LMFDB - Embedded newform 115.4.g.a.6.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.2
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61506 + 3.53648i) q^{2} +(0.822656 + 0.241553i) q^{3} +(-4.65942 - 5.37726i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-2.18289 + 2.51919i) q^{6} +(3.70179 - 25.7465i) q^{7} +(-3.30086 + 0.969220i) q^{8} +(-22.0954 - 14.1999i) q^{9} +O(q^{10})$	\(q+(-1.61506 + 3.53648i) q^{2} +(0.822656 + 0.241553i) q^{3} +(-4.65942 - 5.37726i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-2.18289 + 2.51919i) q^{6} +(3.70179 - 25.7465i) q^{7} +(-3.30086 + 0.969220i) q^{8} +(-22.0954 - 14.1999i) q^{9} +(2.76647 + 19.2412i) q^{10} +(-12.8654 - 28.1712i) q^{11} +(-2.53420 - 5.54913i) q^{12} +(-8.23617 - 57.2839i) q^{13} +(85.0736 + 54.6735i) q^{14} +(4.11328 - 1.20777i) q^{15} +(10.0042 - 69.5805i) q^{16} +(-20.2039 + 23.3166i) q^{17} +(85.9030 - 55.2065i) q^{18} +(68.6786 + 79.2594i) q^{19} +(-34.1346 - 10.0228i) q^{20} +(9.26447 - 20.2864i) q^{21} +120.405 q^{22} +(-94.4871 + 56.9138i) q^{23} -2.94959 q^{24} +(10.3854 - 22.7408i) q^{25} +(215.885 + 63.3896i) q^{26} +(-29.9065 - 34.5140i) q^{27} +(-155.694 + 100.058i) q^{28} +(-17.5076 + 20.2049i) q^{29} +(-2.37193 + 16.4972i) q^{30} +(177.358 - 52.0771i) q^{31} +(206.760 + 132.877i) q^{32} +(-3.77891 - 26.2829i) q^{33} +(-49.8282 - 109.109i) q^{34} +(-54.0274 - 118.304i) q^{35} +(26.5955 + 184.976i) q^{36} +(5.54591 + 3.56414i) q^{37} +(-391.219 + 114.872i) q^{38} +(7.06158 - 49.1144i) q^{39} +(-11.2643 + 12.9997i) q^{40} +(342.602 - 220.177i) q^{41} +(56.7797 + 65.5273i) q^{42} +(-449.985 - 132.127i) q^{43} +(-91.5387 + 200.442i) q^{44} -131.324 q^{45} +(-48.6725 - 426.071i) q^{46} -465.255 q^{47} +(25.0374 - 54.8242i) q^{48} +(-320.075 - 93.9826i) q^{49} +(63.6495 + 73.4554i) q^{50} +(-22.2531 + 14.3012i) q^{51} +(-269.654 + 311.198i) q^{52} +(12.5164 - 87.0534i) q^{53} +(170.359 - 50.0219i) q^{54} +(-130.268 - 83.7179i) q^{55} +(12.7350 + 88.5736i) q^{56} +(37.3535 + 81.7927i) q^{57} +(-43.1783 - 94.5474i) q^{58} +(85.5536 + 595.038i) q^{59} +(-25.6600 - 16.4907i) q^{60} +(-115.787 + 33.9981i) q^{61} +(-102.274 + 711.332i) q^{62} +(-447.390 + 516.316i) q^{63} +(-330.752 + 212.561i) q^{64} +(-189.494 - 218.687i) q^{65} +(99.0521 + 29.0843i) q^{66} +(409.645 - 896.997i) q^{67} +219.518 q^{68} +(-91.4781 + 23.9967i) q^{69} +505.636 q^{70} +(223.817 - 490.090i) q^{71} +(86.6968 + 25.4565i) q^{72} +(309.575 + 357.269i) q^{73} +(-21.5615 + 13.8567i) q^{74} +(14.0367 - 16.1992i) q^{75} +(106.195 - 738.605i) q^{76} +(-772.936 + 226.954i) q^{77} +(162.287 + 104.296i) q^{78} +(-150.897 - 1049.51i) q^{79} +(-146.010 - 319.717i) q^{80} +(278.327 + 609.450i) q^{81} +(225.330 + 1567.21i) q^{82} +(941.688 + 605.186i) q^{83} +(-152.252 + 44.7052i) q^{84} +(-21.9537 + 152.691i) q^{85} +(1194.02 - 1377.97i) q^{86} +(-19.2833 + 12.3926i) q^{87} +(69.7708 + 80.5199i) q^{88} +(857.849 + 251.887i) q^{89} +(212.097 - 464.427i) q^{90} -1505.35 q^{91} +(746.295 + 242.896i) q^{92} +158.484 q^{93} +(751.414 - 1645.37i) q^{94} +(503.135 + 147.734i) q^{95} +(137.996 + 159.255i) q^{96} +(-259.373 + 166.689i) q^{97} +(849.308 - 980.154i) q^{98} +(-115.762 + 805.141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) $ 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−1.61506	+	3.53648i	−0.571009	+	1.25034i	0.375249	+	0.926924i	$0.377557\pi$
$2$	−1.61506	+	3.53648i	−0.571009	+	1.25034i	−0.946258	+	0.323412i	$0.895170\pi$
$3$	0.822656	+	0.241553i	0.158320	+	0.0464870i	0.359932	−	0.932978i	$-0.382800\pi$
$3$	0.822656	+	0.241553i	0.158320	+	0.0464870i	−0.201612	+	0.979465i	$0.564618\pi$
$4$	−4.65942	−	5.37726i	−0.582427	−	0.672157i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	−2.18289	+	2.51919i	−0.148527	+	0.171409i
$7$	3.70179	−	25.7465i	0.199878	−	1.39018i	−0.604756	−	0.796411i	$-0.706729\pi$
$7$	3.70179	−	25.7465i	0.199878	−	1.39018i	0.804634	−	0.593772i	$-0.202362\pi$
$8$	−3.30086	+	0.969220i	−0.145879	+	0.0428339i
$9$	−22.0954	−	14.1999i	−0.818349	−	0.525921i
$10$	2.76647	+	19.2412i	0.0874835	+	0.608461i
$11$	−12.8654	−	28.1712i	−0.352641	−	0.772176i	−0.999951	−	0.00994868i	$-0.996833\pi$
$11$	−12.8654	−	28.1712i	−0.352641	−	0.772176i	0.647310	−	0.762227i	$-0.275894\pi$
$12$	−2.53420	−	5.54913i	−0.0609634	−	0.133491i
$13$	−8.23617	−	57.2839i	−0.175716	−	1.22213i	−0.866540	−	0.499107i	$-0.833661\pi$
$13$	−8.23617	−	57.2839i	−0.175716	−	1.22213i	0.690825	−	0.723022i	$-0.257248\pi$
$14$	85.0736	+	54.6735i	1.62406	+	1.04372i
$15$	4.11328	−	1.20777i	0.0708029	−	0.0207896i
$16$	10.0042	−	69.5805i	0.156315	−	1.08719i
$17$	−20.2039	+	23.3166i	−0.288246	+	0.332653i	−0.881343	−	0.472478i	$-0.843360\pi$
$17$	−20.2039	+	23.3166i	−0.288246	+	0.332653i	0.593097	+	0.805131i	$0.297905\pi$
$18$	85.9030	−	55.2065i	1.12486	−	0.722906i
$19$	68.6786	+	79.2594i	0.829261	+	0.957018i	0.999598	−	0.0283679i	$-0.00903098\pi$
$19$	68.6786	+	79.2594i	0.829261	+	0.957018i	−0.170337	+	0.985386i	$0.554486\pi$
$20$	−34.1346	−	10.0228i	−0.381636	−	0.112059i
$21$	9.26447	−	20.2864i	0.0962701	−	0.210802i
$22$	120.405			1.16684
$23$	−94.4871	+	56.9138i	−0.856606	+	0.515972i
$23$	−94.4871	+	56.9138i	−0.856606	+	0.515972i
$24$	−2.94959			−0.0250868
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	215.885	+	63.3896i	1.62841	+	0.478144i
$27$	−29.9065	−	34.5140i	−0.213167	−	0.246008i
$28$	−155.694	+	100.058i	−1.05084	+	0.675331i
$29$	−17.5076	+	20.2049i	−0.112106	+	0.129378i	−0.809029	−	0.587769i	$-0.800007\pi$
$29$	−17.5076	+	20.2049i	−0.112106	+	0.129378i	0.696923	+	0.717146i	$0.254552\pi$
$30$	−2.37193	+	16.4972i	−0.0144351	+	0.100398i
$31$	177.358	−	52.0771i	1.02756	−	0.301720i	0.275844	−	0.961202i	$-0.411043\pi$
$31$	177.358	−	52.0771i	1.02756	−	0.301720i	0.751720	+	0.659482i	$0.229224\pi$
$32$	206.760	+	132.877i	1.14220	+	0.734047i
$33$	−3.77891	−	26.2829i	−0.0199340	−	0.138644i
$34$	−49.8282	−	109.109i	−0.251337	−	0.550352i
$35$	−54.0274	−	118.304i	−0.260923	−	0.571342i
$36$	26.5955	+	184.976i	0.123127	+	0.856370i
$37$	5.54591	+	3.56414i	0.0246417	+	0.0158363i	0.552904	−	0.833245i	$-0.313520\pi$
$37$	5.54591	+	3.56414i	0.0246417	+	0.0158363i	−0.528262	+	0.849081i	$0.677156\pi$
$38$	−391.219	+	114.872i	−1.67011	+	0.490388i
$39$	7.06158	−	49.1144i	0.0289938	−	0.201656i
$40$	−11.2643	+	12.9997i	−0.0445261	+	0.0513858i
$41$	342.602	−	220.177i	1.30501	−	0.838680i	0.311264	−	0.950324i	$-0.399248\pi$
$41$	342.602	−	220.177i	1.30501	−	0.838680i	0.993748	+	0.111643i	$0.0356114\pi$
$42$	56.7797	+	65.5273i	0.208602	+	0.240740i
$43$	−449.985	−	132.127i	−1.59586	−	0.468587i	−0.641470	−	0.767148i	$-0.721675\pi$
$43$	−449.985	−	132.127i	−1.59586	−	0.468587i	−0.954391	+	0.298561i	$0.903493\pi$
$44$	−91.5387	+	200.442i	−0.313636	+	0.686766i
$45$	−131.324			−0.435038
$46$	−48.6725	−	426.071i	−0.156008	−	1.36567i
$47$	−465.255			−1.44392			−0.721962	−	0.691932i	$-0.756760\pi$
$47$	−465.255			−1.44392			−0.721962	+	0.691932i	$0.756760\pi$
$48$	25.0374	−	54.8242i	0.0752882	−	0.164858i
$49$	−320.075	−	93.9826i	−0.933164	−	0.274002i
$50$	63.6495	+	73.4554i	0.180028	+	0.207763i
$51$	−22.2531	+	14.3012i	−0.0610991	+	0.0392660i
