LMFDB - Embedded newform 87.2.g.a.82.3

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			82.3
Root			$-0.353498 + 1.54877i$ of defining polynomial
Character	$\chi$	$=$	87.82
Dual form			87.2.g.a.52.3

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

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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	0.885685	+	0.464287i	$0.153689\pi$
$2$	1.61397	+	2.02385i	1.14125	+	1.43108i	0.255563	+	0.966792i	$0.417739\pi$
$3$	−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	0.595408	−	0.803424i	$-0.296991\pi$
$5$	−0.716354	−	0.898279i	−0.320363	−	0.401723i	−0.915771	+	0.401701i	$0.868419\pi$
$6$	1.61397	−	2.02385i	0.658900	−	0.826234i
$7$	−0.615328	−	2.69593i	−0.232572	−	1.01897i	−0.947497	−	0.319764i	$-0.896396\pi$
$7$	−0.615328	−	2.69593i	−0.232572	−	1.01897i	0.714925	−	0.699201i	$-0.246461\pi$
$8$	−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	0.918732	−	0.394881i	$-0.129214\pi$
$11$	3.92298	+	1.88921i	1.18282	+	0.569617i	0.264090	+	0.964498i	$0.414929\pi$
$12$	4.70087			1.35702
$13$	−5.07168	−	2.44239i	−1.40663	−	0.677397i	−0.432135	−	0.901809i	$-0.642240\pi$
$13$	−5.07168	−	2.44239i	−1.40663	−	0.677397i	−0.974494	+	0.224411i	$0.927954\pi$
$14$	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	−0.999969	−	0.00786845i	$-0.997495\pi$
$19$	−0.416772	+	1.82600i	−0.0956141	+	0.418913i	0.904355	+	0.426781i	$0.140353\pi$
$20$	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	−0.266210	+	0.963915i	$0.585771\pi$
$23$	−5.49948	+	6.89613i	−1.14672	+	1.43794i	−0.880510	+	0.474027i	$0.842800\pi$
$24$	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	0.861492	−	0.507771i	$-0.169530\pi$
$31$	0.972977	+	1.22007i	0.174752	+	0.219132i	−0.686740	+	0.726903i	$0.740959\pi$
$32$	−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	−0.909000	−	0.416797i	$-0.863153\pi$
$37$	−6.99449	+	3.36837i	−1.14989	+	0.553756i	−0.240887	+	0.970553i	$0.577438\pi$
$38$	−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	−0.846543	−	0.532320i	$-0.821320\pi$
$43$	−0.912772	+	1.14458i	−0.139196	+	0.174547i	0.707347	+	0.706867i	$0.249892\pi$
$44$	−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	0.410255	−	0.911971i	$-0.365440\pi$
$47$	−0.321962	−	0.155049i	−0.0469630	−	0.0226162i	−0.457218	+	0.889355i	$0.651154\pi$
$48$	−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	0.706874	−	0.707339i	$-0.250105\pi$
$53$	−1.01940	−	1.27828i	−0.140025	−	0.175586i	−0.846899	+	0.531754i	$0.821533\pi$
$54$	−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	0.947931	−	0.318474i	$-0.103171\pi$
$61$	−0.346042	−	1.51611i	−0.0443062	−	0.194118i	−0.992238	+	0.124356i	$0.960313\pi$
$62$	−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	0.182055	−	0.983288i	$-0.441725\pi$
$67$	8.71192	−	4.19544i	1.06433	−	0.512554i	0.882275	+	0.470734i	$0.156011\pi$
$68$	−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	0.816710	−	0.577049i	$-0.195796\pi$
$71$	7.37090	+	3.54964i	0.874765	+	0.421264i	0.0580551	+	0.998313i	$0.481510\pi$
$72$	4.35912	−	5.46616i	0.513727	−	0.644193i
$73$	7.09446	−	8.89617i	0.830344	−	1.04122i	−0.168117	−	0.985767i	$-0.553769\pi$
