LMFDB - Embedded newform 115.4.g.a.6.7

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			6.7
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.274193 - 0.600398i) q^{2} +(0.833837 + 0.244837i) q^{3} +(4.95359 + 5.71675i) q^{4} +(4.20627 - 2.70320i) q^{5} +(0.375631 - 0.433502i) q^{6} +(-4.72226 + 32.8441i) q^{7} +(9.85703 - 2.89429i) q^{8} +(-22.0785 - 14.1890i) q^{9} +O(q^{10})$	\(q+(0.274193 - 0.600398i) q^{2} +(0.833837 + 0.244837i) q^{3} +(4.95359 + 5.71675i) q^{4} +(4.20627 - 2.70320i) q^{5} +(0.375631 - 0.433502i) q^{6} +(-4.72226 + 32.8441i) q^{7} +(9.85703 - 2.89429i) q^{8} +(-22.0785 - 14.1890i) q^{9} +(-0.469671 - 3.26663i) q^{10} +(17.0273 + 37.2845i) q^{11} +(2.73082 + 5.97966i) q^{12} +(-4.80412 - 33.4134i) q^{13} +(18.4247 + 11.8408i) q^{14} +(4.16919 - 1.22418i) q^{15} +(-7.64714 + 53.1870i) q^{16} +(21.3976 - 24.6941i) q^{17} +(-14.5728 + 9.36537i) q^{18} +(44.5912 + 51.4610i) q^{19} +(36.2897 + 10.6556i) q^{20} +(-11.9790 + 26.2304i) q^{21} +27.0543 q^{22} +(52.9307 + 96.7747i) q^{23} +8.92778 q^{24} +(10.3854 - 22.7408i) q^{25} +(-21.3786 - 6.27732i) q^{26} +(-30.3016 - 34.9699i) q^{27} +(-211.153 + 135.700i) q^{28} +(164.016 - 189.285i) q^{29} +(0.408163 - 2.83883i) q^{30} +(134.639 - 39.5336i) q^{31} +(98.9753 + 63.6076i) q^{32} +(5.06935 + 35.2581i) q^{33} +(-8.95924 - 19.6180i) q^{34} +(68.9211 + 150.916i) q^{35} +(-28.2530 - 196.504i) q^{36} +(-369.717 - 237.603i) q^{37} +(43.1237 - 12.6623i) q^{38} +(4.17497 - 29.0376i) q^{39} +(33.6375 - 38.8197i) q^{40} +(179.988 - 115.671i) q^{41} +(12.4641 + 14.3844i) q^{42} +(-73.7935 - 21.6677i) q^{43} +(-128.800 + 282.033i) q^{44} -131.224 q^{45} +(72.6165 - 5.24460i) q^{46} -419.749 q^{47} +(-19.3986 + 42.4770i) q^{48} +(-727.326 - 213.562i) q^{49} +(-10.8059 - 12.4707i) q^{50} +(23.8881 - 15.3520i) q^{51} +(167.218 - 192.980i) q^{52} +(-5.00404 + 34.8039i) q^{53} +(-29.3043 + 8.60453i) q^{54} +(172.409 + 110.800i) q^{55} +(48.5126 + 337.412i) q^{56} +(24.5823 + 53.8277i) q^{57} +(-68.6742 - 150.376i) q^{58} +(-55.1150 - 383.333i) q^{59} +(27.6508 + 17.7701i) q^{60} +(709.595 - 208.356i) q^{61} +(13.1811 - 91.6768i) q^{62} +(570.285 - 658.144i) q^{63} +(-296.303 + 190.422i) q^{64} +(-110.531 - 127.559i) q^{65} +(22.5589 + 6.62388i) q^{66} +(157.655 - 345.215i) q^{67} +247.165 q^{68} +(20.4416 + 93.6537i) q^{69} +109.507 q^{70} +(-98.8141 + 216.373i) q^{71} +(-258.695 - 75.9598i) q^{72} +(-159.714 - 184.320i) q^{73} +(-244.030 + 156.829i) q^{74} +(14.2275 - 16.4194i) q^{75} +(-73.3030 + 509.834i) q^{76} +(-1304.98 + 383.177i) q^{77} +(-16.2893 - 10.4685i) q^{78} +(-7.05386 - 49.0607i) q^{79} +(111.609 + 244.391i) q^{80} +(277.662 + 607.995i) q^{81} +(-20.0974 - 139.781i) q^{82} +(-541.167 - 347.787i) q^{83} +(-209.292 + 61.4536i) q^{84} +(23.2507 - 161.712i) q^{85} +(-33.2429 + 38.3643i) q^{86} +(183.107 - 117.676i) q^{87} +(275.750 + 318.233i) q^{88} +(1145.93 + 336.477i) q^{89} +(-35.9806 + 78.7865i) q^{90} +1120.12 q^{91} +(-291.039 + 781.974i) q^{92} +121.946 q^{93} +(-115.092 + 252.017i) q^{94} +(326.672 + 95.9197i) q^{95} +(66.9558 + 77.2711i) q^{96} +(854.509 - 549.159i) q^{97} +(-327.650 + 378.128i) q^{98} +(153.093 - 1064.79i) 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 $

$2$	0.274193	−	0.600398i	0.0969417	−	0.212273i	−0.854948	−	0.518714i	$-0.826411\pi$
$2$	0.274193	−	0.600398i	0.0969417	−	0.212273i	0.951890	+	0.306441i	$0.0991383\pi$
$3$	0.833837	+	0.244837i	0.160472	+	0.0471188i	0.360982	−	0.932573i	$-0.382442\pi$
$3$	0.833837	+	0.244837i	0.160472	+	0.0471188i	−0.200510	+	0.979692i	$0.564260\pi$
$4$	4.95359	+	5.71675i	0.619199	+	0.714593i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	0.375631	−	0.433502i	0.0255585	−	0.0294961i
$7$	−4.72226	+	32.8441i	−0.254978	+	1.77341i	0.312396	+	0.949952i	$0.398868\pi$
$7$	−4.72226	+	32.8441i	−0.254978	+	1.77341i	−0.567374	+	0.823460i	$0.692041\pi$
$8$	9.85703	−	2.89429i	0.435623	−	0.127911i
$9$	−22.0785	−	14.1890i	−0.817722	−	0.525518i
$10$	−0.469671	−	3.26663i	−0.0148523	−	0.103300i
$11$	17.0273	+	37.2845i	0.466719	+	1.02197i	0.985904	+	0.167311i	$0.0535083\pi$
$11$	17.0273	+	37.2845i	0.466719	+	1.02197i	−0.519185	+	0.854662i	$0.673764\pi$
$12$	2.73082	+	5.97966i	0.0656933	+	0.143848i
$13$	−4.80412	−	33.4134i	−0.102494	−	0.712862i	−0.974666	−	0.223664i	$-0.928198\pi$
$13$	−4.80412	−	33.4134i	−0.102494	−	0.712862i	0.872172	−	0.489199i	$-0.162711\pi$