$52$	−269.654	+	311.198i	−0.719121	+	0.829910i
$53$	12.5164	−	87.0534i	0.0324388	−	0.225617i	−0.967153	−	0.254196i	$-0.918189\pi$
$53$	12.5164	−	87.0534i	0.0324388	−	0.225617i	0.999592	+	0.0285790i	$0.00909822\pi$
$54$	170.359	−	50.0219i	0.429313	−	0.126058i
$55$	−130.268	−	83.7179i	−0.319369	−	0.205246i
$56$	12.7350	+	88.5736i	0.0303890	+	0.211360i
$57$	37.3535	+	81.7927i	0.0867998	+	0.190065i
$58$	−43.1783	−	94.5474i	−0.0977516	−	0.214046i
$59$	85.5536	+	595.038i	0.188782	+	1.31301i	0.835168	+	0.549996i	$0.185371\pi$
$59$	85.5536	+	595.038i	0.188782	+	1.31301i	−0.646386	+	0.763011i	$0.723720\pi$
$60$	−25.6600	−	16.4907i	−0.0552114	−	0.0354822i
$61$	−115.787	+	33.9981i	−0.243033	+	0.0713608i	−0.400980	−	0.916087i	$-0.631330\pi$
$61$	−115.787	+	33.9981i	−0.243033	+	0.0713608i	0.157948	+	0.987447i	$0.449512\pi$
$62$	−102.274	+	711.332i	−0.209497	+	1.45709i
$63$	−447.390	+	516.316i	−0.894697	+	1.03253i
$64$	−330.752	+	212.561i	−0.646000	+	0.415159i
$65$	−189.494	−	218.687i	−0.361597	−	0.417305i
$66$	99.0521	+	29.0843i	0.184734	+	0.0542429i
$67$	409.645	−	896.997i	0.746956	−	1.63561i	−0.0248041	−	0.999692i	$-0.507896\pi$
$67$	409.645	−	896.997i	0.746956	−	1.63561i	0.771760	−	0.635914i	$-0.219377\pi$
$68$	219.518			0.391477
$69$	−91.4781	+	23.9967i	−0.159604	+	0.0418677i
$70$	505.636			0.863358
$71$	223.817	−	490.090i	0.374115	−	0.819197i	−0.625137	−	0.780515i	$-0.714957\pi$
$71$	223.817	−	490.090i	0.374115	−	0.819197i	0.999252	−	0.0386818i	$-0.0123159\pi$
$72$	86.6968	+	25.4565i	0.141907	+	0.0416677i
$73$	309.575	+	357.269i	0.496343	+	0.572810i	0.947549	−	0.319609i	$-0.103552\pi$
$73$	309.575	+	357.269i	0.496343	+	0.572810i	−0.451207	+	0.892420i	$0.649006\pi$
$74$	−21.5615	+	13.8567i	−0.0338713	+	0.0217677i
$75$	14.0367	−	16.1992i	0.0216109	−	0.0249403i
$76$	106.195	−	738.605i	0.160282	−	1.11479i
$77$	−772.936	+	226.954i	−1.14395	+	0.335894i
$78$	162.287	+	104.296i	0.235582	+	0.151400i
$79$	−150.897	−	1049.51i	−0.214902	−	1.49467i	−0.756476	−	0.654021i	$-0.773081\pi$
$79$	−150.897	−	1049.51i	−0.214902	−	1.49467i	0.541575	−	0.840653i	$-0.317828\pi$
$80$	−146.010	−	319.717i	−0.204055	−	0.446819i
$81$	278.327	+	609.450i	0.381792	+	0.836009i
$82$	225.330	+	1567.21i	0.303458	+	2.11060i
$83$	941.688	+	605.186i	1.24535	+	0.800335i	0.986209	−	0.165505i	$-0.0529254\pi$
$83$	941.688	+	605.186i	1.24535	+	0.800335i	0.259137	+	0.965840i	$0.416562\pi$
$84$	−152.252	+	44.7052i	−0.197763	+	0.0580683i
$85$	−21.9537	+	152.691i	−0.0280142	+	0.194843i
$86$	1194.02	−	1377.97i	1.49714	−	1.72779i
$87$	−19.2833	+	12.3926i	−0.0237630	+	0.0152716i
$88$	69.7708	+	80.5199i	0.0845182	+	0.0975391i
$89$	857.849	+	251.887i	1.02171	+	0.300000i	0.749334	−	0.662192i	$-0.230374\pi$
$89$	857.849	+	251.887i	1.02171	+	0.300000i	0.272372	+	0.962192i	$0.412192\pi$
$90$	212.097	−	464.427i	0.248410	−	0.543943i
$91$	−1505.35			−1.73410
$92$	746.295	+	242.896i	0.845725	+	0.275258i
$93$	158.484			0.176710
$94$	751.414	−	1645.37i	0.824494	−	1.80539i
$95$	503.135	+	147.734i	0.543374	+	0.159549i
$96$	137.996	+	159.255i	0.146710	+	0.169312i
$97$	−259.373	+	166.689i	−0.271498	+	0.174481i	−0.669305	−	0.742988i	$-0.733408\pi$
$97$	−259.373	+	166.689i	−0.271498	+	0.174481i	0.397807	+	0.917469i	$0.369772\pi$
$98$	849.308	−	980.154i	0.875439	−	1.01031i
$99$	−115.762	+	805.141i	−0.117520	+	0.817371i
$100$	−170.673	+	50.1141i	−0.170673	+	0.0501141i
$101$	−125.970	−	80.9559i	−0.124104	−	0.0797566i	0.477116	−	0.878840i	$-0.341682\pi$
$101$	−125.970	−	80.9559i	−0.124104	−	0.0797566i	−0.601220	+	0.799084i	$0.705318\pi$
$102$	−14.6359	−	101.795i	−0.0142076	−	0.0988157i
$103$	−102.781	−	225.060i	−0.0983237	−	0.215299i	0.854078	−	0.520145i	$-0.174122\pi$
$103$	−102.781	−	225.060i	−0.0983237	−	0.215299i	−0.952402	+	0.304846i	$0.901395\pi$
$104$	82.7072	+	181.103i	0.0779818	+	0.170756i
$105$	−15.8693	−	110.374i	−0.0147494	−	0.102584i
$106$	287.648	+	184.860i	0.263574	+	0.169389i
$107$	1047.07	−	307.448i	0.946022	−	0.277777i	0.227893	−	0.973686i	$-0.426817\pi$
$107$	1047.07	−	307.448i	0.946022	−	0.277777i	0.718130	+	0.695909i	$0.244998\pi$
$108$	−46.2435	+	321.630i	−0.0412017	+	0.286564i
$109$	−1385.28	+	1598.70i	−1.21730	+	1.40484i	−0.329795	+	0.944052i	$0.606980\pi$
$109$	−1385.28	+	1598.70i	−1.21730	+	1.40484i	−0.887509	+	0.460791i	$0.847566\pi$
$110$	506.457	−	325.480i	0.438989	−	0.282121i
$111$	3.70145	+	4.27170i	0.00316510	+	0.00365272i
$112$	−1754.42	−	515.145i	−1.48016	−	0.434613i
$113$	411.572	−	901.216i	0.342632	−	0.750259i	−0.657363	−	0.753575i	$-0.728328\pi$
$113$	411.572	−	901.216i	0.342632	−	0.750259i	0.999995	+	0.00331509i	$0.00105523\pi$
$114$	−349.587			−0.287209
$115$	−243.589	+	494.813i	−0.197520	+	0.401231i
$116$	190.222			0.152256
$117$	−631.442	+	1382.66i	−0.498947	+	1.09254i
$118$	−2242.52	−	658.462i	−1.74950	−	0.513698i
$119$	525.531	+	606.495i	0.404835	+	0.467204i
$120$	−12.4068	+	7.97335i	−0.00943815	+	0.00606553i
$121$	243.521	−	281.038i	0.182961	−	0.211148i
$122$	66.7688	−	464.387i	0.0495489	−	0.344620i
$123$	335.028	−	98.3732i	0.245597	−	0.0721139i
$124$	−1106.42	−	711.052i	−0.801285	−	0.514954i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	−1103.38	−	2416.07i	−0.780135	−	1.70826i
$127$	−793.762	−	1738.10i	−0.554606	−	1.21442i	−0.954597	−	0.297899i	$-0.903714\pi$
$127$	−793.762	−	1738.10i	−0.554606	−	1.21442i	0.399991	−	0.916519i	$-0.369013\pi$
$128$	62.2846	+	433.199i	0.0430097	+	0.299139i
$129$	−338.267	−	217.391i	−0.230874	−	0.148374i
$130$	1079.43	−	316.948i	0.728246	−	0.213832i
$131$	196.218	−	1364.73i	0.130868	−	0.910204i	−0.813559	−	0.581482i	$-0.802473\pi$
$131$	196.218	−	1364.73i	0.130868	−	0.910204i	0.944427	−	0.328722i	$-0.106618\pi$
$132$	−123.722	+	142.783i	−0.0815806	+	0.0941490i
$133$	2294.89	−	1474.84i	1.49618	−	0.961537i
$134$	2510.61	+	2897.40i	1.61854	+	1.86789i
$135$	−219.093	−	64.3316i	−0.139678	−	0.0410132i
$136$	44.0915	−	96.5469i	0.0278001	−	0.0608737i
$137$	−1835.69			−1.14477			−0.572384	−	0.819986i	$-0.693981\pi$
$137$	−1835.69			−1.14477			−0.572384	+	0.819986i	$0.693981\pi$
$138$	62.8784	−	362.267i	0.0387867	−	0.223465i
$139$	588.059			0.358838			0.179419	−	0.983773i	$-0.442578\pi$
$139$	588.059			0.358838			0.179419	+	0.983773i	$0.442578\pi$
$140$	−384.412	+	841.745i	−0.232063	+	0.508146i
$141$	−382.745	−	112.384i	−0.228602	−	0.0671237i
$142$	1371.72	+	1583.05i	0.810648	+	0.935538i
$143$	−1507.79	+	969.000i	−0.881734	+	0.566656i
$144$	−1209.08	+	1395.35i	−0.699699	+	0.807496i
$145$	−19.0238	+	132.314i	−0.0108955	+	0.0757797i
$146$	−1763.46	+	517.798i	−0.999621	+	0.293515i
$147$	−240.610	−	154.631i	−0.135001	−	0.0867600i
$148$	−6.67543	−	46.4286i	−0.00370755	−	0.0257865i
$149$	347.333	+	760.553i	0.190971	+	0.418167i	0.980762	−	0.195209i	$-0.0625384\pi$
$149$	347.333	+	760.553i	0.190971	+	0.418167i	−0.789791	+	0.613376i	$0.789811\pi$
$150$	34.6182	+	75.8033i	0.0188438	+	0.0412621i
$151$	123.532	+	859.180i	0.0665752	+	0.463041i	0.995652	+	0.0931532i	$0.0296946\pi$
$151$	123.532	+	859.180i	0.0665752	+	0.463041i	−0.929077	+	0.369887i	$0.879396\pi$
$152$	−303.518	−	195.059i	−0.161964	−	0.104088i
$153$	777.507	−	228.297i	0.410835	−	0.120632i
$154$	445.716	−	3100.02i	0.233226	−	1.62212i