$73$	7.09446	−	8.89617i	0.830344	−	1.04122i	0.998461	−	0.0554515i	$-0.0176598\pi$
$74$	−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	0.0262567	−	0.999655i	$-0.491641\pi$
$79$	7.32556	−	3.52780i	0.824189	−	0.396909i	0.797933	+	0.602747i	$0.205927\pi$
$80$	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	−0.968703	−	0.248224i	$-0.920153\pi$
$83$	0.107218	−	0.469754i	0.0117687	−	0.0515622i	0.980471	+	0.196662i	$0.0630102\pi$
$84$	−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	0.711479	−	0.702707i	$-0.248026\pi$
$89$	−1.24461	−	1.56070i	−0.131929	−	0.165434i	−0.843408	+	0.537274i	$0.819454\pi$
$90$	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	0.895189	+	0.445687i	$0.147041\pi$
$97$	−1.03142	+	4.51895i	−0.104725	+	0.458830i	−0.999914	+	0.0131424i	$0.995817\pi$
$98$	−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	−0.837243	−	0.546831i	$-0.815834\pi$
$101$	−1.18405	+	1.48475i	−0.117817	+	0.147738i	0.719425	+	0.694570i	$0.244405\pi$
$102$	3.89799	−	4.88793i	0.385959	−	0.483977i
$103$	7.40706	+	3.56705i	0.729840	+	0.351472i	0.761621	−	0.648023i	$-0.224404\pi$
$103$	7.40706	+	3.56705i	0.729840	+	0.351472i	−0.0317815	+	0.999495i	$0.510118\pi$
$104$	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	−0.617828	−	0.786313i	$-0.711987\pi$
$107$	−4.01632	+	1.93416i	−0.388273	+	0.186982i	0.229555	+	0.973296i	$0.426273\pi$
$108$	−4.23534	+	2.03963i	−0.407545	+	0.196264i
$109$	−3.89981	−	17.0862i	−0.373534	−	1.63656i	−0.716768	−	0.697311i	$-0.754380\pi$
$109$	−3.89981	−	17.0862i	−0.373534	−	1.63656i	0.343234	−	0.939250i	$-0.388478\pi$
$110$	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	−0.987560	−	0.157240i	$-0.949740\pi$
$113$	−1.76485	−	7.73232i	−0.166023	−	0.727395i	0.821537	−	0.570155i	$-0.193117\pi$
$114$	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	0.563178	−	0.826335i	$-0.309578\pi$
$127$	3.02313	+	1.45586i	0.268259	+	0.129187i	−0.294919	+	0.955522i	$0.595293\pi$
$128$	−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	−0.960038	−	0.279869i	$-0.909709\pi$
$131$	−5.42012	+	6.79661i	−0.473558	+	0.593823i	0.486480	+	0.873692i	$0.338281\pi$
$132$	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	−0.553826	−	0.832632i	$-0.686833\pi$
$137$	−2.90456	+	1.39876i	−0.248153	+	0.119504i	0.305673	+	0.952137i	$0.401119\pi$
$138$	5.08076	+	22.2603i	0.432503	+	1.89492i
$139$	−14.0213	+	17.5821i	−1.18927	+	1.49130i	−0.359544	+	0.933128i	$0.617068\pi$
$139$	−14.0213	+	17.5821i	−1.18927	+	1.49130i	−0.829726	+	0.558170i	$0.811504\pi$
$140$	−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	−0.985319	−	0.170721i	$-0.945390\pi$
$149$	−0.286904	+	1.25701i	−0.0235041	+	0.102978i	0.961815	+	0.273700i	$0.0882474\pi$
$150$	−5.93929	−	7.44764i	−0.484941	−	0.608097i
$151$	4.08507	−	5.12252i	0.332439	−	0.416865i	−0.587317	−	0.809357i	$-0.699816\pi$
$151$	4.08507	−	5.12252i	0.332439	−	0.416865i	0.919755	+	0.392492i	$0.128387\pi$
$152$	−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	−0.233446	−	0.972370i	$-0.575000\pi$
$163$	−14.5447	−	7.00435i	−1.13923	−	0.548623i	−0.905781	+	0.423747i	$0.860715\pi$
$164$	−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	0.999914	−	0.0131071i	$-0.00417224\pi$
