	−1.77812	+	7.79044i	−0.0740240	+	0.324320i	−0.998359	−	0.0572611i	$-0.981763\pi$
$577$	−1.77812	+	7.79044i	−0.0740240	+	0.324320i	0.924335	+	0.381581i	$0.124620\pi$
$578$	−18.0232	+	22.6003i	−0.749665	+	0.940050i
$579$	10.5761			0.439528
$580$	15.2694	+	24.7549i	0.634029	+	1.02789i
$581$	−1.33240			−0.0552772
$582$	7.48100	−	9.38088i	0.310097	−	0.388850i
$583$	−1.58413	+	6.94052i	−0.0656079	+	0.287447i
$584$	−17.7023	−	77.5589i	−0.732527	−	3.20941i
$585$	−4.03245	+	5.05654i	−0.166721	+	0.209062i
$586$	0.0125339	+	0.0157171i	0.000517772	+	0.000649266i
$587$	9.42720	−	41.3033i	0.389102	−	1.70477i	−0.278657	−	0.960391i	$-0.589889\pi$
$587$	9.42720	−	41.3033i	0.389102	−	1.70477i	0.667759	−	0.744378i	$-0.267254\pi$
$588$	−2.73885	−	1.31896i	−0.112948	−	0.0543930i
$589$	−2.63336	−	1.26816i	−0.108506	−	0.0522537i
$590$	−3.20996	−	14.0638i	−0.132152	−	0.578996i
$591$	10.9153	−	5.25652i	0.448995	−	0.216224i
$592$	67.5130			2.77477
$593$	23.7641	−	11.4442i	0.975873	−	0.469956i	0.123189	−	0.992383i	$-0.460688\pi$
$593$	23.7641	−	11.4442i	0.975873	−	0.469956i	0.852684	+	0.522427i	$0.174973\pi$
$594$	−7.02750	−	8.81221i	−0.288342	−	0.361569i
$595$	−4.78421	−	5.99920i	−0.196133	−	0.245943i
$596$	−5.46078	+	2.62977i	−0.223682	+	0.107720i
$597$	4.99592			0.204469
$598$	115.800	−	55.7664i	4.73542	−	2.28046i
$599$	−1.41472	−	6.19828i	−0.0578038	−	0.253255i	0.937768	−	0.347263i	$-0.112889\pi$
$599$	−1.41472	−	6.19828i	−0.0578038	−	0.253255i	−0.995571	+	0.0940086i	$0.970032\pi$
$600$	23.1803	+	11.1630i	0.946331	+	0.455729i
$601$	15.2278	+	7.33332i	0.621155	+	0.299133i	0.717867	−	0.696180i	$-0.245118\pi$
$601$	15.2278	+	7.33332i	0.621155	+	0.299133i	−0.0967123	+	0.995312i	$0.530833\pi$
$602$	2.33188	−	10.2166i	0.0950402	−	0.416398i
$603$	−6.02883	−	7.55992i	−0.245513	−	0.307864i
$604$	19.2034	−	24.0803i	0.781375	−	0.979813i
$605$	2.03479	+	8.91498i	0.0827259	+	0.362446i
$606$	1.09390	−	4.79269i	0.0444366	−	0.194690i
$607$	−4.62349	+	5.79767i	−0.187662	+	0.235320i	−0.866758	−	0.498729i	$-0.833800\pi$
$607$	−4.62349	+	5.79767i	−0.187662	+	0.235320i	0.679096	+	0.734049i	$0.262372\pi$
$608$	15.9738			0.647823
$609$	−7.81777	−	12.6742i	−0.316792	−	0.513585i
$610$	−4.62511			−0.187265
$611$	1.25420	−	1.57271i	0.0507394	−	0.0636252i
$612$	−2.52636	+	11.0687i	−0.102122	+	0.447426i
$613$	6.43653	+	28.2003i	0.259969	+	1.13900i	0.921284	+	0.388891i	$0.127142\pi$
$613$	6.43653	+	28.2003i	0.259969	+	1.13900i	−0.661315	+	0.750109i	$0.730001\pi$
$614$	0.346908	−	0.435009i	0.0140001	−	0.0175555i