$155$	605.241	−	698.486i	0.313640	−	0.361960i
$156$	−297.003	+	190.872i	−0.152431	+	0.0979617i
$157$	976.976	+	1127.49i	0.496632	+	0.573143i	0.947625	−	0.319384i	$-0.103476\pi$
$157$	976.976	+	1127.49i	0.496632	+	0.573143i	−0.450994	+	0.892527i	$0.648930\pi$
$158$	3955.29	+	1161.38i	1.99156	+	0.584773i
$159$	31.3247	−	68.5916i	0.0156240	−	0.0342117i
$160$	1228.88			0.607197
$161$	1115.56	+	2643.40i	0.546078	+	1.29397i
$162$	−2604.82			−1.26330
$163$	246.846	−	540.517i	0.118616	−	0.259734i	−0.841006	−	0.541026i	$-0.818036\pi$
$163$	246.846	−	540.517i	0.118616	−	0.259734i	0.959622	+	0.281293i	$0.0907632\pi$
$164$	−2780.28	−	816.363i	−1.32380	−	0.388703i
$165$	−86.9430	−	100.338i	−0.0410212	−	0.0473410i
$166$	−3661.11	+	2352.85i	−1.71179	+	1.10010i
$167$	−905.108	+	1044.55i	−0.419397	+	0.484010i	−0.925653	−	0.378373i	$-0.876484\pi$
$167$	−905.108	+	1044.55i	−0.419397	+	0.484010i	0.506256	+	0.862383i	$0.331029\pi$
$168$	−10.9188	+	75.9418i	−0.00501430	+	0.0348752i
$169$	−1105.60	+	324.633i	−0.503231	+	0.147762i
$170$	−504.533	−	324.244i	−0.227623	−	0.146285i
$171$	−392.011	−	2726.50i	−0.175309	−	1.21930i
$172$	1386.18	+	3035.32i	0.614509	+	1.34559i
$173$	917.047	+	2008.05i	0.403016	+	0.882483i	0.996955	+	0.0779727i	$0.0248447\pi$
$173$	917.047	+	2008.05i	0.403016	+	0.882483i	−0.593939	+	0.804510i	$0.702428\pi$
$174$	−12.6827	−	88.2098i	−0.00552569	−	0.0384320i
$175$	−547.053	−	351.569i	−0.236304	−	0.151864i
$176$	−2088.87	+	613.348i	−0.894628	+	0.262687i
$177$	−73.3524	+	510.177i	−0.0311498	+	0.216651i
$178$	−2276.27	+	2626.96i	−0.958504	+	1.10617i
$179$	2058.08	−	1322.64i	0.859373	−	0.552285i	−0.0351121	−	0.999383i	$-0.511179\pi$
$179$	2058.08	−	1322.64i	0.859373	−	0.552285i	0.894485	+	0.447098i	$0.147542\pi$
$180$	611.896	+	706.165i	0.253378	+	0.292414i
$181$	774.316	+	227.360i	0.317980	+	0.0933674i	0.436828	−	0.899545i	$-0.356102\pi$
$181$	774.316	+	227.360i	0.317980	+	0.0933674i	−0.118848	+	0.992912i	$0.537920\pi$
$182$	2431.23	−	5323.65i	0.990190	−	2.16821i
$183$	−103.465			−0.0417943
$184$	256.727	−	279.443i	0.102860	−	0.111961i
$185$	32.9622			0.0130996
$186$	−255.961	+	560.477i	−0.100903	+	0.220947i
$187$	916.787	+	269.193i	0.358514	+	0.105269i
$188$	2167.82	+	2501.80i	0.840981	+	0.970544i
$189$	−999.324	+	642.227i	−0.384604	+	0.247170i
$190$	−1335.05	+	1540.73i	−0.509762	+	0.588296i
$191$	25.5544	−	177.735i	0.00968091	−	0.0673322i	−0.984408	−	0.175899i	$-0.943717\pi$
$191$	25.5544	−	177.735i	0.00968091	−	0.0673322i	0.994089	+	0.108566i	$0.0346260\pi$
$192$	−323.440	+	94.9705i	−0.121574	+	0.0356974i
$193$	1691.43	+	1087.02i	0.630838	+	0.405415i	0.816620	−	0.577176i	$-0.195845\pi$
$193$	1691.43	+	1087.02i	0.630838	+	0.405415i	−0.185782	+	0.982591i	$0.559482\pi$
$194$	−170.590	−	1186.48i	−0.0631322	−	0.439094i
$195$	−103.063	−	225.677i	−0.0378488	−	0.0828773i
$196$	985.996	+	2159.03i	0.359328	+	0.786819i
$197$	−481.374	−	3348.03i	−0.174094	−	1.21085i	−0.870123	−	0.492835i	$-0.835961\pi$
$197$	−481.374	−	3348.03i	−0.174094	−	1.21085i	0.696029	−	0.718014i	$-0.254949\pi$
$198$	−2660.41	−	1709.74i	−0.954883	−	0.613666i
$199$	−2595.69	+	762.163i	−0.924641	+	0.271499i	−0.709192	−	0.705016i	$-0.750940\pi$
$199$	−2595.69	+	762.163i	−0.924641	+	0.271499i	−0.215450	+	0.976515i	$0.569122\pi$
$200$	−12.2398	+	85.1300i	−0.00432744	+	0.0300980i
$201$	553.669	−	638.968i	0.194293	−	0.224226i
$202$	489.748	−	314.742i	0.170587	−	0.109629i
$203$	455.396	+	525.555i	0.157451	+	0.181708i
$204$	180.588	+	53.0253i	0.0619787	+	0.0181986i
$205$	845.893	−	1852.25i	0.288194	−	0.631057i
$206$	961.918			0.325340
$207$	2895.90	+	84.1707i	0.972363	+	0.0282622i
$208$	−4068.23			−1.35616
$209$	1349.26	−	2954.46i	0.446555	−	0.977819i
$210$	415.964	+	122.138i	0.136687	+	0.0401349i
$211$	1278.37	+	1475.32i	0.417093	+	0.481351i	0.924949	−	0.380091i	$-0.124107\pi$
$211$	1278.37	+	1475.32i	0.417093	+	0.481351i	−0.507856	+	0.861442i	$0.669562\pi$
$212$	−526.428	+	338.314i	−0.170543	+	0.109602i
$213$	302.507	−	349.112i	0.0973119	−	0.112304i
$214$	−603.798	+	4199.51i	−0.192873	+	1.34146i
$215$	−2249.92	+	660.637i	−0.713691	+	0.209558i
$216$	132.169	+	84.9399i	0.0416341	+	0.0267566i
$217$	−684.261	−	4759.14i	−0.214058	−	1.48881i
$218$	−3416.47	−	7481.03i	−1.06143	−	2.32422i
$219$	168.374	+	368.688i	0.0519528	+	0.113761i
$220$	156.799	+	1090.56i	0.0480517	+	0.334207i
$221$	1502.07	+	965.320i	0.457195	+	0.293821i
$222$	−21.0848	+	6.19107i	−0.00637442	+	0.00187170i
$223$	331.119	−	2302.99i	0.0994323	−	0.691567i	−0.877743	−	0.479132i	$-0.840952\pi$
$223$	331.119	−	2302.99i	0.0994323	−	0.691567i	0.977175	−	0.212435i	$-0.0681393\pi$
$224$	4186.50	−	4831.48i	1.24876	−	1.44115i
$225$	−552.386	+	354.997i	−0.163670	+	0.105184i
$226$	2522.43	+	2911.03i	0.742430	+	0.856810i
$227$	−3905.33	−	1146.71i	−1.14188	−	0.335285i	−0.344511	−	0.938782i	$-0.611955\pi$
$227$	−3905.33	−	1146.71i	−1.14188	−	0.335285i	−0.797365	+	0.603497i	$0.793774\pi$
$228$	265.775	−	581.966i	0.0771990	−	0.169042i
$229$	4434.70			1.27971			0.639854	−	0.768496i	$-0.278995\pi$
$229$	4434.70			1.27971			0.639854	+	0.768496i	$0.278995\pi$
$230$	−1356.49	−	1660.60i	−0.388887	−	0.476072i
$231$	−690.682			−0.196725
$232$	38.2072	−	83.6622i	0.0108122	−	0.0236754i
$233$	−3170.67	−	930.993i	−0.891491	−	0.261765i	−0.196260	−	0.980552i	$-0.562880\pi$
$233$	−3170.67	−	930.993i	−0.891491	−	0.261765i	−0.695231	+	0.718786i	$0.744698\pi$
$234$	−3869.95	−	4466.17i	−1.08114	−	1.24770i
$235$	−1956.99	+	1257.68i	−0.543233	+	0.349115i
$236$	2801.04	−	3232.58i	0.772595	−	0.891622i
$237$	129.377	−	899.836i	0.0354596	−	0.246627i
$238$	−2993.62	+	879.007i	−0.815327	+	0.239401i
$239$	−3100.49	−	1992.56i	−0.839139	−	0.539282i	0.0490311	−	0.998797i	$-0.484387\pi$
$239$	−3100.49	−	1992.56i	−0.839139	−	0.539282i	−0.888170	+	0.459516i	$0.848023\pi$
$240$	−42.8871	−	298.286i	−0.0115348	−	0.0802263i
$241$	1527.55	+	3344.88i	0.408292	+	0.894036i	0.996362	+	0.0852251i	$0.0271609\pi$
$241$	1527.55	+	3344.88i	0.408292	+	0.894036i	−0.588069	+	0.808811i	$0.700112\pi$
$242$	600.586	+	1315.10i	0.159534	+	0.349330i
$243$	257.234	+	1789.10i	0.0679076	+	0.472308i
$244$	722.316	+	464.204i	0.189515	+	0.121794i
$245$	−1600.38	+	469.913i	−0.417324	+	0.122537i
$246$	−193.195	+	1343.70i	−0.0500718	+	0.348257i
$247$	3974.63	−	4586.97i	1.02389	−	1.18163i
$248$	−534.961	+	343.799i	−0.136976	+	0.0880291i
$249$	628.500	+	725.328i	0.159958	+	0.184602i
$250$	466.292	+	136.916i	0.117964	+	0.0346372i
$251$	370.266	−	810.770i	0.0931116	−	0.203886i	−0.857346	−	0.514741i	$-0.827888\pi$
$251$	370.266	−	810.770i	0.0931116	−	0.203886i	0.950457	+	0.310855i	$0.100615\pi$
$252$	4860.94			1.21512
$253$	2818.94	+	1929.60i	0.700495	+	0.479498i
$254$	7428.72			1.83512
$255$	−54.9434	+	120.309i	−0.0134929	+	0.0295453i
$256$	−4650.51	−	1365.51i	−1.13538	−	0.333377i
$257$	4081.97	+	4710.85i	0.990765	+	1.14340i	0.989664	+	0.143404i	$0.0458048\pi$
$257$	4081.97	+	4710.85i	0.990765	+	1.14340i	0.00110025	+	0.999999i	$0.499650\pi$
$258$	1315.12	−	845.175i	0.317348	−	0.203947i
$259$	112.294	−	129.594i	0.0269406	−	0.0310911i
$260$	−293.007	+	2037.91i	−0.0698905	+	0.486099i
$261$	673.745	−	197.829i	0.159784	−	0.0469169i