$14$	18.4247	+	11.8408i	0.351729	+	0.226043i
$15$	4.16919	−	1.22418i	0.0717653	−	0.0210722i
$16$	−7.64714	+	53.1870i	−0.119487	+	0.831047i
$17$	21.3976	−	24.6941i	0.305275	−	0.352306i	−0.582296	−	0.812977i	$-0.697846\pi$
$17$	21.3976	−	24.6941i	0.305275	−	0.352306i	0.887571	+	0.460671i	$0.152391\pi$
$18$	−14.5728	+	9.36537i	−0.190825	+	0.122636i
$19$	44.5912	+	51.4610i	0.538417	+	0.621367i	0.958145	−	0.286283i	$-0.0924198\pi$
$19$	44.5912	+	51.4610i	0.538417	+	0.621367i	−0.419728	+	0.907650i	$0.637874\pi$
$20$	36.2897	+	10.6556i	0.405731	+	0.119133i
$21$	−11.9790	+	26.2304i	−0.124478	+	0.272569i
$22$	27.0543			0.262182
$23$	52.9307	+	96.7747i	0.479862	+	0.877344i
$23$	52.9307	+	96.7747i	0.479862	+	0.877344i
$24$	8.92778			0.0759323
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	−21.3786	−	6.27732i	−0.161257	−	0.0473494i
$27$	−30.3016	−	34.9699i	−0.215983	−	0.249258i
$28$	−211.153	+	135.700i	−1.42515	+	0.915889i
$29$	164.016	−	189.285i	1.05024	−	1.21205i	0.0735756	−	0.997290i	$-0.476559\pi$
$29$	164.016	−	189.285i	1.05024	−	1.21205i	0.976668	−	0.214756i	$-0.0688956\pi$
$30$	0.408163	−	2.83883i	0.00248400	−	0.0172766i
$31$	134.639	−	39.5336i	0.780060	−	0.229046i	0.132625	−	0.991166i	$-0.457660\pi$
$31$	134.639	−	39.5336i	0.780060	−	0.229046i	0.647436	+	0.762120i	$0.275841\pi$
$32$	98.9753	+	63.6076i	0.546766	+	0.351385i
$33$	5.06935	+	35.2581i	0.0267412	+	0.185989i
$34$	−8.95924	−	19.6180i	−0.0451911	−	0.0989547i
$35$	68.9211	+	150.916i	0.332851	+	0.728842i
$36$	−28.2530	−	196.504i	−0.130801	−	0.909739i
$37$	−369.717	−	237.603i	−1.64273	−	1.05572i	−0.938225	−	0.346025i	$-0.887531\pi$
$37$	−369.717	−	237.603i	−1.64273	−	1.05572i	−0.704508	−	0.709696i	$-0.748832\pi$
$38$	43.1237	−	12.6623i	0.184094	−	0.0540550i
$39$	4.17497	−	29.0376i	0.0171418	−	0.119224i
$40$	33.6375	−	38.8197i	0.132964	−	0.153448i
$41$	179.988	−	115.671i	0.685596	−	0.440606i	−0.150922	−	0.988546i	$-0.548224\pi$
$41$	179.988	−	115.671i	0.685596	−	0.440606i	0.836518	+	0.547940i	$0.184588\pi$
$42$	12.4641	+	14.3844i	0.0457918	+	0.0528466i
$43$	−73.7935	−	21.6677i	−0.261707	−	0.0768441i	0.148247	−	0.988950i	$-0.452637\pi$
$43$	−73.7935	−	21.6677i	−0.261707	−	0.0768441i	−0.409954	+	0.912106i	$0.634455\pi$
$44$	−128.800	+	282.033i	−0.441303	+	0.966319i
$45$	−131.224			−0.434704
$46$	72.6165	−	5.24460i	0.232755	−	0.0168103i
$47$	−419.749			−1.30270			−0.651348	−	0.758779i	$-0.725796\pi$
$47$	−419.749			−1.30270			−0.651348	+	0.758779i	$0.725796\pi$
$48$	−19.3986	+	42.4770i	−0.0583322	+	0.127730i
$49$	−727.326	−	213.562i	−2.12048	−	0.622630i
$50$	−10.8059	−	12.4707i	−0.0305638	−	0.0352725i
$51$	23.8881	−	15.3520i	0.0655883	−	0.0421511i
$52$	167.218	−	192.980i	0.445943	−	0.514645i
$53$	−5.00404	+	34.8039i	−0.0129690	+	0.0902015i	−0.995278	−	0.0970663i	$-0.969054\pi$
$53$	−5.00404	+	34.8039i	−0.0129690	+	0.0902015i	0.982309	+	0.187268i	$0.0599632\pi$
$54$	−29.3043	+	8.60453i	−0.0738484	+	0.0216838i
$55$	172.409	+	110.800i	0.422684	+	0.271642i
$56$	48.5126	+	337.412i	0.115764	+	0.805154i
$57$	24.5823	+	53.8277i	0.0571229	+	0.125082i
$58$	−68.6742	−	150.376i	−0.155472	−	0.340436i
$59$	−55.1150	−	383.333i	−0.121616	−	0.845860i	−0.955725	−	0.294260i	$-0.904927\pi$
$59$	−55.1150	−	383.333i	−0.121616	−	0.845860i	0.834109	−	0.551599i	$-0.185982\pi$
$60$	27.6508	+	17.7701i	0.0594950	+	0.0382351i
$61$	709.595	−	208.356i	1.48942	−	0.437332i	0.567061	−	0.823676i	$-0.308081\pi$
$61$	709.595	−	208.356i	1.48942	−	0.437332i	0.922355	+	0.386344i	$0.126262\pi$
$62$	13.1811	−	91.6768i	0.0270001	−	0.187790i
$63$	570.285	−	658.144i	1.14046	−	1.31616i
$64$	−296.303	+	190.422i	−0.578717	+	0.371919i
$65$	−110.531	−	127.559i	−0.210918	−	0.243412i
$66$	22.5589	+	6.62388i	0.0420728	+	0.0123537i
$67$	157.655	−	345.215i	0.287471	−	0.629474i	−0.709711	−	0.704493i	$-0.751174\pi$
$67$	157.655	−	345.215i	0.287471	−	0.629474i	0.997182	+	0.0750189i	$0.0239017\pi$
$68$	247.165			0.440781
$69$	20.4416	+	93.6537i	0.0356649	+	0.163400i
$70$	109.507			0.186981
$71$	−98.8141	+	216.373i	−0.165170	+	0.361672i	−0.974061	−	0.226287i	$-0.927341\pi$
$71$	−98.8141	+	216.373i	−0.165170	+	0.361672i	0.808891	+	0.587959i	$0.200068\pi$
$72$	−258.695	−	75.9598i	−0.423438	−	0.124333i
$73$	−159.714	−	184.320i	−0.256071	−	0.295521i	0.613129	−	0.789983i	$-0.289911\pi$
$73$	−159.714	−	184.320i	−0.256071	−	0.295521i	−0.869199	+	0.494462i	$0.835365\pi$
$74$	−244.030	+	156.829i	−0.383350	+	0.246364i