$615$	−2.26419	−	2.83921i	−0.0913011	−	0.114488i
$616$	18.7319	−	82.0698i	0.754730	−	3.30669i
$617$	31.4553	+	15.1481i	1.26634	+	0.609839i	0.941845	−	0.336047i	$-0.109090\pi$
$617$	31.4553	+	15.1481i	1.26634	+	0.609839i	0.324499	+	0.945886i	$0.394804\pi$
$618$	19.1739	+	9.23369i	0.771289	+	0.371433i
$619$	−10.0433	−	44.0026i	−0.403674	−	1.76861i	−0.612309	−	0.790618i	$-0.709759\pi$
$619$	−10.0433	−	44.0026i	−0.403674	−	1.76861i	0.208635	−	0.977994i	$-0.433098\pi$
$620$	7.59381	−	3.65698i	0.304975	−	0.146868i
$621$	−8.82048			−0.353954
$622$	−65.8315	+	31.7028i	−2.63960	+	1.27117i
$623$	−3.44168	−	4.31574i	−0.137888	−	0.172906i
$624$	30.5219	+	38.2733i	1.22186	+	1.53216i
$625$	−6.25412	+	3.01183i	−0.250165	+	0.120473i
$626$	−26.4819			−1.05843
$627$	7.34756	−	3.53840i	0.293433	−	0.141310i
$628$	25.2283	+	110.532i	1.00672	+	4.41072i
$629$	−16.8928	−	8.13515i	−0.673561	−	0.324370i
$630$	7.40985	+	3.56840i	0.295216	+	0.142168i
$631$	−6.51100	+	28.5266i	−0.259199	+	1.13562i	0.662912	+	0.748698i	$0.269321\pi$
$631$	−6.51100	+	28.5266i	−0.259199	+	1.13562i	−0.922110	+	0.386927i	$0.873537\pi$
$632$	−35.4429	−	44.4440i	−1.40984	−	1.76789i
$633$	−11.9777	+	15.0196i	−0.476073	+	0.596976i
$634$	−13.6971	−	60.0108i	−0.543980	−	2.38333i
$635$	−0.857859	+	3.75853i	−0.0340431	+	0.149153i
$636$	−4.79205	+	6.00904i	−0.190017	+	0.238274i
$637$	3.64017			0.144229
$638$	43.2743	−	42.5619i	1.71325	−	1.68504i
$639$	−8.18108			−0.323638
$640$	3.53244	−	4.42954i	0.139632	−	0.175093i
$641$	−3.94382	+	17.2790i	−0.155772	+	0.682480i	0.835372	+	0.549685i	$0.185252\pi$
$641$	−3.94382	+	17.2790i	−0.155772	+	0.682480i	−0.991144	+	0.132795i	$0.957605\pi$
$642$	−2.56776	−	11.2501i	−0.101342	−	0.444006i
$643$	23.9696	−	30.0569i	0.945269	−	1.18533i	−0.0372759	−	0.999305i	$-0.511868\pi$
$643$	23.9696	−	30.0569i	0.945269	−	1.18533i	0.982545	−	0.186025i	$-0.0595605\pi$
$644$	−71.4884	−	89.6436i	−2.81704	−	3.53245i
$645$	−0.374285	+	1.63985i	−0.0147375	+	0.0645690i
$646$	−10.5499	−	5.08057i	−0.415081	−	0.199893i
$647$	−36.5712	−	17.6118i	−1.43776	−	0.692391i	−0.457340	−	0.889292i	$-0.651198\pi$
$647$	−36.5712	−	17.6118i	−1.43776	−	0.692391i	−0.980423	+	0.196901i	$0.936912\pi$
$648$	−1.55575	−	6.81619i	−0.0611157	−	0.267765i
$649$	−19.0275	+	9.16314i	−0.746893	+	0.359685i
$650$	−53.6225			−2.10325
$651$	−3.88794	+	1.87233i	−0.152380	+	0.0733825i
$652$	47.3153	+	59.3315i	1.85301	+	2.32360i
$653$	−16.5954	−	20.8099i	−0.649427	−	0.814356i	0.342719	−	0.939438i	$-0.388652\pi$
$653$	−16.5954	−	20.8099i	−0.649427	−	0.814356i	−0.992146	+	0.125082i	$0.960081\pi$