$167$	1.20616	+	5.28454i	0.0933357	+	0.408930i	−0.906578	+	0.422037i	$0.861315\pi$
$168$	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	0.468937	−	0.883232i	$-0.344637\pi$
$179$	−6.64270	−	8.32969i	−0.496499	−	0.622590i	−0.965436	+	0.260642i	$0.916066\pi$
$180$	−3.36749	+	4.22269i	−0.250998	+	0.314741i
$181$	2.73554	+	11.9852i	0.203331	+	0.890853i	0.968891	+	0.247488i	$0.0796051\pi$
$181$	2.73554	+	11.9852i	0.203331	+	0.890853i	−0.765559	+	0.643365i	$0.777538\pi$
$182$	−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	0.816837	+	0.576869i	$0.195726\pi$
$193$	−2.35340	+	10.3109i	−0.169402	+	0.742197i	−0.986239	+	0.165328i	$0.947132\pi$
$194$	−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	−0.974356	−	0.225011i	$-0.927758\pi$
$197$	−7.55361	+	9.47193i	−0.538172	+	0.674847i	0.436184	+	0.899858i	$0.356330\pi$
$198$	−7.02750	−	8.81221i	−0.499423	−	0.626256i
$199$	−1.11170	+	4.87066i	−0.0788060	+	0.345272i	−0.998924	−	0.0463686i	$-0.985235\pi$
$199$	−1.11170	+	4.87066i	−0.0788060	+	0.345272i	0.920118	+	0.391640i	$0.128092\pi$
$200$	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	0.270298	−	0.962777i	$-0.412878\pi$
$211$	17.3083	−	8.33526i	1.19156	−	0.573823i	0.921257	+	0.388954i	$0.127163\pi$
$212$	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	0.335898	−	0.941898i	$-0.390960\pi$
$223$	19.1403	−	9.21751i	1.28173	−	0.617250i	0.945835	+	0.324649i	$0.105246\pi$
$224$	−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	0.999126	+	0.0417977i	$0.0133085\pi$
$227$	12.3176	+	15.4458i	0.817549	+	1.02517i	−0.181577	+	0.983377i	$0.558120\pi$
$228$	−1.95919	+	8.58378i	−0.129751	+	0.568474i
$229$	−4.60927	−	20.1945i	−0.304589	−	1.33449i	−0.863116	−	0.505005i	$-0.831491\pi$
$229$	−4.60927	−	20.1945i	−0.304589	−	1.33449i	0.558528	−	0.829486i	$-0.311366\pi$
$230$	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	0.988657	−	0.150190i	$-0.0479885\pi$
$239$	0.506194	+	2.21778i	0.0327430	+	0.143456i	−0.955914	+	0.293646i	$0.905131\pi$
$240$	9.00221	−	4.33524i	0.581090	−	0.279838i
$241$	−10.6119	+	5.11041i	−0.683571	+	0.329190i	−0.743237	−	0.669028i	$-0.766711\pi$
$241$	−10.6119	+	5.11041i	−0.683571	+	0.329190i	0.0596665	+	0.998218i	$0.480996\pi$
$242$	−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	−0.963916	−	0.266206i	$-0.914230\pi$
$251$	0.317569	−	1.39136i	0.0200448	−	0.0878219i	0.983961	+	0.178384i	$0.0570870\pi$
$252$	−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	−0.239167	−	0.970978i	$-0.576874\pi$
$257$	6.37412	−	27.9268i	0.397607	−	1.74203i	0.636774	−	0.771051i	$-0.280268\pi$
$258$	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	0.997813	−	0.0660957i	$-0.0210543\pi$
$263$	11.5360	+	14.4657i	0.711340	+	0.891993i	−0.286473	+	0.958088i	$0.592483\pi$
$264$	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	0.578564	−	0.815637i	$-0.303613\pi$
$269$	25.8645	−	12.4557i	1.57698	−	0.759435i	0.998419	+	0.0562017i	$0.0178990\pi$
$270$	2.67962	−	1.29044i	0.163077	−	0.0785336i
$271$	−0.401519	+	1.75917i	−0.0243905	+	0.106862i	−0.985658	−	0.168756i	$-0.946025\pi$
$271$	−0.401519	+	1.75917i	−0.0243905	+	0.106862i	0.961267	+	0.275617i	$0.0888823\pi$