$75$	14.2275	−	16.4194i	0.0219047	−	0.0252793i
$76$	−73.3030	+	509.834i	−0.110637	+	0.769499i
$77$	−1304.98	+	383.177i	−1.93138	+	0.567105i
$78$	−16.2893	−	10.4685i	−0.0236462	−	0.0151965i
$79$	−7.05386	−	49.0607i	−0.0100458	−	0.0698704i	0.984182	−	0.177161i	$-0.0566914\pi$
$79$	−7.05386	−	49.0607i	−0.0100458	−	0.0698704i	−0.994228	+	0.107291i	$0.965782\pi$
$80$	111.609	+	244.391i	0.155979	+	0.341546i
$81$	277.662	+	607.995i	0.380881	+	0.834012i
$82$	−20.0974	−	139.781i	−0.0270657	−	0.188246i
$83$	−541.167	−	347.787i	−0.715673	−	0.459935i	0.131457	−	0.991322i	$-0.458035\pi$
$83$	−541.167	−	347.787i	−0.715673	−	0.459935i	−0.847129	+	0.531387i	$0.821671\pi$
$84$	−209.292	+	61.4536i	−0.271852	+	0.0798231i
$85$	23.2507	−	161.712i	0.0296693	−	0.206355i
$86$	−33.2429	+	38.3643i	−0.0416822	+	0.0481039i
$87$	183.107	−	117.676i	0.225645	−	0.145013i
$88$	275.750	+	318.233i	0.334035	+	0.385497i
$89$	1145.93	+	336.477i	1.36482	+	0.400747i	0.880459	−	0.474123i	$-0.157235\pi$
$89$	1145.93	+	336.477i	1.36482	+	0.400747i	0.484359	+	0.874869i	$0.339053\pi$
$90$	−35.9806	+	78.7865i	−0.0421410	+	0.0922759i
$91$	1120.12			1.29033
$92$	−291.039	+	781.974i	−0.329815	+	0.886156i
$93$	121.946			0.135970
$94$	−115.092	+	252.017i	−0.126286	+	0.276527i
$95$	326.672	+	95.9197i	0.352799	+	0.103591i
$96$	66.9558	+	77.2711i	0.0711838	+	0.0821505i
$97$	854.509	−	549.159i	0.894456	−	0.574832i	−0.0106855	−	0.999943i	$-0.503401\pi$
$97$	854.509	−	549.159i	0.894456	−	0.574832i	0.905141	+	0.425111i	$0.139765\pi$
$98$	−327.650	+	378.128i	−0.337731	+	0.389762i
$99$	153.093	−	1064.79i	0.155419	−	1.08096i
$100$	181.448	−	53.2780i	0.181448	−	0.0532780i
$101$	686.593	+	441.246i	0.676421	+	0.434710i	0.833235	−	0.552919i	$-0.186486\pi$
$101$	686.593	+	441.246i	0.676421	+	0.434710i	−0.156814	+	0.987628i	$0.550122\pi$
$102$	−2.66734	−	18.5518i	−0.00258928	−	0.0180088i
$103$	319.485	+	699.575i	0.305629	+	0.669235i	0.998664	−	0.0516692i	$-0.0164541\pi$
$103$	319.485	+	699.575i	0.305629	+	0.669235i	−0.693035	+	0.720904i	$0.743727\pi$
$104$	−144.062	−	315.452i	−0.135831	−	0.297429i
$105$	20.5192	+	142.714i	0.0190711	+	0.132642i
$106$	19.5241	+	12.5474i	0.0178901	+	0.0114973i
$107$	−486.157	+	142.749i	−0.439239	+	0.128972i	−0.493873	−	0.869534i	$-0.664419\pi$
$107$	−486.157	+	142.749i	−0.439239	+	0.128972i	0.0546337	+	0.998506i	$0.482601\pi$
$108$	49.8124	−	346.453i	0.0443815	−	0.308680i
$109$	−200.599	+	231.504i	−0.176274	+	0.203431i	−0.837011	−	0.547187i	$-0.815699\pi$
$109$	−200.599	+	231.504i	−0.176274	+	0.203431i	0.660736	+	0.750618i	$0.270244\pi$
$110$	113.798	−	73.1333i	0.0986379	−	0.0633908i
$111$	−250.110	−	288.642i	−0.213868	−	0.246817i
$112$	−1710.77	−	502.326i	−1.44332	−	0.423798i
$113$	−499.209	+	1093.11i	−0.415590	+	0.910014i	0.579859	+	0.814717i	$0.303108\pi$
$113$	−499.209	+	1093.11i	−0.415590	+	0.910014i	−0.995449	+	0.0952975i	$0.969620\pi$
$114$	39.0583			0.0320890
$115$	484.243	+	263.978i	0.392660	+	0.214053i
$116$	1894.56			1.51643
$117$	−368.035	+	805.884i	−0.290810	+	0.636786i
$118$	−245.265	−	72.0162i	−0.191343	−	0.0561833i
$119$	710.010	+	819.395i	0.546945	+	0.631209i
$120$	37.5527	−	24.1336i	0.0285673	−	0.0183591i
$121$	−228.586	+	263.803i	−0.171740	+	0.198199i
$122$	69.4692	−	483.169i	0.0515529	−	0.358558i
$123$	178.401	−	52.3834i	0.130780	−	0.0384004i
$124$	892.950	+	573.864i	0.646687	+	0.415601i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	−238.780	−	522.856i	−0.168827	−	0.369680i
$127$	−458.736	−	1004.49i	−0.320521	−	0.701844i	0.678956	−	0.734179i	$-0.262433\pi$
$127$	−458.736	−	1004.49i	−0.320521	−	0.701844i	−0.999477	+	0.0323352i	$0.989706\pi$
$128$	167.034	+	1161.75i	0.115343	+	0.802227i
$129$	−56.2267	−	36.1347i	−0.0383759	−	0.0246627i
$130$	−106.893	+	31.3866i	−0.0721164	+	0.0211753i
$131$	36.0212	−	250.533i	0.0240243	−	0.167093i	−0.974277	−	0.225353i	$-0.927646\pi$
$131$	36.0212	−	250.533i	0.0240243	−	0.167093i	0.998301	+	0.0582605i	$0.0185554\pi$
$132$	−176.450	+	203.634i	−0.116349	+	0.134273i
$133$	−1900.76	+	1221.54i	−1.23922	+	0.796401i
$134$	−164.039	−	189.311i	−0.105752	−	0.122045i
$135$	−221.987	−	65.1814i	−0.141523	−	0.0415550i
$136$	139.445	−	305.341i	0.0879212	−	0.192521i
$137$	2364.05			1.47427			0.737134	−	0.675746i	$-0.236179\pi$
$137$	2364.05			1.47427			0.737134	+	0.675746i	$0.236179\pi$
$138$	61.8344	+	13.4060i	0.0381427	+	0.00826955i
$139$	−3056.66			−1.86520			−0.932598	−	0.360916i	$-0.882464\pi$