$654$	−40.8741	+	19.6839i	−1.59830	+	0.769703i
$655$	9.98798			0.390263
$656$	−24.7649	+	11.9262i	−0.966908	+	0.465638i
$657$	−2.53198	−	11.0933i	−0.0987821	−	0.432793i
$658$	−2.30466	−	1.10986i	−0.0898449	−	0.0432670i
$659$	20.8219	+	10.0273i	0.811105	+	0.390608i	0.792995	−	0.609228i	$-0.208521\pi$
$659$	20.8219	+	10.0273i	0.811105	+	0.390608i	0.0181105	+	0.999836i	$0.494235\pi$
$660$	−5.23303	+	22.9274i	−0.203695	+	0.892448i
$661$	14.6279	+	18.3428i	0.568958	+	0.713450i	0.980185	−	0.198082i	$-0.0634713\pi$
$661$	14.6279	+	18.3428i	0.568958	+	0.713450i	−0.411228	+	0.911533i	$0.634900\pi$
$662$	−11.4246	+	14.3260i	−0.444029	+	0.556794i
$663$	−3.02523	−	13.2544i	−0.117490	−	0.514759i
$664$	0.749614	−	3.28427i	0.0290907	−	0.127455i
$665$	−3.71015	+	4.65238i	−0.143873	+	0.180412i
$666$	20.0961			0.778708
$667$	−4.92632	−	47.2436i	−0.190748	−	1.82928i
$668$	−25.4808			−0.985882
$669$	−13.2455	+	16.6094i	−0.512102	+	0.642155i
$670$	−6.39939	+	28.0376i	−0.247230	+	1.08319i
$671$	1.50673	+	6.60141i	0.0581666	+	0.254845i
$672$	14.7044	−	18.4387i	0.567233	−	0.711287i
$673$	−16.8106	−	21.0798i	−0.648000	−	0.812567i	0.343978	−	0.938978i	$-0.388226\pi$
$673$	−16.8106	−	21.0798i	−0.648000	−	0.812567i	−0.991978	+	0.126411i	$0.959654\pi$
$674$	4.04597	−	17.7265i	0.155845	−	0.682801i
$675$	3.31550	+	1.59666i	0.127614	+	0.0614556i
$676$	−79.1465	−	38.1149i	−3.04409	−	1.46596i
$677$	−7.46144	−	32.6907i	−0.286766	−	1.25641i	−0.888934	−	0.458035i	$-0.848553\pi$
$677$	−7.46144	−	32.6907i	−0.286766	−	1.25641i	0.602168	−	0.798370i	$-0.294304\pi$
$678$	−18.4975	+	8.90792i	−0.710391	+	0.342106i
$679$	12.8174			0.491888
$680$	17.4793	−	8.41757i	0.670299	−	0.322799i
$681$	12.3176	+	15.4458i	0.472012	+	0.591885i
$682$	−10.9667	−	13.7517i	−0.419935	−	0.526582i
$683$	11.1128	−	5.35164i	0.425219	−	0.204775i	−0.209021	−	0.977911i	$-0.567028\pi$
$683$	11.1128	−	5.35164i	0.425219	−	0.204775i	0.634240	+	0.773137i	$0.281313\pi$
$684$	8.80452			0.336649
$685$	3.33717	−	1.60710i	0.127507	−	0.0614040i
$686$	10.1199	+	44.3380i	0.386378	+	1.69283i
$687$	−18.6625	−	8.98740i	−0.712020	−	0.342891i
$688$	11.4705	+	5.52392i	0.437310	+	0.210598i
$689$	2.04798	−	8.97280i	0.0780219	−	0.341836i
$690$	16.3563	+	20.5102i	0.622674	+	0.780808i
$691$	1.26022	−	1.58026i	0.0479410	−	0.0601161i	−0.757283	−	0.653087i	$-0.773474\pi$
$691$	1.26022	−	1.58026i	0.0479410	−	0.0601161i	0.805224	+	0.592971i	$0.202045\pi$
$692$	11.8122	+	51.7526i	0.449033	+	1.96734i
$693$	2.67925	−	11.7386i	0.101776	−	0.445911i