$272$	−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	0.776667	−	0.629911i	$-0.216909\pi$
$277$	12.7892	+	6.15895i	0.768428	+	0.370055i	−0.00823988	+	0.999966i	$0.502623\pi$
$278$	−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	−0.864862	−	0.502010i	$-0.832594\pi$
$281$	−16.9576	+	8.16637i	−1.01161	+	0.487165i	−0.146746	+	0.989174i	$0.546880\pi$
$282$	−0.833432	+	0.401360i	−0.0496302	+	0.0239006i
$283$	−4.86946	−	21.3345i	−0.289460	−	1.26821i	−0.885269	−	0.465079i	$-0.846026\pi$
$283$	−4.86946	−	21.3345i	−0.289460	−	1.26821i	0.595809	−	0.803126i	$-0.296831\pi$
$284$	−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	0.974877	−	0.222742i	$-0.0715008\pi$
$293$	−0.00172808	−	0.00757121i	−0.000100955	−	0.000442315i	−0.974978	+	0.222300i	$0.928644\pi$
$294$	−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	−0.981199	−	0.192998i	$-0.938179\pi$
$311$	−25.4313	+	12.2471i	−1.44207	+	0.694467i	−0.460876	+	0.887465i	$0.652465\pi$
$312$	−8.75753	−	38.3693i	−0.495798	−	2.17223i
$313$	−6.37841	+	7.99827i	−0.360529	+	0.452089i	−0.928706	−	0.370817i	$-0.879078\pi$
$313$	−6.37841	+	7.99827i	−0.360529	+	0.452089i	0.568177	+	0.822907i	$0.307649\pi$
$314$	−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	0.998317	+	0.0579872i	$0.0184683\pi$
$317$	14.8259	+	18.5911i	0.832704	+	1.04418i	−0.165613	+	0.986191i	$0.552960\pi$
$318$	−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	0.598235	−	0.801320i	$-0.295869\pi$
$337$	6.32843	+	3.04761i	0.344731	+	0.166014i	−0.253504	+	0.967334i	$0.581583\pi$
$338$	−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	0.999715	+	0.0238707i	$0.00759901\pi$
$353$	15.0406	+	18.8603i	0.800530	+	1.00383i	−0.199185	+	0.979962i	$0.563830\pi$
$354$	−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	0.714592	−	0.699541i	$-0.246612\pi$
$359$	11.6187	+	5.59526i	0.613210	+	0.295307i	−0.101382	+	0.994848i	$0.532326\pi$
$360$	−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	−0.361659	−	0.932310i	$-0.617790\pi$
$367$	7.06325	−	30.9461i	0.368699	−	1.61537i	0.730358	−	0.683064i	$-0.239353\pi$
$368$	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	−0.994906	−	0.100810i	$-0.967857\pi$
$373$	−1.05811	+	4.63589i	−0.0547869	+	0.240037i	0.940119	+	0.340847i	$0.110714\pi$
$374$	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	0.814614	−	0.580004i	$-0.196949\pi$
$379$	1.32155	+	1.65717i	0.0678834	+	0.0851231i	−0.746730	+	0.665127i	$0.768377\pi$
$380$	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	−0.491860	−	0.870675i	$-0.663683\pi$
$383$	9.12830	−	11.4465i	0.466434	−	0.584890i	0.958294	+	0.285784i	$0.0922541\pi$
$384$	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	0.393357	−	0.919386i	$-0.371314\pi$
$397$	27.0463	−	13.0248i	1.35742	−	0.653697i	0.964059	+	0.265689i	$0.0855995\pi$
$398$	−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	0.963730	−	0.266879i	$-0.0859923\pi$
$401$	9.79407	+	12.2814i	0.489093	+	0.613303i	−0.474638	+	0.880181i	$0.657421\pi$
$402$	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	0.994633	−	0.103464i	$-0.0329928\pi$
$409$	1.08416	+	4.75001i	0.0536081	+	0.234873i	−0.941025	+	0.338337i	$0.890136\pi$
$410$	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	−0.0341812	−	0.999416i	$-0.510882\pi$