$139$	−3056.66			−1.86520			−0.932598	+	0.360916i	$0.882464\pi$
$140$	−521.343	+	1141.58i	−0.314725	+	0.689151i
$141$	−350.003	−	102.770i	−0.209046	−	0.0613816i
$142$	102.816	+	118.656i	0.0607613	+	0.0701222i
$143$	1164.00	−	748.058i	0.680690	−	0.437453i
$144$	923.508	−	1065.79i	0.534438	−	0.616774i
$145$	178.221	−	1239.55i	0.102072	−	0.709926i
$146$	−154.458	+	45.3530i	−0.0875550	+	0.0257085i
$147$	−554.184	−	356.152i	−0.310941	−	0.199830i
$148$	−473.112	−	3290.57i	−0.262767	−	1.82759i
$149$	−1320.86	−	2892.29i	−0.726238	−	1.59024i	−0.804950	−	0.593342i	$-0.797808\pi$
$149$	−1320.86	−	2892.29i	−0.726238	−	1.59024i	0.0787124	−	0.996897i	$-0.474919\pi$
$150$	−5.95710	−	13.0442i	−0.00324264	−	0.00710038i
$151$	195.132	+	1357.17i	0.105163	+	0.731424i	0.972365	+	0.233467i	$0.0750072\pi$
$151$	195.132	+	1357.17i	0.105163	+	0.731424i	−0.867202	+	0.497957i	$0.834084\pi$
$152$	588.480	+	378.193i	0.314027	+	0.201813i
$153$	−822.811	+	241.599i	−0.434773	+	0.127661i
$154$	−127.757	+	888.573i	−0.0668506	+	0.464956i
$155$	459.460	−	530.245i	0.238095	−	0.274776i
$156$	186.682	−	119.973i	0.0958108	−	0.0615739i
$157$	−361.388	−	417.064i	−0.183706	−	0.212008i	0.656425	−	0.754391i	$-0.272068\pi$
$157$	−361.388	−	417.064i	−0.183706	−	0.212008i	−0.840131	+	0.542383i	$0.817522\pi$
$158$	−31.3901	−	9.21695i	−0.0158054	−	0.00464089i
$159$	−12.6938	+	27.7956i	−0.00633136	+	0.0138637i
$160$	588.261			0.290663
$161$	−3428.43	+	1281.46i	−1.67825	+	0.627289i
$162$	441.172			0.213961
$163$	1323.05	−	2897.07i	0.635761	−	1.39212i	−0.267722	−	0.963496i	$-0.586271\pi$
$163$	1323.05	−	2897.07i	0.635761	−	1.39212i	0.903482	−	0.428625i	$-0.141002\pi$
$164$	1552.85	+	455.958i	0.739374	+	0.217100i
$165$	116.633	+	134.601i	0.0550294	+	0.0635073i
$166$	−357.195	+	229.555i	−0.167010	+	0.107331i
$167$	−1389.19	+	1603.21i	−0.643705	+	0.742875i	−0.980025	−	0.198872i	$-0.936272\pi$
$167$	−1389.19	+	1603.21i	−0.643705	+	0.742875i	0.336320	+	0.941748i	$0.390818\pi$
$168$	−42.1593	+	293.225i	−0.0193611	+	0.134659i
$169$	1014.63	−	297.922i	0.461825	−	0.135604i
$170$	−90.7164	−	58.2999i	−0.0409273	−	0.0263024i
$171$	−254.328	−	1768.89i	−0.113736	−	0.791054i
$172$	−241.674	−	529.192i	−0.107136	−	0.234596i
$173$	−208.267	−	456.042i	−0.0915276	−	0.200418i	0.858332	−	0.513095i	$-0.171501\pi$
$173$	−208.267	−	456.042i	−0.0915276	−	0.200418i	−0.949859	+	0.312678i	$0.898774\pi$
$174$	−20.4457	−	142.203i	−0.00890794	−	0.0619561i
$175$	697.858	+	448.486i	0.301446	+	0.193728i
$176$	−2113.26	+	620.510i	−0.905074	+	0.265754i
$177$	47.8971	−	333.131i	0.0203399	−	0.141467i
$178$	516.226	−	595.757i	0.217375	−	0.250865i
$179$	−1092.51	+	702.115i	−0.456191	+	0.293176i	−0.748484	−	0.663153i	$-0.769218\pi$
$179$	−1092.51	+	702.115i	−0.456191	+	0.293176i	0.292293	+	0.956329i	$0.405582\pi$
$180$	−650.029	−	750.174i	−0.269168	−	0.310637i
$181$	4330.89	+	1271.66i	1.77852	+	0.522221i	0.995065	−	0.0992266i	$-0.0316369\pi$
$181$	4330.89	+	1271.66i	1.77852	+	0.522221i	0.783456	+	0.621447i	$0.213455\pi$
$182$	307.128	−	672.517i	0.125087	−	0.273902i
$183$	642.700			0.259616
$184$	801.833	+	800.714i	0.321260	+	0.320812i
$185$	−2197.42			−0.873283
$186$	33.4368	−	73.2163i	0.0131812	−	0.0288628i
$187$	1285.05	+	377.325i	0.502525	+	0.147555i
$188$	−2079.27	−	2399.60i	−0.806628	−	0.930898i
$189$	1291.65	−	830.090i	0.497108	−	0.319472i
$190$	147.161	−	169.833i	0.0561905	−	0.0648473i
$191$	−313.992	+	2183.86i	−0.118951	+	0.827324i	0.839763	+	0.542953i	$0.182694\pi$
$191$	−313.992	+	2183.86i	−0.118951	+	0.827324i	−0.958714	+	0.284371i	$0.908215\pi$
$192$	−293.691	+	86.2354i	−0.110392	+	0.0324141i
$193$	−2178.99	−	1400.35i	−0.812681	−	0.522279i	0.0670501	−	0.997750i	$-0.478641\pi$
$193$	−2178.99	−	1400.35i	−0.812681	−	0.522279i	−0.879731	+	0.475471i	$0.842278\pi$
$194$	−95.4142	−	663.621i	−0.0353110	−	0.245594i
$195$	−60.9334	−	133.426i	−0.0223771	−	0.0489990i
$196$	−2381.99	−	5215.84i	−0.868074	−	1.90082i
$197$	271.736	+	1889.96i	0.0982760	+	0.683525i	0.978086	+	0.208200i	$0.0667604\pi$
$197$	271.736	+	1889.96i	0.0982760	+	0.683525i	−0.879810	+	0.475325i	$0.842331\pi$
$198$	−597.318	−	383.873i	−0.214392	−	0.137781i
$199$	−1494.82	+	438.918i	−0.532487	+	0.156352i	−0.536912	−	0.843638i	$-0.680409\pi$
$199$	−1494.82	+	438.918i	−0.532487	+	0.156352i	0.00442580	+	0.999990i	$0.498591\pi$
$200$	36.5506	−	254.215i	0.0129226	−	0.0898786i
$201$	215.980	−	249.254i	0.0757912	−	0.0874677i