$694$	16.2679	−	20.3994i	0.617523	−	0.774349i
$695$	25.8379			0.980087
$696$	35.6394	−	12.1397i	1.35091	−	0.460154i
$697$	7.63365			0.289145
$698$	−2.65087	+	3.32409i	−0.100337	+	0.125819i
$699$	−4.62276	+	20.2536i	−0.174849	+	0.766063i
$700$	10.6445	+	46.6366i	0.402324	+	1.76270i
$701$	−21.0103	+	26.3461i	−0.793549	+	0.995079i	0.206313	+	0.978486i	$0.433853\pi$
$701$	−21.0103	+	26.3461i	−0.793549	+	0.995079i	−0.999862	+	0.0165931i	$0.994718\pi$
$702$	9.08525	+	11.3925i	0.342900	+	0.429984i
$703$	−3.23552	+	14.1758i	−0.122030	+	0.534649i
$704$	18.3770	+	8.84988i	0.692608	+	0.333542i
$705$	0.369916	+	0.178142i	0.0139318	+	0.00670922i
$706$	−13.8954	−	60.8798i	−0.522961	−	2.29124i
$707$	4.73137	−	2.27851i	0.177941	−	0.0856921i
$708$	−22.8004			−0.856893
$709$	−11.4001	+	5.48999i	−0.428139	+	0.206181i	−0.635528	−	0.772078i	$-0.719218\pi$
$709$	−11.4001	+	5.48999i	−0.428139	+	0.206181i	0.207389	+	0.978258i	$0.433503\pi$
$710$	15.1706	+	19.0234i	0.569344	+	0.713935i
$711$	−5.06944	−	6.35688i	−0.190119	−	0.238402i
$712$	12.5743	−	6.05547i	0.471243	−	0.226938i
$713$	−13.7647			−0.515490
$714$	−15.5761	+	7.50103i	−0.582919	+	0.280719i
$715$	−6.26638	−	27.4548i	−0.234349	−	1.02675i
$716$	45.1236	+	21.7304i	1.68635	+	0.812102i
$717$	2.04954	+	0.987005i	0.0765413	+	0.0368604i
$718$	7.42820	−	32.5451i	0.277218	−	1.21457i
$719$	8.31590	+	10.4278i	0.310131	+	0.388892i	0.912331	−	0.409453i	$-0.134281\pi$
$719$	8.31590	+	10.4278i	0.310131	+	0.388892i	−0.602200	+	0.798345i	$0.705709\pi$
$720$	−6.22972	+	7.81182i	−0.232168	+	0.291129i
$721$	5.05875	+	22.1638i	0.188398	+	0.825424i
$722$	8.92370	−	39.0973i	0.332106	−	1.45505i
$723$	7.34364	−	9.20864i	0.273113	−	0.342473i
$724$	−57.7898			−2.14774
$725$	−6.70018	+	18.6500i	−0.248838	+	0.692644i
$726$	20.6023			0.764622
$727$	−26.0421	+	32.6558i	−0.965849	+	1.21114i	0.0115932	+	0.999933i	$0.496310\pi$
$727$	−26.0421	+	32.6558i	−0.965849	+	1.21114i	−0.977442	+	0.211203i	$0.932262\pi$
$728$	−24.2169	+	106.101i	−0.897536	+	3.93236i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−21.1000	+	26.4586i	−0.780948	+	0.979277i
$731$	−2.20449	−	2.76435i	−0.0815361	−	0.102243i
$732$	−1.62670	+	7.12703i	−0.0601245	+	0.263423i
$733$	38.3484	+	18.4676i	1.41643	+	0.682116i	0.976420	−	0.215877i	$-0.0692611\pi$
$733$	38.3484	+	18.4676i	1.41643	+	0.682116i	0.440009	+	0.897994i	$0.354975\pi$
$734$	74.0302	+	35.6511i	2.73251	+	1.31591i
$735$	0.165329	+	0.724354i	0.00609825	+	0.0267182i
$736$	67.7770	−	32.6397i	2.49829	−	1.20311i
$737$	42.1027			1.55087