$419$	−17.1303	−	8.24949i	−0.836867	−	0.403014i	−0.802686	+	0.596402i	$0.796597\pi$
$420$	−9.31198	+	11.6768i	−0.454378	+	0.569772i
$421$	7.80429	−	9.78627i	0.380358	−	0.476954i	−0.554394	−	0.832254i	$-0.687050\pi$
$421$	7.80429	−	9.78627i	0.380358	−	0.476954i	0.934752	+	0.355300i	$0.115621\pi$
$422$	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	0.319910	+	0.947448i	$0.396347\pi$
$431$	−7.87657	+	34.5095i	−0.379401	+	1.66227i	−0.699311	+	0.714817i	$0.746510\pi$
$432$	−1.93514	−	8.47839i	−0.0931044	−	0.407917i
$433$	3.65050	+	4.57758i	0.175432	+	0.219984i	0.861772	−	0.507297i	$-0.169355\pi$
$433$	3.65050	+	4.57758i	0.175432	+	0.219984i	−0.686340	+	0.727281i	$0.740784\pi$
$434$	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	0.653502	+	0.756925i	$0.273299\pi$
$439$	−5.52514	+	24.2072i	−0.263700	+	1.15535i	−0.917202	+	0.398422i	$0.869558\pi$
$440$	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	−0.866539	−	0.499109i	$-0.833661\pi$
$443$	−21.3969	+	10.3042i	−1.01660	+	0.489568i	−0.150060	+	0.988677i	$0.547947\pi$
$444$	−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	−0.677856	−	0.735195i	$-0.737091\pi$
$449$	4.02060	−	5.04167i	0.189744	−	0.237931i	0.867599	+	0.497264i	$0.165662\pi$
$450$	−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	0.986753	−	0.162228i	$-0.0518682\pi$
$457$	0.584270	+	2.55985i	0.0273310	+	0.119745i	−0.959422	+	0.281973i	$0.909011\pi$
$458$	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	0.998380	−	0.0568978i	$-0.0181209\pi$
$461$	1.59279	+	6.97847i	0.0741837	+	0.325020i	−0.924196	+	0.381918i	$0.875264\pi$
$462$	−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	−0.739746	−	0.672886i	$-0.765054\pi$
$467$	−7.89230	−	34.5784i	−0.365212	−	1.60010i	0.374534	−	0.927213i	$-0.377803\pi$
$468$	−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	−0.255862	−	0.966713i	$-0.582359\pi$
$479$	16.2734	−	20.4061i	0.743548	−	0.932380i	0.999410	+	0.0343330i	$0.0109307\pi$
$480$	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	−0.363362	−	0.931648i	$-0.618371\pi$
$487$	13.8098	−	17.3170i	0.625783	−	0.784708i	0.989145	+	0.146940i	$0.0469426\pi$
$488$	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	0.588574	−	0.808443i	$-0.299690\pi$
$491$	−7.32494	−	9.18518i	−0.330570	−	0.414521i	−0.919144	+	0.393922i	$0.871118\pi$
$492$	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	−0.955949	−	0.293534i	$-0.905169\pi$
$499$	−10.2098	+	12.8027i	−0.457056	+	0.573130i	0.498893	+	0.866664i	$0.333740\pi$
$500$	−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	0.846465	+	0.532444i	$0.178726\pi$
$503$	−3.30118	+	14.4634i	−0.147192	+	0.644892i	−0.993658	+	0.112448i	$0.964131\pi$
$504$	−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	−0.320467	−	0.947260i	$-0.603840\pi$
$509$	−28.4466	−	13.6992i	−1.26087	−	0.607204i	−0.940405	+	0.340055i	$0.889554\pi$
$510$	−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	0.351112	+	0.936334i	$0.385804\pi$
$541$	−8.64061	+	37.8570i	−0.371489	+	1.62760i	−0.722601	+	0.691266i	$0.757053\pi$
$542$	−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	−0.822853	−	0.568254i	$-0.807619\pi$