$262$	4509.43	+	2898.03i	1.06333	+	0.683363i
$263$	492.543	+	3425.71i	0.115481	+	0.803189i	0.962433	+	0.271519i	$0.0875260\pi$
$263$	492.543	+	3425.71i	0.115481	+	0.803189i	−0.846952	+	0.531669i	$0.821565\pi$
$264$	37.9475	+	83.0935i	0.00884663	+	0.0193714i
$265$	−182.676	−	400.004i	−0.0423460	−	0.0927248i
$266$	1509.35	+	10497.8i	0.347911	+	2.41978i
$267$	644.870	+	414.433i	0.147811	+	0.0949921i
$268$	−6732.09	+	1976.72i	−1.53443	+	0.450550i
$269$	−1032.49	+	7181.13i	−0.234023	+	1.62766i	0.446394	+	0.894837i	$0.352708\pi$
$269$	−1032.49	+	7181.13i	−0.234023	+	1.62766i	−0.680416	+	0.732826i	$0.738201\pi$
$270$	581.356	−	670.921i	0.131038	−	0.151226i
$271$	5038.03	−	3237.75i	1.12929	−	0.725753i	0.163881	−	0.986480i	$-0.447599\pi$
$271$	5038.03	−	3237.75i	1.12929	−	0.725753i	0.965413	+	0.260727i	$0.0839622\pi$
$272$	1420.26	+	1639.06i	0.316602	+	0.365378i
$273$	−1238.38	−	363.623i	−0.274544	−	0.0806133i
$274$	2964.74	−	6491.87i	0.653673	−	1.43134i
$275$	−774.247			−0.169778
$276$	555.272	+	380.090i	0.121099	+	0.0828940i
$277$	4889.35			1.06055			0.530276	−	0.847825i	$-0.322088\pi$
$277$	4889.35			1.06055			0.530276	+	0.847825i	$0.322088\pi$
$278$	−949.750	+	2079.66i	−0.204900	+	0.448668i
$279$	−4658.30	−	1367.80i	−0.999587	−	0.293505i
$280$	292.999	+	338.139i	0.0625359	+	0.0721703i
$281$	2945.14	−	1892.73i	0.625240	−	0.401818i	−0.189304	−	0.981918i	$-0.560623\pi$
$281$	2945.14	−	1892.73i	0.625240	−	0.401818i	0.814545	+	0.580101i	$0.196987\pi$
$282$	1015.60	−	1172.06i	0.214461	−	0.247502i
$283$	876.922	−	6099.13i	0.184196	−	1.28111i	−0.662509	−	0.749054i	$-0.730509\pi$
$283$	876.922	−	6099.13i	0.184196	−	1.28111i	0.846706	−	0.532061i	$-0.178582\pi$
$284$	−3678.20	+	1080.02i	−0.768524	+	0.225659i
$285$	378.221	+	243.068i	0.0786101	+	0.0505197i
$286$	−991.679	−	6897.28i	−0.205032	−	1.42603i
$287$	−4400.56	−	9635.88i	−0.905076	−	1.98184i
$288$	−2681.62	−	5871.93i	−0.548667	−	1.20141i
$289$	563.729	+	3920.82i	0.114742	+	0.798050i
$290$	−437.201	−	280.972i	−0.0885286	−	0.0568939i
$291$	−253.639	+	74.4750i	−0.0510947	+	0.0150028i
$292$	478.685	−	3329.33i	0.0959347	−	0.667241i
$293$	2964.09	−	3420.74i	0.591003	−	0.682054i	−0.378930	−	0.925425i	$-0.623708\pi$
$293$	2964.09	−	3420.74i	0.591003	−	0.682054i	0.969933	+	0.243371i	$0.0782534\pi$
$294$	935.447	−	601.176i	0.185566	−	0.119256i
$295$	1968.37	+	2271.62i	0.388485	+	0.448335i
$296$	−21.7607	−	6.38953i	−0.00427303	−	0.00125467i
$297$	−587.542	+	1286.54i	−0.114790	+	0.251355i
$298$	−3250.65			−0.631896
$299$	4038.45	+	4943.84i	0.781103	+	0.956219i
$300$	−152.510			−0.0293506
$301$	−5067.57	+	11096.4i	−0.970399	+	2.12488i
$302$	−3237.99	−	950.759i	−0.616971	−	0.181159i
$303$	−84.0746	−	97.0273i	−0.0159405	−	0.0183963i
$304$	6201.97	−	3985.77i	1.17009	−	0.751972i
$305$	−395.127	+	456.001i	−0.0741800	+	0.0856083i
$306$	−448.352	+	3118.35i	−0.0837600	+	0.582564i
$307$	−2922.27	+	858.056i	−0.543267	+	0.159517i	−0.541840	−	0.840481i	$-0.682272\pi$
$307$	−2922.27	+	858.056i	−0.543267	+	0.159517i	−0.00142642	+	0.999999i	$0.500454\pi$
$308$	4821.82	+	3098.80i	0.892042	+	0.573281i
$309$	−30.1897	−	209.974i	−0.00555803	−	0.0386569i
$310$	1492.68	+	3268.52i	0.273480	+	0.598837i
$311$	−2063.61	−	4518.68i	−0.376260	−	0.823894i	−0.999135	−	0.0415732i	$-0.986763\pi$
$311$	−2063.61	−	4518.68i	−0.376260	−	0.823894i	0.622876	−	0.782321i	$-0.285964\pi$
$312$	24.2933	+	168.964i	0.00440814	+	0.0306593i
$313$	4855.53	+	3120.46i	0.876840	+	0.563511i	0.899838	−	0.436225i	$-0.143685\pi$
$313$	4855.53	+	3120.46i	0.876840	+	0.563511i	−0.0229980	+	0.999736i	$0.507321\pi$
$314$	−5565.22	+	1634.10i	−1.00020	+	0.293686i
$315$	−486.136	+	3381.15i	−0.0869545	+	0.604782i
$316$	−4940.40	+	5701.52i	−0.879491	+	1.01499i
$317$	−3507.99	+	2254.45i	−0.621541	+	0.399440i	−0.813169	−	0.582027i	$-0.802260\pi$
$317$	−3507.99	+	2254.45i	−0.621541	+	0.399440i	0.191628	+	0.981468i	$0.438623\pi$
$318$	191.982	+	221.559i	0.0338547	+	0.0390704i
$319$	794.437	+	233.268i	0.139435	+	0.0409419i
$320$	−816.634	+	1788.18i	−0.142660	+	0.312382i
$321$	935.646			0.162687
$322$	−11150.0	−	324.081i	−1.92971	−	0.0560880i
$323$	−3235.64			−0.557386
$324$	1980.33	−	4336.32i	0.339563	−	0.743539i
$325$	−1388.22	−	407.617i	−0.236937	−	0.0695709i
$326$	1512.86	+	1745.93i	0.257023	+	0.296621i
$327$	−1525.78	+	980.562i	−0.258031	+	0.165826i
$328$	−917.483	+	1058.83i	−0.154450	+	0.178244i
$329$	−1722.28	+	11978.7i	−0.288609	+	2.00732i
$330$	495.260	−	145.422i	0.0826157	−	0.0242582i
$331$	1259.78	+	809.611i	0.209196	+	0.134442i	0.641043	−	0.767505i	$-0.278502\pi$
$331$	1259.78	+	809.611i	0.209196	+	0.134442i	−0.431848	+	0.901946i	$0.642138\pi$
$332$	−1133.48	−	7883.52i	−0.187373	−	1.30321i
$333$	−71.9290	−	157.502i	−0.0118369	−	0.0259192i
$334$	−2232.23	−	4887.91i	−0.365696	−	0.800762i
$335$	−701.690	−	4880.36i	−0.114440	−	0.795948i
$336$	−1318.85	−	847.574i	−0.214135	−	0.137616i
$337$	−4231.11	+	1242.37i	−0.683927	+	0.200819i	−0.605196	−	0.796077i	$-0.706905\pi$
$337$	−4231.11	+	1242.37i	−0.683927	+	0.200819i	−0.0787314	+	0.996896i	$0.525087\pi$
$338$	637.547	−	4434.24i	0.102598	−	0.713582i
$339$	556.274	−	641.974i	0.0891229	−	0.102853i
$340$	923.351	−	593.402i	0.147282	−	0.0946521i
$341$	−3748.85	−	4326.40i	−0.595342	−	0.687061i
$342$	10275.3	+	3017.11i	1.62464	+	0.477037i
$343$	101.702	−	222.697i	0.0160099	−	0.0350569i
$344$	1613.40			0.252874
$345$	−319.913	+	348.221i	−0.0499233	+	0.0543408i
$346$	−8582.53			−1.33353
$347$	−2388.56	+	5230.22i	−0.369524	+	0.809144i	0.629948	+	0.776637i	$0.283076\pi$
$347$	−2388.56	+	5230.22i	−0.369524	+	0.809144i	−0.999472	+	0.0325064i	$0.989651\pi$
$348$	156.487	+	45.9488i	0.0241052	+	0.00707791i
$349$	−5001.84	−	5772.43i	−0.767170	−	0.885362i	0.228943	−	0.973440i	$-0.426473\pi$
$349$	−5001.84	−	5772.43i	−0.767170	−	0.885362i	−0.996114	+	0.0880781i	$0.971928\pi$
$350$	2126.84	−	1366.84i	0.324813	−	0.208744i
$351$	−1730.78	+	1997.43i	−0.263197	+	0.303746i
$352$	1083.25	−	7534.18i	0.164027	−	1.14083i
$353$	443.178	−	130.129i	0.0668215	−	0.0196206i	−0.248151	−	0.968721i	$-0.579823\pi$
$353$	443.178	−	130.129i	0.0668215	−	0.0196206i	0.314972	+	0.949101i	$0.398005\pi$
$354$	−1685.77	−	1083.38i	−0.253100	−	0.162658i
$355$	−383.381	−	2666.47i	−0.0573176	−	0.398653i
$356$	−2642.62	−	5786.52i	−0.393422	−	0.861475i
$357$	285.830	+	625.880i	0.0423746	+	0.0927874i
$358$	1353.60	+	9414.50i	0.199832	+	1.38986i
$359$	−6248.61	−	4015.74i	−0.918633	−	0.590370i	−0.00637231	−	0.999980i	$-0.502028\pi$
$359$	−6248.61	−	4015.74i	−0.918633	−	0.590370i	−0.912261	+	0.409610i	$0.865665\pi$
$360$	433.484	−	127.282i	0.0634628	−	0.0186344i
$361$	−589.155	+	4097.66i	−0.0858951	+	0.597414i
$362$	−2054.62	+	2371.16i	−0.298310	+	0.344268i
$363$	268.219	−	172.374i	0.0387820	−	0.0249237i
$364$	7014.06	+	8094.65i	1.00999	+	1.16559i
$365$	2267.93	+	665.923i	0.325229	+	0.0954959i
$366$	167.102	−	365.903i	0.0238649	−	0.0522569i
$367$	−536.685			−0.0763344			−0.0381672	−	0.999271i	$-0.512152\pi$
$367$	−536.685			−0.0763344			−0.0381672	+	0.999271i	$0.512152\pi$
$368$	3014.82	+	7143.83i	0.427061	+	1.01195i
$369$	−10696.4			−1.50904
$370$	−53.2359	+	116.570i	−0.00748000	+	0.0163789i
$371$	−2194.99	−	644.508i	−0.307165	−	0.0901918i