$202$	453.182	−	291.243i	0.157850	−	0.101444i
$203$	5442.35	+	6280.81i	1.88167	+	2.17156i
$204$	206.095	+	60.5150i	0.0707331	+	0.0207691i
$205$	444.395	−	973.090i	0.151404	−	0.331529i
$206$	507.624			0.171689
$207$	204.504	−	2887.67i	0.0686667	−	0.969600i
$208$	1813.90			0.604669
$209$	−1159.43	+	2538.80i	−0.383730	+	0.840252i
$210$	91.3113	+	26.8114i	0.0300051	+	0.00881031i
$211$	−1754.42	−	2024.71i	−0.572414	−	0.660601i	0.393542	−	0.919307i	$-0.371249\pi$
$211$	−1754.42	−	2024.71i	−0.572414	−	0.660601i	−0.965956	+	0.258706i	$0.916704\pi$
$212$	−223.753	+	143.797i	−0.0724878	+	0.0465851i
$213$	−135.371	+	156.226i	−0.0435467	+	0.0502556i
$214$	−47.5947	+	331.028i	−0.0152033	+	0.105741i
$215$	−368.968	+	108.339i	−0.117039	+	0.0343657i
$216$	−399.896	−	256.998i	−0.125970	−	0.0809560i
$217$	662.642	+	4608.78i	0.207295	+	1.44177i
$218$	83.9915	+	183.916i	0.0260946	+	0.0571392i
$219$	−88.0474	−	192.797i	−0.0271676	−	0.0594886i
$220$	220.625	+	1534.48i	0.0676114	+	0.470247i
$221$	−927.911	−	596.332i	−0.282435	−	0.181510i
$222$	−241.879	+	71.0220i	−0.0731254	+	0.0214715i
$223$	−538.229	+	3743.46i	−0.161625	+	1.12413i	0.733945	+	0.679209i	$0.237677\pi$
$223$	−538.229	+	3743.46i	−0.161625	+	1.12413i	−0.895570	+	0.444920i	$0.853232\pi$
$224$	−2556.52	+	2950.38i	−0.762565	+	0.880047i
$225$	−551.963	+	354.725i	−0.163544	+	0.105104i
$226$	519.425	+	599.448i	0.152883	+	0.176437i
$227$	3170.34	+	930.895i	0.926972	+	0.272184i	0.710169	−	0.704032i	$-0.248619\pi$
$227$	3170.34	+	930.895i	0.926972	+	0.272184i	0.216804	+	0.976215i	$0.430437\pi$
$228$	−185.949	+	407.171i	−0.0540121	+	0.118270i
$229$	−4690.01			−1.35338			−0.676691	−	0.736267i	$-0.736587\pi$
$229$	−4690.01			−1.35338			−0.676691	+	0.736267i	$0.736587\pi$
$230$	291.267	−	218.358i	0.0835026	−	0.0626003i
$231$	−1181.96			−0.336654
$232$	1068.87	−	2340.50i	0.302477	−	0.662332i
$233$	1484.96	+	436.024i	0.417524	+	0.122596i	0.483745	−	0.875209i	$-0.339276\pi$
$233$	1484.96	+	436.024i	0.417524	+	0.122596i	−0.0662215	+	0.997805i	$0.521094\pi$
$234$	382.939	+	441.935i	0.106981	+	0.123462i
$235$	−1765.58	+	1134.67i	−0.490101	+	0.314969i
$236$	1918.40	−	2213.95i	0.529141	−	0.610661i
$237$	6.13008	−	42.6357i	0.00168013	−	0.0116856i
$238$	686.643	−	201.617i	0.187010	−	0.0549112i
$239$	5189.70	+	3335.22i	1.40458	+	0.902666i	0.999930	−	0.0118068i	$-0.00375832\pi$
$239$	5189.70	+	3335.22i	1.40458	+	0.902666i	0.404646	+	0.914473i	$0.367395\pi$
$240$	33.2283	+	231.108i	0.00893700	+	0.0621582i
$241$	308.986	+	676.586i	0.0825874	+	0.180841i	0.946420	−	0.322937i	$-0.104670\pi$
$241$	308.986	+	676.586i	0.0825874	+	0.180841i	−0.863833	+	0.503778i	$0.831943\pi$
$242$	95.7100	+	209.576i	0.0254234	+	0.0556696i
$243$	260.465	+	1811.57i	0.0687606	+	0.478241i
$244$	4706.16	+	3024.47i	1.23476	+	0.793531i
$245$	−3636.63	+	1067.81i	−0.948309	+	0.278449i
$246$	17.4655	−	121.475i	0.00452666	−	0.0314836i
$247$	1505.27	−	1737.17i	0.387764	−	0.447504i
$248$	1212.72	−	779.367i	0.310515	−	0.199556i
$249$	−366.094	−	422.495i	−0.0931738	−	0.107528i
$250$	−79.1636	−	23.2445i	−0.0200270	−	0.00588045i
$251$	1997.33	−	4373.54i	0.502272	−	1.09982i	−0.473452	−	0.880820i	$-0.656992\pi$
$251$	1997.33	−	4373.54i	0.502272	−	1.09982i	0.975724	−	0.219003i	$-0.0702806\pi$
$252$	6587.40			1.64669
$253$	−2706.93	+	3621.30i	−0.672661	+	0.899879i
$254$	−728.877			−0.180054
$255$	58.9803	−	129.149i	0.0144843	−	0.0317162i
$256$	−1960.28	−	575.590i	−0.478584	−	0.140525i
$257$	1550.70	+	1789.60i	0.376381	+	0.434367i	0.912061	−	0.410054i	$-0.134490\pi$
$257$	1550.70	+	1789.60i	0.376381	+	0.434367i	−0.535680	+	0.844421i	$0.679945\pi$
$258$	−37.1122	+	23.8505i	−0.00895543	+	0.00575531i
$259$	9549.74	−	11021.0i	2.29109	−	2.64406i
$260$	181.700	−	1263.75i	0.0433406	−	0.301441i
$261$	−6307.00	+	1851.90i	−1.49576	+	0.439195i
$262$	−140.543	−	90.3213i	−0.0331403	−	0.0212980i
$263$	−23.8802	−	166.091i	−0.00559893	−	0.0389414i	0.986830	−	0.161758i	$-0.0517164\pi$
$263$	−23.8802	−	166.091i	−0.00559893	−	0.0389414i	−0.992429	+	0.122817i	$0.960807\pi$
$264$	152.016	+	332.868i	0.0354391	+	0.0776008i
$265$	73.0337	+	159.921i	0.0169299	+	0.0370713i
$266$	212.239	+	1476.15i	0.0489217	+	0.340258i
$267$	873.140	+	561.133i	0.200132	+	0.128617i
$268$	2754.46	−	808.784i	0.627820	−	0.184345i
$269$	−41.2800	+	287.109i	−0.00935646	+	0.0650756i	−0.993965	−	0.109700i	$-0.965011\pi$