$738$	−7.37159	+	3.54997i	−0.271352	+	0.130676i
$739$	13.8667	+	17.3883i	0.510095	+	0.639639i	0.968473	−	0.249118i	$-0.0801408\pi$
$739$	13.8667	+	17.3883i	0.510095	+	0.639639i	−0.458378	+	0.888757i	$0.651569\pi$
$740$	−26.1428	−	32.7820i	−0.961028	−	1.20509i
$741$	−9.49903	+	4.57449i	−0.348956	+	0.168048i
$742$	−11.7035			−0.429648
$743$	25.2914	−	12.1797i	0.927853	−	0.446830i	0.0919847	−	0.995760i	$-0.470679\pi$
$743$	25.2914	−	12.1797i	0.927853	−	0.446830i	0.835868	+	0.548930i	$0.184965\pi$
$744$	−2.42780	−	10.6369i	−0.0890075	−	0.389968i
$745$	1.33467	+	0.642744i	0.0488986	+	0.0235483i
$746$	−11.0901	−	5.34071i	−0.406038	−	0.195537i
$747$	0.107218	−	0.469754i	0.00392291	−	0.0171874i
$748$	−30.8219	−	38.6495i	−1.12696	−	1.41316i
$749$	7.68571	−	9.63758i	0.280830	−	0.352149i
$750$	−5.74448	−	25.1682i	−0.209759	−	0.919014i
$751$	−6.35994	+	27.8647i	−0.232077	+	1.01680i	0.715836	+	0.698269i	$0.246046\pi$
$751$	−6.35994	+	27.8647i	−0.232077	+	1.01680i	−0.947913	+	0.318529i	$0.896811\pi$
$752$	1.93761	−	2.42968i	0.0706572	−	0.0886013i
$753$	−1.42714			−0.0520080
$754$	−55.9456	+	55.0245i	−2.03742	+	2.00388i
$755$	−7.52781			−0.273965
$756$	8.10482	−	10.1631i	0.294770	−	0.369629i
$757$	4.77354	−	20.9142i	0.173497	−	0.760140i	−0.811044	−	0.584985i	$-0.801100\pi$
$757$	4.77354	−	20.9142i	0.173497	−	0.760140i	0.984541	−	0.175155i	$-0.0560427\pi$
$758$	−1.22093	−	5.34924i	−0.0443461	−	0.194293i
$759$	23.9457	−	30.0269i	0.869173	−	1.08991i
$760$	−9.38047	−	11.7627i	−0.340265	−	0.426679i
$761$	4.76688	−	20.8851i	0.172799	−	0.757083i	−0.812038	−	0.583604i	$-0.801642\pi$
$761$	4.76688	−	20.8851i	0.172799	−	0.757083i	0.984838	−	0.173479i	$-0.0555009\pi$
$762$	7.82568	+	3.76865i	0.283494	+	0.136524i
$763$	−43.6635	−	21.0272i	−1.58073	−	0.761237i
$764$	1.76061	+	7.71372i	0.0636965	+	0.279072i
$765$	2.50008	−	1.20398i	0.0903906

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.61397 - 2.02385i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(-1.04604 - 4.58301i) q^{4} +(-0.716354 + 0.898279i) q^{5} +(1.61397 + 2.02385i) q^{6} +(-0.615328 + 2.69593i) q^{7} +(-6.29911 - 3.03349i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(1.61397 - 2.02385i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(-1.04604 - 4.58301i) q^{4} +(-0.716354 + 0.898279i) q^{5} +(1.61397 + 2.02385i) q^{6} +(-0.615328 + 2.69593i) q^{7} +(-6.29911 - 3.03349i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.661812 + 2.89959i) q^{10} +(3.92298 - 1.88921i) q^{11} +4.70087 q^{12} +(-5.07168 + 