$372$	−738.444	−	852.210i	−0.102921	−	0.118777i
$373$	−6352.42	+	4082.46i	−0.881813	+	0.566707i	−0.901345	−	0.433103i	$-0.857419\pi$
$373$	−6352.42	+	4082.46i	−0.881813	+	0.566707i	0.0195320	+	0.999809i	$0.493782\pi$
$374$	−2432.66	+	2807.44i	−0.336337	+	0.388153i
$375$	15.2523	−	106.082i	0.00210034	−	0.0146082i
$376$	1535.74	−	450.935i	0.210638	−	0.0618489i
$377$	1301.61	+	836.493i	0.177815	+	0.114275i
$378$	−657.258	−	4571.33i	−0.0894330	−	0.622020i
$379$	−3511.73	−	7689.62i	−0.475951	−	1.04219i	−0.983557	−	0.180599i	$-0.942196\pi$
$379$	−3511.73	−	7689.62i	−0.475951	−	1.04219i	0.507605	−	0.861590i	$-0.330531\pi$
$380$	−1549.91	−	3393.84i	−0.209234	−	0.458159i
$381$	−233.149	−	1621.59i	−0.0313507	−	0.218049i
$382$	587.285	+	377.425i	0.0786600	+	0.0505517i
$383$	5030.46	−	1477.08i	0.671134	−	0.197063i	0.0716261	−	0.997432i	$-0.477181\pi$
$383$	5030.46	−	1477.08i	0.671134	−	0.197063i	0.599508	+	0.800369i	$0.295363\pi$
$384$	−53.4020	+	371.419i	−0.00709676	+	0.0493591i
$385$	−2637.67	+	3044.03i	−0.349164	+	0.402957i
$386$	−6575.97	+	4226.12i	−0.867119	+	0.557264i
$387$	8066.41	+	9309.13i	1.05953	+	1.22276i
$388$	2104.85	+	618.041i	0.275407	+	0.0808667i
$389$	2953.75	−	6467.81i	0.384990	−	0.843010i	−0.613584	−	0.789629i	$-0.710273\pi$
$389$	2953.75	−	6467.81i	0.384990	−	0.843010i	0.998574	−	0.0533809i	$-0.0169998\pi$
$390$	964.556			0.125236
$391$	581.977	−	3353.00i	0.0752733	−	0.433679i
$392$	1147.61			0.147865
$393$	491.074	−	1075.30i	0.0630316	−	0.138020i
$394$	12617.7	+	3704.89i	1.61338	+	0.473730i
$395$	−3471.76	−	4006.62i	−0.442235	−	0.510367i
$396$	4868.83	−	3129.01i	0.617849	−	0.397067i
$397$	6221.04	−	7179.46i	0.786461	−	0.907624i	−0.211098	−	0.977465i	$-0.567704\pi$
$397$	6221.04	−	7179.46i	0.786461	−	0.907624i	0.997558	+	0.0698411i	$0.0222492\pi$
$398$	1496.81	−	10410.6i	0.188514	−	1.31114i
$399$	2244.15	−	658.943i	0.281575	−	0.0826778i
$400$	−1478.42	−	950.122i	−0.184802	−	0.118765i
$401$	954.958	+	6641.88i	0.118924	+	0.827131i	0.958745	+	0.284268i	$0.0917506\pi$
$401$	954.958	+	6641.88i	0.118924	+	0.827131i	−0.839821	+	0.542863i	$0.817340\pi$
$402$	1365.49	+	2990.01i	0.169414	+	0.370966i
$403$	−4443.93	−	9730.85i	−0.549300	−	1.20280i
$404$	151.626	+	1054.58i	0.0186724	+	0.129870i
$405$	2818.18	+	1811.14i	0.345770	+	0.222213i
$406$	−2594.11	+	761.698i	−0.317102	+	0.0931095i
$407$	29.0560	−	202.089i	0.00353870	−	0.0246122i
$408$	59.5934	−	68.7744i	0.00723115	−	0.00834520i
$409$	1046.61	−	672.614i	0.126532	−	0.0813169i	−0.475844	−	0.879530i	$-0.657857\pi$
$409$	1046.61	−	672.614i	0.126532	−	0.0813169i	0.602376	+	0.798213i	$0.294221\pi$
$410$	5184.28	+	5982.98i	0.624471	+	0.720678i
$411$	−1510.14	−	443.416i	−0.181240	−	0.0532168i
$412$	−731.303	+	1601.33i	−0.0874483	+	0.191485i
$413$	15636.9			1.86305
$414$	−4974.72	+	10105.4i	−0.590565	+	1.19964i
$415$	5596.94			0.662031
$416$	5908.77	−	12938.4i	0.696398	−	1.52490i
$417$	483.770	+	142.048i	0.0568113	+	0.0166813i
$418$	8269.27	+	9543.24i	0.967615	+	1.11669i
$419$	−4702.59	+	3022.17i	−0.548297	+	0.352369i	−0.785276	−	0.619146i	$-0.787479\pi$
$419$	−4702.59	+	3022.17i	−0.548297	+	0.352369i	0.236979	+	0.971515i	$0.423843\pi$
$420$	−519.565	+	599.610i	−0.0603624	+	0.0696619i
$421$	1057.38	−	7354.25i	0.122408	−	0.851364i	−0.832408	−	0.554164i	$-0.813038\pi$
$421$	1057.38	−	7354.25i	0.122408	−	0.851364i	0.954815	−	0.297200i	$-0.0960529\pi$
$422$	−7282.08	+	2138.21i	−0.840015	+	0.246651i
$423$	10280.0	+	6606.57i	1.18163	+	0.759391i
$424$	43.0591	+	299.482i	0.00493192	+	0.0343022i
$425$	320.412	+	701.605i	0.0365701	+	0.0800773i
$426$	746.061	+	1633.65i	0.0848516	+	0.185799i
$427$	446.714	+	3106.97i	0.0506277	+	0.352123i
$428$	−6531.98	−	4197.85i	−0.737699	−	0.474091i
$429$	−1474.46	+	432.940i	−0.165938	+	0.0487239i
$430$	1297.42	−	9023.78i	0.145505	−	1.01201i
$431$	1275.49	−	1471.99i	0.142548	−	0.164509i	−0.679986	−	0.733225i	$-0.738014\pi$
$431$	1275.49	−	1471.99i	0.142548	−	0.164509i	0.822534	+	0.568716i	$0.192560\pi$
$432$	−2700.69	+	1735.63i	−0.300780	+	0.193300i
$433$	−5907.15	−	6817.21i	−0.655611	−	0.756615i	0.326443	−	0.945217i	$-0.394150\pi$
$433$	−5907.15	−	6817.21i	−0.655611	−	0.756615i	−0.982054	+	0.188602i	$0.939604\pi$
$434$	17935.7	+	5266.41i	1.98374	+	0.582479i
$435$	−47.6109	+	104.253i	−0.00524774	+	0.0114910i
$436$	15051.3			1.65327
$437$	−11000.2	−	3580.23i	−1.20414	−	0.391912i
$438$	−1575.79			−0.171905
$439$	−3757.09	+	8226.88i	−0.408465	+	0.894414i	0.587876	+	0.808951i	$0.299964\pi$
$439$	−3757.09	+	8226.88i	−0.408465	+	0.894414i	−0.996341	+	0.0854628i	$0.972763\pi$
$440$	511.136	+	150.083i	0.0553806	+	0.0162612i
$441$	5737.66	+	6621.61i	0.619551	+	0.715000i
$442$	−5839.76	+	3752.99i	−0.628437	+	0.403872i
$443$	7332.40	−	8462.04i	0.786394	−	0.907548i	−0.211159	−	0.977452i	$-0.567724\pi$
$443$	7332.40	−	8462.04i	0.786394	−	0.907548i	0.997554	+	0.0699042i	$0.0222693\pi$
$444$	5.72342	−	39.8072i	0.000611760	−	0.00425488i
$445$	4289.25	−	1259.44i	0.456921	−	0.134164i
$446$	7609.70	+	4890.45i	0.807914	+	0.519215i
$447$	102.021	+	709.573i	0.0107952	+	0.0750820i
$448$	4248.34	+	9302.58i	0.448025	+	0.981039i
$449$	−2746.44	−	6013.86i	−0.288669	−	0.632097i	0.708627	−	0.705583i	$-0.249315\pi$
$449$	−2746.44	−	6013.86i	−0.288669	−	0.632097i	−0.997296	+	0.0734858i	$0.976588\pi$
$450$	−363.305	−	2526.84i	−0.0380586	−	0.264703i
$451$	−10610.4	−	6818.86i	−1.10781	−	0.711946i
$452$	−6763.76	+	1986.02i	−0.703850	+	0.206669i
$453$	−105.914	+	736.649i	−0.0109852	+	0.0764035i
$454$	10362.7	−	11959.1i	1.07124	−	1.23628i
$455$	−6331.90	+	4069.27i	−0.652405	+	0.419275i
$456$	−202.574	−	233.783i	−0.0208035	−	0.0240085i
$457$	10678.9	+	3135.61i	1.09308	+	0.320957i	0.778100	−	0.628141i	$-0.216184\pi$
$457$	10678.9	+	3135.61i	1.09308	+	0.320957i	0.314980	+	0.949098i	$0.398002\pi$
$458$	−7162.30	+	15683.2i	−0.730726	+	1.60007i
$459$	1408.98			0.143280
$460$	3795.72	−	995.701i	0.384731	−	0.100923i
$461$	−7489.68			−0.756679			−0.378340	−	0.925667i	$-0.623505\pi$
$461$	−7489.68			−0.756679			−0.378340	+	0.925667i	$0.623505\pi$
$462$	1115.49	−	2442.58i	0.112332	−	0.245973i
$463$	10187.0	+	2991.18i	1.02253	+	0.300242i	0.749670	−	0.661812i	$-0.230212\pi$
$463$	10187.0	+	2991.18i	1.02253	+	0.300242i	0.272860	+	0.962054i	$0.412030\pi$
$464$	1230.71	+	1420.32i	0.123135	+	0.142105i
$465$	666.627	−	428.415i	0.0664819	−	0.0427253i
$466$	8413.26	−	9709.41i	0.836344	−	0.965193i
$467$	285.169	−	1983.39i	0.0282570	−	0.196532i	−0.970803	−	0.239878i	$-0.922893\pi$
$467$	285.169	−	1983.39i	0.0282570	−	0.196532i	0.999060	+	0.0433458i	$0.0138017\pi$
$468$	10377.1	−	3046.99i	1.02496	−	0.300955i
$469$	−21578.1	−	13867.4i	−2.12449	−	1.36533i
$470$	−1287.12	−	8952.08i	−0.126320	−	0.878572i
$471$	531.365	+	1163.53i	0.0519831	+	0.113827i
$472$	−859.124	−	1881.22i	−0.0837805	−	0.183454i
$473$	2067.02	+	14376.5i	0.200934	+	1.39753i
$474$	2973.30	+	1910.83i	0.288119	+	0.185163i
$475$	2515.67	−	738.669i	0.243004	−	0.0713525i
$476$	812.610	−	5651.83i	0.0782477	−	0.544225i
$477$	−1512.70	+	1745.75i	−0.145203	+	0.167573i
$478$	12054.1	−	7746.73i	1.15344	−	0.741270i
$479$	−12680.2	−	14633.7i	−1.20955	−	1.39589i	−0.894652	−	0.446763i	$-0.852577\pi$