$269$	−41.2800	+	287.109i	−0.00935646	+	0.0650756i	0.984608	+	0.174776i	$0.0559200\pi$
$270$	−100.002	+	115.409i	−0.0225405	+	0.0260131i
$271$	−1431.07	+	919.692i	−0.320779	+	0.206152i	−0.691114	−	0.722746i	$-0.742880\pi$
$271$	−1431.07	+	919.692i	−0.320779	+	0.206152i	0.370334	+	0.928899i	$0.379243\pi$
$272$	1149.78	+	1326.91i	0.256307	+	0.295794i
$273$	933.996	+	274.246i	0.207062	+	0.0607990i
$274$	648.206	−	1419.37i	0.142918	−	0.312947i
$275$	1024.71			0.224700
$276$	−434.135	+	580.782i	−0.0946807	+	0.126663i
$277$	−5533.30			−1.20023			−0.600115	−	0.799914i	$-0.704879\pi$
$277$	−5533.30			−1.20023			−0.600115	+	0.799914i	$0.704879\pi$
$278$	−838.113	+	1835.21i	−0.180815	+	0.395930i
$279$	−3533.57	−	1037.55i	−0.758241	−	0.222640i
$280$	1116.15	+	1288.11i	0.238224	+	0.274926i
$281$	−5124.78	+	3293.50i	−1.08797	+	0.699194i	−0.956384	−	0.292111i	$-0.905642\pi$
$281$	−5124.78	+	3293.50i	−1.08797	+	0.699194i	−0.131583	+	0.991305i	$0.542006\pi$
$282$	−157.671	+	181.962i	−0.0332949	+	0.0384244i
$283$	−413.583	+	2876.54i	−0.0868727	+	0.604213i	0.899155	+	0.437631i	$0.144182\pi$
$283$	−413.583	+	2876.54i	−0.0868727	+	0.604213i	−0.986028	+	0.166582i	$0.946727\pi$
$284$	−1726.43	+	506.926i	−0.360722	+	0.105917i
$285$	248.907	+	159.963i	0.0517332	+	0.0332469i
$286$	−129.972	−	903.976i	−0.0268721	−	0.186899i
$287$	2949.17	+	6457.77i	0.606564	+	1.32819i
$288$	−1282.70	−	2808.72i	−0.262444	−	0.574672i
$289$	547.250	+	3806.20i	0.111388	+	0.774721i
$290$	−695.358	−	446.879i	−0.140803	−	0.0904885i
$291$	846.975	−	248.694i	0.170621	−	0.0500987i
$292$	262.553	−	1826.09i	0.0526189	−	0.365973i
$293$	2871.08	−	3313.40i	0.572458	−	0.660652i	−0.393508	−	0.919321i	$-0.628739\pi$
$293$	2871.08	−	3313.40i	0.572458	−	0.660652i	0.965966	+	0.258669i	$0.0832840\pi$
$294$	−365.786	+	235.076i	−0.0725615	+	0.0466324i
$295$	−1268.06	−	1463.41i	−0.250268	−	0.288825i
$296$	−4332.00	−	1271.99i	−0.850651	−	0.249774i
$297$	787.882	−	1725.22i	0.153931	−	0.337062i
$298$	−2098.70			−0.407967
$299$	2979.29	−	2233.51i	0.576243	−	0.431998i
$300$	164.343			0.0316278
$301$	1060.13	−	2321.36i	0.203006	−	0.444521i
$302$	868.347	+	254.970i	0.165456	+	0.0485823i
$303$	464.473	+	536.031i	0.0880637	+	0.101631i
$304$	−3078.06	+	1978.15i	−0.580719	+	0.373205i
$305$	2421.52	−	2794.58i	0.454609	−	0.524647i
$306$	−80.5531	+	560.259i	−0.0150487	+	0.104666i
$307$	−7373.42	+	2165.03i	−1.37076	+	0.402492i	−0.882544	−	0.470231i	$-0.844171\pi$
$307$	−7373.42	+	2165.03i	−1.37076	+	0.402492i	−0.488217	+	0.872722i	$0.662353\pi$
$308$	−8654.87	−	5562.15i	−1.60116	−	1.02900i
$309$	95.1170	+	661.553i	0.0175114	+	0.121794i
$310$	−192.378	−	421.248i	−0.0352462	−	0.0771784i
$311$	−1587.18	−	3475.43i	−0.289391	−	0.633677i	0.707973	−	0.706239i	$-0.249610\pi$
$311$	−1587.18	−	3475.43i	−0.289391	−	0.633677i	−0.997364	+	0.0725619i	$0.976883\pi$
$312$	−42.8902	−	298.308i	−0.00778262	−	0.0541293i
$313$	−7085.52	−	4553.59i	−1.27954	−	0.822313i	−0.288712	−	0.957416i	$-0.593227\pi$
$313$	−7085.52	−	4553.59i	−1.27954	−	0.822313i	−0.990832	+	0.135103i	$0.956863\pi$
$314$	−349.494	+	102.621i	−0.0628124	+	0.0184434i
$315$	619.673	−	4309.92i	0.110840	−	0.770910i
$316$	245.526	−	283.352i	0.0437085	−	0.0504423i
$317$	5786.06	−	3718.47i	1.02516	−	0.658834i	0.0838902	−	0.996475i	$-0.473266\pi$
$317$	5786.06	−	3718.47i	1.02516	−	0.658834i	0.941275	+	0.337641i	$0.109629\pi$
$318$	13.2079	+	15.2427i	0.00232912	+	0.00268795i
$319$	9850.14	+	2892.26i	1.72885	+	0.507635i
$320$	−731.579	+	1601.94i	−0.127802	+	0.279847i
$321$	−440.326			−0.0765626
$322$	−170.660	+	2409.79i	−0.0295358	+	0.417057i
$323$	2224.93			0.383277
$324$	−2100.33	+	4599.08i	−0.360139	+	0.788594i
$325$	−809.740	−	237.761i	−0.138204	−	0.0405804i
$326$	−1376.62	−	1588.71i	−0.233878	−	0.269909i
$327$	−223.947	+	143.922i	−0.0378725	+	0.0243392i
$328$	1439.36	−	1661.11i	0.242303	−	0.279633i
$329$	1982.17	−	13786.3i	0.332159	−	2.31022i
$330$	112.794	−	33.1194i	0.0188155	−	0.00552474i
$331$	−3930.39	−	2525.91i	−0.652670	−	0.419445i	0.171971	−	0.985102i	$-0.444986\pi$
$331$	−3930.39	−	2525.91i	−0.652670	−	0.419445i	−0.824641	+	0.565657i	$0.808623\pi$
$332$	−692.510	−	4816.51i	−0.114477	−	0.796206i
$333$	4791.46	+	10491.8i	0.788499	+	1.72657i
$334$	581.659	+	1273.66i	0.0952903	+	0.208657i
$335$	−270.050	−	1878.24i	−0.0440430	−	0.306326i
$336$	−1303.51	−	837.717i	−0.211644	−	0.136015i
$337$	−4215.56	+	1237.80i	−0.681414	+	0.200081i	−0.604079	−	0.796924i	$-0.706459\pi$