2.44239i) q^{13} +(4.46304 + 5.59648i) q^{14} +(-0.716354 - 0.898279i) q^{15} +(-7.83521 + 3.77324i) q^{16} +2.41516 q^{17} +(-2.33225 + 1.12315i) q^{18} +(-0.416772 - 1.82600i) q^{19} +(4.86616 + 2.34342i) q^{20} +(-2.49141 - 1.19980i) q^{21} +(2.50809 - 10.9886i) q^{22} +(-5.49948 - 6.89613i) q^{23} +(4.35912 - 5.46616i) q^{24} +(0.818862 + 3.58767i) q^{25} +(-3.24249 + 14.2063i) q^{26} +(0.623490 - 0.781831i) q^{27} +12.9991 q^{28} +(4.53581 + 2.90283i) q^{29} -2.97416 q^{30} +(0.972977 - 1.22007i) q^{31} +(-1.89780 + 8.31482i) q^{32} +(0.968895 + 4.24501i) q^{33} +(3.89799 - 4.88793i) q^{34} +(-1.98091 - 2.48398i) q^{35} +(-1.04604 + 4.58301i) q^{36} +(-6.99449 - 3.36837i) q^{37} +(-4.36821 - 2.10362i) q^{38} +(-1.25260 - 5.48800i) q^{39} +(7.23731 - 3.48530i) q^{40} +3.16072 q^{41} +(-6.44928 + 3.10581i) q^{42} +(-0.912772 - 1.14458i) q^{43} +(-12.7618 - 16.0028i) q^{44} +(1.03516 - 0.498507i) q^{45} -22.8327 q^{46} +(-0.321962 + 0.155049i) q^{47} +(-1.93514 - 8.47839i) q^{48} +(-0.582626 - 0.280578i) q^{49} +(8.58252 + 4.13313i) q^{50} +(-0.537424 + 2.35461i) q^{51} +(16.4987 + 20.6887i) q^{52} +(-1.01940 + 1.27828i) q^{53} +(-0.576019 - 2.52370i) q^{54} +(-1.11320 + 4.87727i) q^{55} +(12.0541 - 15.1154i) q^{56} +1.87296 q^{57} +(13.1955 - 4.49474i) q^{58} -4.85026 q^{59} +(-3.36749 + 4.22269i) q^{60} +(-0.346042 + 1.51611i) q^{61} +(-0.898897 - 3.93832i) q^{62} +(1.72411 - 2.16197i) q^{63} +(2.92070 + 3.66245i) q^{64} +(1.43917 - 6.30540i) q^{65} +(10.1550 + 4.89040i) q^{66} +(8.71192 + 4.19544i) q^{67} +(-2.52636 - 11.0687i) q^{68} +(7.94698 - 3.82706i) q^{69} -8.22432 q^{70} +(7.37090 - 3.54964i) q^{71} +(4.35912 + 5.46616i) q^{72} +(7.09446 + 8.89617i) q^{73} +(-18.1060 + 8.71937i) q^{74} -3.67993 q^{75} +(-7.93260 + 3.82014i) q^{76} +(2.67925 + 11.7386i) q^{77} +(-13.1286 - 6.32238i) q^{78} +(7.32556 + 3.52780i) q^{79} +(2.22336 - 9.74119i) q^{80} +(0.623490 + 0.781831i) q^{81} +(5.10130 - 6.39683i) q^{82} +(0.107218 + 0.469754i) q^{83} +(-2.89258 + 12.6732i) q^{84} +(-1.73011 + 2.16949i) q^{85} -3.78965 q^{86} +(-3.83936 + 3.77615i) q^{87} -30.4421 q^{88} +(-1.24461 + 1.56070i) q^{89} +(0.661812 - 2.89959i) q^{90} +(-3.46377 - 15.1758i) q^{91} +(-25.8523 + 32.4178i) q^{92} +(0.972977 + 1.22007i) q^{93} +(-0.205841 + 0.901847i) q^{94} +(1.93881 + 0.933683i) q^{95} +(-7.68405 - 3.70044i) q^{96} +(-1.03142 - 4.51895i) q^{97} +(-1.50819 + 0.726305i) q^{98} -4.35418 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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