$479$	−12680.2	−	14633.7i	−1.20955	−	1.39589i	−0.314894	−	0.949127i	$-0.601969\pi$
$480$	1010.95	+	296.841i	0.0961316	+	0.0282268i
$481$	158.491	−	347.046i	0.0150240	−	0.0328980i
$482$	−14296.2			−1.35098
$483$	279.200	+	2444.08i	0.0263024	+	0.230247i
$484$	−2645.88			−0.248486
$485$	−640.397	+	1402.27i	−0.0599566	+	0.131287i
$486$	−6742.57	−	1979.80i	−0.629319	−	0.184785i
$487$	10878.5	+	12554.5i	1.01222	+	1.16817i	0.985699	+	0.168518i	$0.0538981\pi$
$487$	10878.5	+	12554.5i	1.01222	+	1.16817i	0.0265231	+	0.999648i	$0.491556\pi$
$488$	349.245	−	224.446i	0.0323967	−	0.0208201i
$489$	333.633	−	385.033i	0.0308536	−	0.0356069i
$490$	922.861	−	6418.64i	0.0850829	−	0.591765i
$491$	−15130.3	+	4442.65i	−1.39067	+	0.408338i	−0.889470	−	0.456994i	$-0.848926\pi$
$491$	−15130.3	+	4442.65i	−1.39067	+	0.408338i	−0.501200	+	0.865331i	$0.667108\pi$
$492$	−2090.01	−	1343.17i	−0.191515	−	0.123079i
$493$	−117.386	−	816.435i	−0.0107237	−	0.0745850i
$494$	9802.48	+	21464.4i	0.892783	+	1.95492i
$495$	1689.54	+	3699.57i	0.153412	+	0.335926i
$496$	−1849.23	−	12861.7i	−0.167405	−	1.16433i
$497$	−11789.6	−	7576.72i	−1.06406	−	0.683827i
$498$	−3580.18	+	1051.23i	−0.322152	+	0.0945923i
$499$	1824.74	−	12691.3i	0.163700	−	1.13856i	−0.727882	−	0.685702i	$-0.759495\pi$
$499$	1824.74	−	12691.3i	0.163700	−	1.13856i	0.891583	−	0.452858i	$-0.149596\pi$
$500$	−582.427	+	672.157i	−0.0520939	+	0.0601196i
$501$	−996.907	+	640.673i	−0.0888993	+	0.0571321i
$502$	2269.27	+	2618.88i	0.201758	+	0.232842i
$503$	−16559.5	−	4862.31i	−1.46790	−	0.431013i	−0.552481	−	0.833525i	$-0.686319\pi$
$503$	−16559.5	−	4862.31i	−1.46790	−	0.431013i	−0.915415	+	0.402512i	$0.868137\pi$
$504$	976.350	−	2137.91i	0.0862898	−	0.188948i
$505$	−748.703			−0.0659740
$506$	−11376.7	+	6852.72i	−0.999522	+	0.602056i
$507$	−987.944			−0.0865407
$508$	−5647.72	+	12366.8i	−0.493262	+	1.08009i
$509$	15058.5	+	4421.58i	1.31131	+	0.385036i	0.861350	−	0.508012i	$-0.169620\pi$
$509$	15058.5	+	4421.58i	1.31131	+	0.385036i	0.449961	+	0.893048i	$0.351438\pi$
$510$	−336.735	−	388.613i	−0.0292370	−	0.0337413i
$511$	10344.4	−	6647.95i	0.895519	−	0.575515i
$512$	10047.1	−	11595.0i	0.867237	−	1.00084i
$513$	681.617	−	4740.75i	0.0586630	−	0.408010i
$514$	−23252.5	+	6827.54i	−1.99537	+	0.585895i
$515$	−1040.71	−	668.823i	−0.0890468	−	0.0572269i
$516$	407.160	+	2831.86i	0.0347369	+	0.241600i
$517$	5985.67	+	13106.8i	0.509187	+	1.11496i
$518$	276.947	+	606.429i	0.0234910	+	0.0514381i
$519$	269.362	+	1873.45i	0.0227816	+	0.158450i
$520$	837.448	+	538.195i	0.0706241	+	0.0453873i
$521$	15326.6	−	4500.29i	1.28881	−	0.378429i	0.435668	−	0.900108i	$-0.356512\pi$
$521$	15326.6	−	4500.29i	1.28881	−	0.378429i	0.853142	+	0.521679i	$0.174694\pi$
$522$	−388.517	+	2702.19i	−0.0325765	+	0.226574i
$523$	4839.34	−	5584.90i	0.404607	−	0.466942i	−0.516479	−	0.856300i	$-0.672758\pi$
$523$	4839.34	−	5584.90i	0.404607	−	0.466942i	0.921087	+	0.389358i	$0.127303\pi$
$524$	−8252.74	+	5303.72i	−0.688021	+	0.442164i
$525$	−365.113	−	421.363i	−0.0303521	−	0.0350282i
$526$	−12910.5	−	3790.86i	−1.07020	−	0.314238i
$527$	−2369.08	+	5187.55i	−0.195823	+	0.428792i
$528$	−1866.58			−0.153849
$529$	5688.64	−	10755.2i	0.467547	−	0.883968i
$530$	1709.64			0.140117
$531$	6559.12	−	14362.5i	0.536048	−	1.17378i
$532$	−18623.4	−	5468.33i	−1.51772	−	0.445643i
$533$	−15434.3	−	17812.2i	−1.25429	−	1.44752i
$534$	−2507.14	+	1611.24i	−0.203173	+	0.130571i
$535$	3573.17	−	4123.66i	0.288751	−	0.333236i
$536$	−482.793	+	3357.90i	−0.0389057	+	0.270595i
$537$	2012.58	−	590.946i	0.161730	−	0.0474883i
$538$	−23728.4	−	15249.3i	−1.90150	−	1.22202i
$539$	1470.28	+	10226.0i	0.117494	+	0.817191i
$540$	674.920	+	1477.87i	0.0537851	+	0.117773i
$541$	−8251.03	−	18067.2i	−0.655711	−	1.43581i	−0.886466	−	0.462794i	$-0.846847\pi$
$541$	−8251.03	−	18067.2i	−0.655711	−	1.43581i	0.230755	−	0.973012i	$-0.425880\pi$
$542$	3313.52	+	23046.1i	0.262598	+	1.82641i
$543$	582.076	+	374.077i	0.0460023	+	0.0295639i
$544$	−7275.60	+	2136.31i	−0.573417	+	0.168370i
$545$	−1505.25	+	10469.3i	−0.118308	+	0.822852i
$546$	3286.01	−	3792.26i	0.257561	−	0.297241i
$547$	−14408.9	+	9260.04i	−1.12629	+	0.723822i	−0.964782	−	0.263050i	$-0.915272\pi$
$547$	−14408.9	+	9260.04i	−1.12629	+	0.723822i	−0.161507	+	0.986872i	$0.551635\pi$
$548$	8553.23	+	9870.95i	0.666744	+	0.769464i
$549$	3041.13	+	892.956i	0.236416	+	0.0694179i
$550$	1250.45	−	2738.11i	0.0969446	−	0.212279i
$551$	−2803.82			−0.216782
$552$	278.698	−	167.872i	0.0214895	−	0.0129441i
$553$	−27579.9			−2.12082
$554$	−7896.59	+	17291.1i	−0.605584	+	1.32605i
$555$	27.1165	+	7.96213i	0.00207393	+	0.000608962i
$556$	−2740.01	−	3162.15i	−0.208997	−	0.241196i
$557$	8072.25	−	5187.72i	0.614061	−	0.394633i	−0.196317	−	0.980541i	$-0.562898\pi$
$557$	8072.25	−	5187.72i	0.614061	−	0.394633i	0.810378	+	0.585907i	$0.199262\pi$
$558$	12360.6	−	14264.9i	0.937754	−	1.08223i
$559$	−3862.61	+	26865.1i	−0.292256	+	2.03269i
$560$	−8772.12	+	2575.73i	−0.661946	+	0.194365i
$561$	689.176	+	442.906i	0.0518663	+	0.0333325i
$562$	1937.03	+	13472.3i	0.145389	+	1.01120i
$563$	2368.88	+	5187.13i	0.177329	+	0.388297i	0.977336	−	0.211694i	$-0.0678980\pi$
$563$	2368.88	+	5187.13i	0.177329	+	0.388297i	−0.800007	+	0.599991i	$0.795171\pi$
$564$	1179.05	+	2581.76i	0.0880266	+	0.192751i
$565$	−704.991	−	4903.32i	−0.0524941	−	0.365105i
$566$	20153.2	+	12951.7i	1.49665	+	0.961836i
$567$	16721.5	−	4909.89i	1.23852	−	0.363661i
$568$	−263.782	+	1834.65i	−0.0194860	+	0.135528i
$569$	−10575.9	+	12205.3i	−0.779202	+	0.899247i	−0.997052	−	0.0767351i	$-0.975550\pi$
$569$	−10575.9	+	12205.3i	−0.779202	+	0.899247i	0.217849	+	0.975982i	$0.430096\pi$
$570$	−1470.46	+	945.004i	−0.108054	+	0.0694419i
$571$	−879.895	−	1015.45i	−0.0644877	−	0.0744227i	0.722589	−	0.691278i	$-0.242952\pi$
$571$	−879.895	−	1015.45i	−0.0644877	−	0.0744227i	−0.787077	+	0.616855i	$0.788406\pi$
$572$	12236.0	+	3592.81i	0.894428	+	0.262628i
$573$	63.9550	−	140.042i	0.00466276	−	0.0102100i
$574$	41184.3			2.99477
$575$	312.981	+	2739.78i	0.0226995	+	0.198708i
$576$	10326.4			0.746994
$577$	−6175.66	+	13522.8i	−0.445574	+	0.975670i	0.544968	+	0.838457i	$0.316542\pi$
$577$	−6175.66	+	13522.8i	−0.445574	+	0.975670i	−0.990542	+	0.137213i	$0.956185\pi$
$578$	−14776.4	−	4338.73i	−1.06335	−	0.312227i
$579$	1128.89	+	1302.81i	0.0810279	+	0.0935111i
$580$	800.125	−	514.209i	0.0572817	−	0.0368127i
$581$	19067.4	−	22005.0i	1.36153	−	1.57129i
$582$	146.261	−	1017.27i	0.0104171	−	0.0724523i
$583$	−2613.43	+	767.371i	−0.185655	+	0.0545133i
$584$	−1368.14	−	879.248i	−0.0969416	−	0.0623006i
$585$	1081.61	+	7522.77i	0.0764429	+	0.531672i
$586$	7310.22	+	16007.1i	0.515328	+	1.12841i
$587$	−808.330	−	1770.00i	−0.0568371	−	0.124456i	0.879082	−	0.476670i	$-0.158156\pi$
$587$	−808.330	−	1770.00i	−0.0568371	−	0.124456i	−0.935920	+	0.352214i	$0.885429\pi$
$588$	289.614	+	2014.31i	0.0203120	+	0.141273i
$589$	16308.3	+	10480.7i	1.14087	+	0.733193i
$590$	−11212.6	+	3292.31i	−0.782398	+	0.229733i
$591$	412.723	−	2870.55i	0.0287262	−	0.199795i
$592$	303.477	−	350.231i	0.0210690	−	0.0243149i
$593$	1662.49	−	1068.42i	0.115127	−	0.0739877i	−0.481810	−	0.876276i	$-0.660020\pi$