$337$	−4215.56	+	1237.80i	−0.681414	+	0.200081i	−0.0773342	+	0.997005i	$0.524641\pi$
$338$	99.3321	−	690.870i	0.0159851	−	0.111179i
$339$	−683.894	+	789.255i	−0.109569	+	0.126450i
$340$	1039.64	−	668.137i	0.165831	−	0.106573i
$341$	3766.52	+	4346.80i	0.598148	+	0.690300i
$342$	−1131.77	−	332.318i	−0.178945	−	0.0525430i
$343$	5720.89	−	12527.0i	0.900580	−	1.97199i
$344$	−790.097			−0.123835
$345$	339.148	+	338.675i	0.0529250	+	0.0528511i
$346$	−330.912			−0.0514160
$347$	36.1765	−	79.2156i	0.00559671	−	0.0122551i	−0.906813	−	0.421533i	$-0.861492\pi$
$347$	36.1765	−	79.2156i	0.00559671	−	0.0122551i	0.912410	+	0.409278i	$0.134219\pi$
$348$	1579.76	+	463.859i	0.243344	+	0.0714524i
$349$	2209.50	+	2549.90i	0.338888	+	0.391098i	0.899456	−	0.437011i	$-0.143963\pi$
$349$	2209.50	+	2549.90i	0.338888	+	0.391098i	−0.560568	+	0.828108i	$0.689417\pi$
$350$	460.617	−	296.021i	0.0703458	−	0.0452085i
$351$	−1022.89	+	1180.48i	−0.155549	+	0.179514i
$352$	−686.298	+	4773.31i	−0.103920	+	0.722779i
$353$	−4125.34	+	1211.31i	−0.622010	+	0.182639i	−0.577527	−	0.816371i	$-0.695982\pi$
$353$	−4125.34	+	1211.31i	−0.622010	+	0.182639i	−0.0444831	+	0.999010i	$0.514164\pi$
$354$	−186.878	−	120.099i	−0.0280578	−	0.0180317i
$355$	169.261	+	1177.24i	0.0253055	+	0.176003i
$356$	3752.93	+	8217.78i	0.558722	+	1.22343i
$357$	391.415	+	857.079i	0.0580276	+	0.127063i
$358$	121.990	+	848.457i	0.0180094	+	0.125258i
$359$	−7928.76	−	5095.51i	−1.16564	−	0.749110i	−0.192946	−	0.981209i	$-0.561804\pi$
$359$	−7928.76	−	5095.51i	−1.16564	−	0.749110i	−0.972692	+	0.232099i	$0.925441\pi$
$360$	−1293.48	+	379.799i	−0.189367	+	0.0556033i
$361$	316.278	−	2199.76i	0.0461114	−	0.320712i
$362$	1951.00	−	2251.58i	0.283266	−	0.326907i
$363$	−255.193	+	164.002i	−0.0368984	+	0.0237132i
$364$	5548.61	+	6403.43i	0.798972	+	0.922063i
$365$	−1170.06	−	343.560i	−0.167791	−	0.0492678i
$366$	176.224	−	385.876i	0.0251676	−	0.0551094i
$367$	6105.76			0.868441			0.434221	−	0.900807i	$-0.357024\pi$
$367$	6105.76			0.868441			0.434221	+	0.900807i	$0.357024\pi$
$368$	−5551.93	+	2075.18i	−0.786452	+	0.293957i
$369$	−5615.13			−0.792174
$370$	−602.516	+	1319.33i	−0.0846576	+	0.185374i
$371$	−1119.47	−	328.706i	−0.156658	−	0.0459988i
$372$	604.072	+	697.136i	0.0841926	+	0.0971635i
$373$	−6382.30	+	4101.66i	−0.885960	+	0.569372i	−0.902596	−	0.430490i	$-0.858341\pi$
$373$	−6382.30	+	4101.66i	−0.885960	+	0.569372i	0.0166353	+	0.999862i	$0.494705\pi$
$374$	578.896	−	668.082i	0.0800374	−	0.0923681i
$375$	15.4596	−	107.524i	0.00212889	−	0.0148067i
$376$	−4137.48	+	1214.87i	−0.567485	+	0.166629i
$377$	−7112.61	−	4570.99i	−0.971665	−	0.624451i
$378$	−144.225	−	1003.11i	−0.0196247	−	0.136493i
$379$	−4306.36	−	9429.62i	−0.583649	−	1.27801i	−0.939205	−	0.343358i	$-0.888436\pi$
$379$	−4306.36	−	9429.62i	−0.583649	−	1.27801i	0.355556	−	0.934655i	$-0.384292\pi$
$380$	1069.85	+	2342.65i	0.144427	+	0.316251i
$381$	−136.575	−	949.898i	−0.0183647	−	0.127729i
$382$	1225.09	+	787.320i	0.164087	+	0.105452i
$383$	846.308	−	248.499i	0.112910	−	0.0331532i	−0.224790	−	0.974407i	$-0.572170\pi$
$383$	846.308	−	248.499i	0.112910	−	0.0331532i	0.337699	+	0.941254i	$0.390351\pi$
$384$	−145.159	+	1009.61i	−0.0192907	+	0.134170i
$385$	−4453.29	+	5139.38i	−0.589509	+	0.680329i
$386$	−1438.23	+	924.297i	−0.189648	+	0.121880i
$387$	1321.81	+	1525.45i	0.173621	+	0.200369i
$388$	7372.29	+	2164.70i	0.964617	+	0.283237i
$389$	716.215	−	1568.29i	0.0933511	−	0.204410i	−0.857196	−	0.514990i	$-0.827796\pi$
$389$	716.215	−	1568.29i	0.0933511	−	0.204410i	0.950547	+	0.310579i	$0.100523\pi$
$390$	−96.8159			−0.0125704
$391$	3522.35	+	763.666i	0.455583	+	0.0987730i
$392$	−7787.38			−1.00337
$393$	91.3755	−	200.084i	0.0117285	−	0.0256817i
$394$	1209.24	+	355.065i	0.154621	+	0.0454007i
$395$	−162.291	−	187.294i	−0.0206728	−	0.0238577i
$396$	6845.47	−	4399.32i	0.868681	−	0.558268i
$397$	9178.86	−	10593.0i	1.16039	−	1.33916i	0.229735	−	0.973253i	$-0.426214\pi$
$397$	9178.86	−	10593.0i	1.16039	−	1.33916i	0.930652	−	0.365905i	$-0.119240\pi$
$398$	−146.342	+	1017.83i	−0.0184309	+	0.128189i
$399$	−1884.00	+	553.193i	−0.236386	+	0.0694093i
$400$	1130.10	+	726.269i	0.141262	+	0.0907837i
$401$	−477.455	−	3320.78i	−0.0594588	−	0.413545i	−0.997713	−	0.0675976i	$-0.978467\pi$
$401$	−477.455	−	3320.78i	−0.0594588	−	0.413545i	0.938254	−	0.345948i	$-0.112443\pi$
$402$	−90.4314	−	198.017i	−0.0112197	−	0.0245677i