$547$	3.86062	−	16.9145i	0.165068	−	0.723210i	0.987921	−	0.154956i	$-0.0495237\pi$
$548$	−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	−0.195833	−	0.980637i	$-0.562741\pi$
$557$	18.9702	−	23.7879i	0.803794	−	1.00793i	0.999628	−	0.0272889i	$-0.00868740\pi$
$558$	−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	0.492569	−	0.870273i	$-0.336058\pi$
$569$	2.84513	+	1.37014i	0.119274	+	0.0574393i	−0.373295	+	0.927713i	$0.621772\pi$
$570$	1.23955	−	5.43080i	0.0519188	−	0.227471i
$571$	−21.9308	+	10.5613i	−0.917776	+	0.441977i	−0.832276	−	0.554361i	$-0.812963\pi$
$571$	−21.9308	+	10.5613i	−0.917776	+	0.441977i	−0.0854992	+	0.996338i	$0.527249\pi$
$572$	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	0.924335	−	0.381581i	$-0.124620\pi$
$577$	−1.77812	−	7.79044i	−0.0740240	−	0.324320i	−0.998359	+	0.0572611i	$0.981763\pi$
$578$	−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	0.667759	+	0.744378i	$0.267254\pi$
$587$	9.42720	+	41.3033i	0.389102	+	1.70477i	−0.278657	+	0.960391i	$0.589889\pi$
$588$	−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	0.852684	−	0.522427i	$-0.174973\pi$
$593$	23.7641	+	11.4442i	0.975873	+	0.469956i	0.123189	+	0.992383i	$0.460688\pi$
$594$	−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	−0.995571	−	0.0940086i	$-0.970032\pi$
$599$	−1.41472	+	6.19828i	−0.0578038	+	0.253255i	0.937768	+	0.347263i	$0.112889\pi$
$600$	23.1803	−	11.1630i	0.946331	−	0.455729i
$601$	15.2278	−	7.33332i	0.621155	−	0.299133i	−0.0967123	−	0.995312i	$-0.530833\pi$
$601$	15.2278	−	7.33332i	0.621155	−	0.299133i	0.717867	+	0.696180i	$0.245118\pi$
$602$	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	0.679096	−	0.734049i	$-0.262372\pi$
$607$	−4.62349	−	5.79767i	−0.187662	−	0.235320i	−0.866758	+	0.498729i	$0.833800\pi$
$608$	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	−0.661315	−	0.750109i	$-0.730001\pi$
$613$	6.43653	−	28.2003i	0.259969	−	1.13900i	0.921284	−	0.388891i	$-0.127142\pi$
$614$	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	0.324499	−	0.945886i	$-0.394804\pi$
$617$	31.4553	−	15.1481i	1.26634	−	0.609839i	0.941845	+	0.336047i	$0.109090\pi$
$618$	19.1739	−	9.23369i	0.771289	−	0.371433i
$619$	−10.0433	+	44.0026i	−0.403674	+	1.76861i	0.208635	+	0.977994i	$0.433098\pi$
$619$	−10.0433	+	44.0026i	−0.403674	+	1.76861i	−0.612309	+	0.790618i	$0.709759\pi$
$620$	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	−0.922110	−	0.386927i	$-0.873537\pi$
$631$	−6.51100	−	28.5266i	−0.259199	−	1.13562i	0.662912	−	0.748698i	$-0.269321\pi$
$632$	−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	−0.991144	−	0.132795i	$-0.957605\pi$
$641$	−3.94382	−	17.2790i	−0.155772	−	0.682480i	0.835372	−	0.549685i	$-0.185252\pi$
$642$	−2.56776	+	11.2501i	−0.101342	+	0.444006i
$643$	23.9696	+	30.0569i	0.945269	+	1.18533i	0.982545	+	0.186025i	$0.0595605\pi$
$643$	23.9696	+	30.0569i	0.945269	+	1.18533i	−0.0372759	+	0.999305i	$0.511868\pi$
$644$	−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	−0.980423	−	0.196901i	$-0.936912\pi$
$647$	−36.5712	+	17.6118i	−1.43776	+	0.692391i	−0.457340	+	0.889292i	$0.651198\pi$
$648$	−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	−0.992146	−	0.125082i	$-0.960081\pi$