$593$	1662.49	−	1068.42i	0.115127	−	0.0739877i	0.596937	+	0.802288i	$0.296384\pi$
$594$	−3600.91	−	4155.67i	−0.248732	−	0.287052i
$595$	3850.00	+	1130.46i	0.265268	+	0.0778898i
$596$	2471.32	−	5411.43i	0.169848	−	0.371914i
$597$	−2319.46			−0.159011
$598$	−24006.1	+	6297.34i	−1.64161	+	0.430631i
$599$	−11667.9			−0.795887			−0.397943	−	0.917410i	$-0.630276\pi$
$599$	−11667.9			−0.795887			−0.397943	+	0.917410i	$0.630276\pi$
$600$	−30.6326	+	67.0761i	−0.00208429	+	0.00456395i
$601$	15258.9	+	4480.41i	1.03564	+	0.304093i	0.755004	−	0.655720i	$-0.227635\pi$
$601$	15258.9	+	4480.41i	1.03564	+	0.304093i	0.280640	+	0.959813i	$0.409453\pi$
$602$	−31058.0	−	35842.8i	−2.10270	−	2.42665i
$603$	−21788.5	+	14002.6i	−1.47147	+	0.945657i
$604$	4044.45	−	4667.54i	0.272461	−	0.314436i
$605$	264.611	−	1840.41i	0.0177817	−	0.123675i
$606$	478.921	−	140.624i	0.0321037	−	0.00942649i
$607$	23406.6	+	15042.5i	1.56515	+	1.00586i	0.980953	+	0.194246i	$0.0622260\pi$
$607$	23406.6	+	15042.5i	1.56515	+	1.00586i	0.584195	+	0.811613i	$0.301410\pi$
$608$	3668.28	+	25513.5i	0.244685	+	1.70182i
$609$	247.684	+	542.353i	0.0164806	+	0.0360874i
$610$	−974.486	−	2133.83i	−0.0646816	−	0.141633i
$611$	3831.92	+	26651.6i	0.253720	+	1.76466i
$612$	−4850.34	−	3117.13i	−0.320365	−	0.205886i
$613$	9064.52	−	2661.58i	0.597247	−	0.175368i	0.0308833	−	0.999523i	$-0.490168\pi$
$613$	9064.52	−	2661.58i	0.597247	−	0.175368i	0.566364	+	0.824155i	$0.308350\pi$
$614$	1685.14	−	11720.4i	0.110760	−	0.770352i
$615$	1143.30	−	1319.43i	0.0749628	−	0.0865117i
$616$	2331.39	−	1498.29i	0.152491	−	0.0979997i
$617$	−7356.42	−	8489.76i	−0.479997	−	0.553946i	0.463168	−	0.886270i	$-0.346713\pi$
$617$	−7356.42	−	8489.76i	−0.479997	−	0.553946i	−0.943165	+	0.332324i	$0.892167\pi$
$618$	791.327	+	232.355i	0.0515078	+	0.0151241i
$619$	7420.19	−	16247.9i	0.481813	−	1.05502i	−0.500148	−	0.865940i	$-0.666721\pi$
$619$	7420.19	−	16247.9i	0.481813	−	1.05502i	0.981961	−	0.189084i	$-0.0605518\pi$
$620$	−6576.01			−0.425966
$621$	4790.11	+	1559.03i	0.309534	+	0.100744i
$622$	19313.1			1.24499
$623$	9660.81	−	21154.2i	0.621271	−	1.36039i
$624$	−3346.75	−	982.696i	−0.214707	−	0.0630438i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	−18877.4	+	12131.8i	−1.20526	+	0.774574i
$627$	1823.63	−	2104.58i	0.116155	−	0.134049i
$628$	1510.66	−	10506.9i	0.0959905	−	0.667629i
$629$	−195.153	+	57.3021i	−0.0123708	+	0.00363241i
$630$	−11172.2	−	7179.97i	−0.706529	−	0.454058i
$631$	2922.12	+	20323.8i	0.184355	+	1.28222i	0.846317	+	0.532679i	$0.178815\pi$
$631$	2922.12	+	20323.8i	0.184355	+	1.28222i	−0.661963	+	0.749537i	$0.730276\pi$
$632$	1515.30	+	3318.04i	0.0953723	+	0.208836i
$633$	695.291	+	1522.47i	0.0436577	+	0.0955970i
$634$	−2307.22	−	16047.0i	−0.144529	−	1.00522i
$635$	−8037.20	−	5165.20i	−0.502278	−	0.322795i
$636$	−514.790	+	151.156i	−0.0320955	+	0.00942409i
$637$	−2747.49	+	19109.2i	−0.170894	+	1.18859i
$638$	−2108.01	+	2432.77i	−0.130810	+	0.150963i
$639$	−11904.5	+	7650.58i	−0.736990	+	0.473634i
$640$	1433.01	+	1653.78i	0.0885074	+	0.102143i
$641$	12840.7	+	3770.36i	0.791226	+	0.232325i	0.652283	−	0.757975i	$-0.273811\pi$
$641$	12840.7	+	3770.36i	0.791226	+	0.232325i	0.138943	+	0.990300i	$0.455630\pi$
$642$	−1511.12	+	3308.90i	−0.0928960	+	0.203414i
$643$	−43.1844			−0.00264856			−0.00132428	−	0.999999i	$-0.500422\pi$
$643$	−43.1844			−0.00264856			−0.00132428	+	0.999999i	$0.500422\pi$
$644$	9016.38	−	18315.4i	0.551700	−	1.12069i
$645$	−2010.49			−0.122733
$646$	5225.74	−	11442.8i	0.318273	−	0.696920i
$647$	24107.8	+	7078.70i	1.46488	+	0.430128i	0.914431	−	0.404741i	$-0.132638\pi$
$647$	24107.8	+	7078.70i	1.46488	+	0.430128i	0.550449	+	0.834869i	$0.314457\pi$
$648$	−1509.41	−	1741.95i	−0.0915049	−	0.105602i
$649$	15662.3	−	10065.5i	0.947300	−	0.608793i
$650$	3683.58	−	4251.08i	0.222280	−	0.256525i
$651$	586.676	−	4080.42i	0.0353205	−	0.245659i
$652$	−4056.66	+	1191.14i	−0.243667	+	0.0715471i
$653$	16119.2	+	10359.2i	0.965992	+	0.620805i	0.925650	−	0.378381i	$-0.123519\pi$
$653$	16119.2	+	10359.2i	0.965992	+	0.620805i	0.0403418	+	0.999186i	$0.487155\pi$
$654$	−1003.51	−	6979.57i	−0.0600006	−	0.417313i
$655$	−2863.79	−	6270.82i	−0.170836	−	0.374078i
$656$	−11892.6	−	26041.1i	−0.707816	−	1.54990i
$657$	−1767.03	−	12289.9i	−0.104929	−	0.729796i
$658$	−39581.0	−	25437.1i	−2.34503	−	1.50706i
$659$	−19616.2	+	5759.85i	−1.15954	+	0.340473i	−0.804256	−	0.594283i	$-0.797436\pi$
$659$	−19616.2	+	5759.85i	−1.15954	+	0.340473i	−0.355289	+	0.934756i	$0.615618\pi$
$660$	−134.437	+	935.030i	−0.00792872	+	0.0551454i
$661$	9664.00	−	11152.9i	0.568663	−	0.656272i	−0.396465	−	0.918050i	$-0.629763\pi$
$661$	9664.00	−	11152.9i	0.568663	−	0.656272i	0.965128	+	0.261778i	$0.0843088\pi$
$662$	−4897.79	+	3147.62i	−0.287550	+	0.184797i
$663$	1002.51	+	1156.96i	0.0587242	+	0.0677714i
$664$	−3694.94	−	1084.93i	−0.215951	−	0.0634090i
$665$	5666.14	−	12407.1i	0.330411	−	0.723499i
$666$	673.174			0.0391666
$667$	504.309	−	2905.52i	0.0292758	−	0.168669i
$668$	9834.09			0.569600
$669$	828.692	−	1814.58i	0.0478910	−	0.104867i
$670$	18392.6	+	5400.55i	1.06055	+	0.311405i
$671$	2447.41	+	2824.46i	0.140806	+	0.162499i
$672$	4611.11	−	2963.38i	0.264698	−	0.170111i
$673$	−17199.7	+	19849.5i	−0.985142	+	1.13691i	0.00543873	+	0.999985i	$0.498269\pi$
$673$	−17199.7	+	19849.5i	−0.985142	+	1.13691i	−0.990581	+	0.136929i	$0.956277\pi$
$674$	2439.88	−	16969.8i	0.139437	−	0.969808i
$675$	−1095.47	+	321.658i	−0.0624660	+	0.0183417i
$676$	6897.09	+	4432.49i	0.392415	+	0.252190i
$677$	−2909.56	−	20236.4i	−0.165175	−	1.14882i	−0.888690	−	0.458508i	$-0.848384\pi$
$677$	−2909.56	−	20236.4i	−0.165175	−	1.14882i	0.723515	−	0.690308i	$-0.242525\pi$
$678$	1371.92	+	3004.08i	0.0777111	+	0.170164i
$679$	3331.51	+	7295.00i	0.188294	+	0.412307i
$680$	−75.5254	−	525.290i	−0.00425921	−	0.0296235i
$681$	−2935.75	−	1886.69i	−0.165196	−	0.106165i
$682$	21354.9	−	6270.35i	1.19900	−	0.352059i
$683$	304.814	−	2120.03i	0.0170767	−	0.118771i	−0.979500	−	0.201444i	$-0.935437\pi$
$683$	304.814	−	2120.03i	0.0170767	−	0.118771i	0.996577	+	0.0826730i	$0.0263457\pi$
$684$	−12834.5	+	14811.8i	−0.717457	+	0.827989i
$685$	−7721.38	+	4962.23i	−0.430684	+	0.276784i
$686$	623.309	+	719.337i	0.0346910	+	0.0400356i
$687$	3648.23	+	1071.22i	0.202604	+	0.0594898i
$688$	−13695.2	+	29988.3i	−0.758902	+	1.66176i
$689$	−5089.84			−0.281433
$690$	−714.798	−	1693.76i	−0.0394376	−	0.0934500i
$691$	−4084.75			−0.224879			−0.112440	−	0.993659i	$-0.535866\pi$
$691$	−4084.75			−0.224879			−0.112440	+	0.993659i	$0.535866\pi$
$692$	6524.91	−	14287.6i	0.358439	−	0.784872i
$693$	20301.1	+	5960.93i	1.11281	+	0.326749i
$694$	−14638.9	−	16894.2i	−0.800700	−	0.924057i
$695$	2473.53	−	1589.64i	0.135002	−	0.0867606i
$696$	51.6403	−	59.5961i	0.00281239	−	0.00324567i
$697$	−1788.14	+	12436.8i	−0.0971743	+	0.675862i
$698$	28492.4	−	8366.12i	1.54506	−	0.453671i
$699$	−2383.48	−	1531.77i	−0.128972	−	0.0828855i
$700$	658.469	+	4579.75i	0.0355540	+	0.247283i
$701$	4148.07	+	9083.01i	0.223496	+	0.489388i	0.987850	−	0.155409i	$-0.0496695\pi$
$701$	4148.07	+	9083.01i	0.223496	+	0.489388i	−0.764354	+	0.644796i	$0.776942\pi$
$702$	−4268.55	−	9346.83i	−0.229496	−	0.502526i