$653$	−16.5954	+	20.8099i	−0.649427	+	0.814356i	0.342719	+	0.939438i	$0.388652\pi$
$654$	−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	0.0181105	−	0.999836i	$-0.494235\pi$
$659$	20.8219	−	10.0273i	0.811105	−	0.390608i	0.792995	+	0.609228i	$0.208521\pi$
$660$	−5.23303	−	22.9274i	−0.203695	−	0.892448i
$661$	14.6279	−	18.3428i	0.568958	−	0.713450i	−0.411228	−	0.911533i	$-0.634900\pi$
$661$	14.6279	−	18.3428i	0.568958	−	0.713450i	0.980185	+	0.198082i	$0.0634713\pi$
$662$	−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	−0.991978	−	0.126411i	$-0.959654\pi$
$673$	−16.8106	+	21.0798i	−0.648000	+	0.812567i	0.343978	+	0.938978i	$0.388226\pi$
$674$	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	0.602168	+	0.798370i	$0.294304\pi$
$677$	−7.46144	+	32.6907i	−0.286766	+	1.25641i	−0.888934	+	0.458035i	$0.848553\pi$
$678$	−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	0.634240	−	0.773137i	$-0.281313\pi$
$683$	11.1128	+	5.35164i	0.425219	+	0.204775i	−0.209021	+	0.977911i	$0.567028\pi$
$684$	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	0.805224	−	0.592971i	$-0.202045\pi$
$691$	1.26022	+	1.58026i	0.0479410	+	0.0601161i	−0.757283	+	0.653087i	$0.773474\pi$
$692$	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	−0.999862	−	0.0165931i	$-0.994718\pi$
$701$	−21.0103	−	26.3461i	−0.793549	−	0.995079i	0.206313	−	0.978486i	$-0.433853\pi$
$702$	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	0.207389	−	0.978258i	$-0.433503\pi$
$709$	−11.4001	−	5.48999i	−0.428139	−	0.206181i	−0.635528	+	0.772078i	$0.719218\pi$
$710$	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	−0.602200	−	0.798345i	$-0.705709\pi$
$719$	8.31590	−	10.4278i	0.310131	−	0.388892i	0.912331	+	0.409453i	$0.134281\pi$
$720$	−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	−0.977442	−	0.211203i	$-0.932262\pi$
$727$	−26.0421	−	32.6558i	−0.965849	−	1.21114i	0.0115932	−	0.999933i	$-0.496310\pi$
$728$	−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	0.440009	−	0.897994i	$-0.354975\pi$
$733$	38.3484	−	18.4676i	1.41643	−	0.682116i	0.976420	+	0.215877i	$0.0692611\pi$
$734$	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	−0.458378	−	0.888757i	$-0.651569\pi$
$739$	13.8667	−	17.3883i	0.510095	−	0.639639i	0.968473	+	0.249118i	$0.0801408\pi$
$740$	−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	0.835868	−	0.548930i	$-0.184965\pi$
$743$	25.2914	+	12.1797i	0.927853	+	0.446830i	0.0919847	+	0.995760i	$0.470679\pi$
$744$	−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	−0.947913	−	0.318529i	$-0.896811\pi$
$751$	−6.35994	−	27.8647i	−0.232077	−	1.01680i	0.715836	−	0.698269i	$-0.246046\pi$
$752$	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	0.984541	+	0.175155i	$0.0560427\pi$
$757$	4.77354	+	20.9142i	0.173497	+	0.760140i	−0.811044	+	0.584985i	$0.801100\pi$
$758$	−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	0.984838	+	0.173479i	$0.0555009\pi$
$761$	4.76688	+	20.8851i	0.172799	+	0.757083i	−0.812038	+	0.583604i	$0.801642\pi$
$762$	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	+	0.0435298i

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

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