$703$	98.3941	+	684.346i	0.00527881	+	0.0367149i
$704$	10243.3	+	6583.00i	0.548382	+	0.352423i
$705$	−1913.72	+	561.920i	−0.102234	+	0.0300186i
$706$	−255.560	+	1777.46i	−0.0136234	+	0.0947528i
$707$	−2550.65	+	2943.61i	−0.135682	+	0.156585i
$708$	3085.13	−	1982.70i	0.163766	−	0.105246i
$709$	3131.94	+	3614.46i	0.165899	+	0.191458i	0.832612	−	0.553857i	$-0.186845\pi$
$709$	3131.94	+	3614.46i	0.165899	+	0.191458i	−0.666712	+	0.745315i	$0.732299\pi$
$710$	10049.1	+	2950.69i	0.531178	+	0.155968i
$711$	−11568.8	+	25332.1i	−0.610216	+	1.33619i
$712$	−3075.78			−0.161895
$713$	−13794.2	+	15014.7i	−0.724538	+	0.788649i
$714$	−2675.05			−0.140212
$715$	−3722.78	+	8151.75i	−0.194719	+	0.426375i
$716$	−16701.6	−	4904.04i	−0.871745	−	0.255967i
$717$	−2069.33	−	2388.13i	−0.107783	−	0.124388i
$718$	24293.5	−	15612.5i	1.26271	−	0.811493i
$719$	5678.33	−	6553.14i	0.294528	−	0.339904i	−0.589128	−	0.808040i	$-0.700529\pi$
$719$	5678.33	−	6553.14i	0.294528	−	0.339904i	0.883657	+	0.468136i	$0.155074\pi$
$720$	−1313.79	+	9137.61i	−0.0680029	+	0.472971i
$721$	−6174.99	+	1813.14i	−0.318958	+	0.0936544i
$722$	−13539.8	−	8701.50i	−0.697921	−	0.448527i
$723$	448.685	+	3120.67i	0.0230799	+	0.160524i
$724$	−2385.29	−	5223.06i	−0.122443	−	0.268112i
$725$	277.652	+	607.972i	0.0142231	+	0.0311442i
$726$	176.409	+	1226.95i	0.00901809	+	0.0627222i
$727$	4660.44	+	2995.08i	0.237753	+	0.152794i	0.654092	−	0.756415i	$-0.273051\pi$
$727$	4660.44	+	2995.08i	0.237753	+	0.152794i	−0.416339	+	0.909209i	$0.636687\pi$
$728$	4968.95	−	1459.02i	0.252969	−	0.0742785i
$729$	2353.91	−	16371.8i	0.119591	−	0.831775i
$730$	−6017.86	+	6944.98i	−0.305111	+	0.352117i
$731$	12172.2	−	7822.61i	0.615877	−	0.395800i
$732$	482.087	+	556.358i	0.0243422	+	0.0280923i
$733$	−4654.65	−	1366.73i	−0.234548	−	0.0688694i	0.162346	−	0.986734i	$-0.448094\pi$
$733$	−4654.65	−	1366.73i	−0.234548	−	0.0688694i	−0.396894	+	0.917864i	$0.629912\pi$
$734$	866.777	−	1897.98i	0.0435876	−	0.0954436i
$735$	−1430.07			−0.0717671
$736$	−27098.7	−	787.636i	−1.35716	−	0.0394465i
$737$	−30539.7			−1.52638
$738$	17275.4	−	37827.8i	0.861673	−	1.88680i
$739$	35065.0	+	10296.0i	1.74545	+	0.512510i	0.989800	−	0.142466i	$-0.0455033\pi$
$739$	35065.0	+	10296.0i	1.74545	+	0.512510i	0.755649	+	0.654976i	$0.227321\pi$
$740$	−153.585	−	177.246i	−0.00762957	−	0.00880500i
$741$	4377.75	−	2813.41i	0.217032	−	0.139478i
$742$	5824.33	−	6721.63i	0.288164	−	0.332559i
$743$	4643.20	−	32294.2i	0.229263	−	1.59456i	−0.471961	−	0.881620i	$-0.656454\pi$
$743$	4643.20	−	32294.2i	0.229263	−	1.59456i	0.701224	−	0.712941i	$-0.252637\pi$
$744$	−523.134	+	153.606i	−0.0257783	+	0.00756918i
$745$	3516.91	+	2260.18i	0.172952	+	0.111150i
$746$	−4178.00	−	29058.6i	−0.205050	−	1.42616i
$747$	−12213.4	−	26743.7i	−0.598215	−	1.30991i
$748$	−2824.18	−	6184.08i	−0.138051	−	0.302289i
$749$	−4039.69	−	28096.6i	−0.197072	−	1.37067i
$750$	350.525	+	225.269i	0.0170658	+	0.0109675i
$751$	−20778.2	+	6101.03i	−1.00960	+	0.296444i	−0.744388	−	0.667747i	$-0.767259\pi$
$751$	−20778.2	+	6101.03i	−1.00960	+	0.296444i	−0.265208	+	0.964191i	$0.585441\pi$
$752$	−4654.49	+	32372.7i	−0.225707	+	1.56983i
$753$	500.446	−	577.546i	0.0242195	−	0.0279508i
$754$	−5060.41	+	3252.13i	−0.244416	+	0.157076i
$755$	2842.15	+	3280.01i	0.137002	+	0.158108i
$756$	8109.69	+	2381.22i	0.390141	+	0.114556i
$757$	5074.57	−	11111.8i	0.243644	−	0.533505i	−0.747818	−	0.663904i	$-0.768898\pi$
$757$	5074.57	−	11111.8i	0.243644	−	0.533505i	0.991462	+	0.130399i	$0.0416257\pi$
$758$	32865.9			1.57486
$759$	1852.92	+	2268.32i	0.0886121	+	0.108478i
$760$	−1803.97			−0.0861009
$761$	−16018.0	+	35074.5i	−0.763011	+	1.67076i	−0.0215479	+	0.999768i	$0.506859\pi$
$761$	−16018.0	+	35074.5i	−0.763011	+	1.67076i	−0.741463	+	0.670994i	$0.765868\pi$
$762$	6111.28	+	1794.43i	0.290536	+	0.0853090i
$763$	36033.0	+	41584.3i	1.70968	+	1.97307i
$764$	−1074.80	+	690.729i	−0.0508963	+	0.0327090i
$765$	2653.27	−

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61506 + 3.53648i) q^{2} +(0.822656 + 0.241553i) q^{3} +(-4.65942 - 5.37726i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-2.18289 + 2.51919i) q^{6} +(3.70179 - 25.7465i) q^{7} +(-3.30086 + 0.969220i) q^{8} +(-22.0954 - 14.1999i) q^{9} +O(q^{10})\)	\(q+(-1.61506 + 3.53648i) q^{2} +(0.822656 + 0.241553i) q^{3} +(-4.65942 - 5.37726i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-2.18289 + 2.51919i) q^{6} +(3.70179 - 25.7465i) q^{7} +(-3.30086 + 0.969220i) q^{8} +(-22.0954 - 14.1999i) q^{9} +(2.76647 + 19.2412i) q^{10} +(-12.8654 - 28.1712i) q^{11} +(-2.53420 - 5.54913i) q^{12} +(-8.23617 - 57.2839i) q^{13} +(85.0736 + 54.6735i) q^{14} +(4.11328 - 1.20777i) q^{15} +(10.0042 - 69.5805i) q^{16} +(-20.2039 + 23.3166i) q^{17} +(85.9030 - 55.2065i) q^{18} +(68.6786 + 79.2594i) q^{19} +(-34.1346 - 10.0228i) q^{20} +(9.26447 - 20.2864i) q^{21} +120.405 q^{22} +(-94.4871 + 56.9138i) q^{23} -2.94959 q^{24} +(10.3854 - 22.7408i) q^{25} +(215.885 + 63.3896i) q^{26} +(-29.9065 - 34.5140i) q^{27} +(-155.694 + 100.058i) q^{28} +(-17.5076 + 20.2049i) q^{29} +(-2.37193 + 16.4972i) q^{30} +(177.358 - 52.0771i) q^{31} +(206.760 + 132.877i) q^{32} +(-3.77891 - 26.2829i) q^{33} +(-49.8282 - 109.109i) q^{34} +(-54.0274 - 118.304i) q^{35} +(26.5955 + 184.976i) q^{36} +(5.54591 + 3.56414i) q^{37} +(-391.219 + 114.872i) q^{38} +(7.06158 - 49.1144i) q^{39} +(-11.2643 + 12.9997i) q^{40} +(342.602 - 220.177i) q^{41} +(56.7797 + 65.5273i) q^{42} +(-449.985 - 132.127i) q^{43} +(-91.5387 + 200.442i) q^{44} -131.324 q^{45} +(-48.6725 - 426.071i) q^{46} -465.255 q^{47} +(25.0374 - 54.8242i) q^{48} +(-320.075 - 93.9826i) q^{49} +(63.6495 + 73.4554i) q^{50} +(-22.2531 + 14.3012i) q^{51} +(-269.654 + 311.198i) q^{52} +(12.5164 - 87.0534i) q^{53} +(170.359 - 50.0219i) q^{54} +(-130.268 - 83.7179i) q^{55} +(12.7350 + 88.5736i) q^{56} +(37.3535 + 81.7927i) q^{57} +(-43.1783 - 94.5474i) q^{58} +(85.5536 + 595.038i) q^{59} +(-25.6600 - 16.4907i) q^{60} +(-115.787 + 33.9981i) q^{61} +(-102.274 + 711.332i) q^{62} +(-447.390 + 516.316i) q^{63} +(-330.752 + 212.561i) q^{64} +(-189.494 - 218.687i) q^{65} +(99.0521 + 29.0843i) q^{66} +(409.645 - 896.997i) q^{67} +219.518 q^{68} +(-91.4781 + 23.9967i) q^{69} +505.636 q^{70} +(223.817 - 490.090i) q^{71} +(86.6968 + 25.4565i) q^{72} +(309.575 + 357.269i) q^{73} +(-21.5615 + 13.8567i) q^{74} +(14.0367 - 16.1992i) q^{75} +(106.195 - 738.605i) q^{76} +(-772.936 + 226.954i) q^{77} +(162.287 + 104.296i) q^{78} +(-150.897 - 1049.51i) q^{79} +(-146.010 - 319.717i) q^{80} +(278.327 + 609.450i) q^{81} +(225.330 + 1567.21i) q^{82} +(941.688 + 605.186i) q^{83} +(-152.252 + 44.7052i) q^{84} +(-21.9537 + 152.691i) q^{85} +(1194.02 - 1377.97i) q^{86} +(-19.2833 + 12.3926i) q^{87} +(69.7708 + 80.5199i) q^{88} +(857.849 + 251.887i) q^{89} +(212.097 - 464.427i) q^{90} -1505.35 q^{91} +(746.295 + 242.896i) q^{92} +158.484 q^{93} +(751.414 - 1645.37i) q^{94} +(503.135 + 147.734i) q^{95} +(137.996 + 159.255i) q^{96} +(-259.373 + 166.689i) q^{97} +(849.308 - 980.154i) q^{98} +(-115.762 + 805.141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

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