$403$	−1967.77	−	4308.82i	−0.243230	−	0.532600i
$404$	878.605	+	6110.83i	0.108199	+	0.752538i
$405$	2811.46	+	1806.81i	0.344944	+	0.221682i
$406$	5263.24	−	1545.43i	0.643375	−	0.188912i
$407$	2563.63	−	17830.4i	0.312222	−	2.17155i
$408$	191.033	−	220.464i	0.0231802	−	0.0267514i
$409$	−10027.9	+	6444.55i	−1.21234	+	0.779126i	−0.981049	−	0.193758i	$-0.937932\pi$
$409$	−10027.9	+	6444.55i	−1.21234	+	0.779126i	−0.231294	+	0.972884i	$0.574296\pi$
$410$	−462.391	−	533.628i	−0.0556973	−	0.0642781i
$411$	1971.24	+	578.807i	0.236579	+	0.0694658i
$412$	−2416.70	+	5291.82i	−0.288985	+	0.632790i
$413$	12850.5			1.53107
$414$	−1677.68	−	914.563i	−0.199163	−	0.108571i
$415$	−3216.43			−0.380454
$416$	1649.86	−	3612.68i	0.194449	−	0.425784i
$417$	−2548.75	−	748.382i	−0.299312	−	0.0878859i
$418$	1206.38	+	1392.24i	0.141163	+	0.162911i
$419$	−6191.98	+	3979.34i	−0.721952	+	0.463970i	−0.849315	−	0.527886i	$-0.822985\pi$
$419$	−6191.98	+	3979.34i	−0.721952	+	0.463970i	0.127363	+	0.991856i	$0.459349\pi$
$420$	−714.216	+	824.249i	−0.0829766	+	0.0957601i
$421$	−238.211	+	1656.79i	−0.0275764	+	0.191798i	−0.998953	−	0.0457461i	$-0.985433\pi$
$421$	−238.211	+	1656.79i	−0.0275764	+	0.191798i	0.971377	+	0.237545i	$0.0763426\pi$
$422$	−1696.68	+	498.191i	−0.195718	+	0.0574681i
$423$	9267.44	+	5955.82i	1.06524	+	0.684591i
$424$	51.4074	+	357.546i	0.00588812	+	0.0409528i
$425$	−339.342	−	743.056i	−0.0387306	−	0.0848082i
$426$	56.6803	+	124.112i	0.00644640	+	0.0141157i
$427$	3492.36	+	24289.9i	0.395801	+	2.75286i
$428$	−3224.28	−	2072.12i	−0.364139	−	0.234018i
$429$	1153.74	−	338.768i	0.129844	−	0.0381256i
$430$	−36.1219	+	251.233i	−0.00405105	+	0.0281757i
$431$	7259.32	−	8377.70i	0.811297	−	0.936287i	−0.187646	−	0.982237i	$-0.560086\pi$
$431$	7259.32	−	8377.70i	0.811297	−	0.936287i	0.998944	+	0.0459495i	$0.0146313\pi$
$432$	2091.67	−	1344.23i	0.232952	−	0.149709i
$433$	4996.20	+	5765.92i	0.554508	+	0.639937i	0.961928	−	0.273305i	$-0.0881167\pi$
$433$	4996.20	+	5765.92i	0.554508	+	0.639937i	−0.407419	+	0.913241i	$0.633571\pi$
$434$	2948.79	+	865.844i	0.326144	+	0.0957646i
$435$	452.095	−	989.950i	0.0498306	−	0.109114i
$436$	−2317.13			−0.254520
$437$	−2619.88	+	7039.17i	−0.286787	+	0.770548i
$438$	−139.897			−0.0152615
$439$	−4141.97	+	9069.65i	−0.450309	+	0.986039i	0.539282	+	0.842126i	$0.318696\pi$
$439$	−4141.97	+	9069.65i	−0.450309	+	0.986039i	−0.989590	+	0.143913i	$0.954031\pi$
$440$	2020.13	+	593.163i	0.218877	+	0.0642680i
$441$	13028.0	+	15035.2i	1.40676	+	1.62349i
$442$	−612.463	+	393.606i	−0.0659093	+	0.0423573i
$443$	−3670.66	+	4236.16i	−0.393675	+	0.454326i	−0.917639	−	0.397415i	$-0.869907\pi$
$443$	−3670.66	+	4236.16i	−0.393675	+	0.454326i	0.523964	+	0.851741i	$0.324453\pi$
$444$	411.153	−	2859.63i	0.0439470	−	0.305658i
$445$	5729.67	−	1682.38i	0.610365	−	0.179219i
$446$	2099.99	+	1349.58i	0.222954	+	0.143284i
$447$	−393.247	−	2735.10i	−0.0416107	−	0.289408i
$448$	−4855.02	−	10631.0i	−0.512005	−	1.12113i
$449$	−7710.54	−	16883.7i	−0.810430	−	1.77459i	−0.605552	−	0.795806i	$-0.707047\pi$
$449$	−7710.54	−	16883.7i	−0.810430	−	1.77459i	−0.204878	−	0.978787i	$-0.565680\pi$
$450$	61.6320	+	428.660i	0.00645636	+	0.0449050i
$451$	7377.45	+	4741.20i	0.770268	+	0.495021i
$452$	−8721.94	+	2560.99i	−0.907623	+	0.266502i
$453$	−169.577	+	1179.44i	−0.0175882	+	0.122328i
$454$	1428.19	−	1648.22i	0.147639	−	0.170385i
$455$	4711.52	−	3027.91i	0.485449	−	0.311979i
$456$	398.101	+	459.433i	0.0408833	+	0.0471818i
$457$	4659.04	+	1368.02i	0.476895	+	0.140029i	0.511341	−	0.859378i	$-0.329149\pi$
$457$	4659.04	+	1368.02i	0.476895	+	0.140029i	−0.0344469	+	0.999407i	$0.510967\pi$
$458$	−1285.97	+	2815.87i	−0.131199	+	0.287286i
$459$	−1511.93			−0.153749
$460$	889.645	+	4075.93i	0.0901737	+	0.413133i
$461$	3719.98			0.375828			0.187914	−	0.982186i	$-0.439827\pi$
$461$	3719.98			0.375828			0.187914	+	0.982186i	$0.439827\pi$
$462$	−324.084	+	709.645i	−0.0326358	+	0.0714625i
$463$	−8237.48	−	2418.74i	−0.826843	−	0.242783i	−0.159183	−	0.987249i	$-0.550886\pi$
$463$	−8237.48	−	2418.74i	−0.826843	−	0.242783i	−0.667660	+	0.744466i	$0.732704\pi$
$464$	8813.25	+	10171.0i	0.881777	+	1.01763i
$465$	512.938	−	329.646i	0.0511547	−	0.0328752i
$466$	668.953	−	772.013i	0.0664992	−	0.0767442i
$467$	−582.989	+	4054.78i	−0.0577677	+	0.401783i	0.940337	+	0.340245i	$0.110510\pi$
$467$	−582.989	+	4054.78i	−0.0577677	+	0.401783i	−0.998105	+	0.0615388i	$0.980399\pi$
$468$	−6430.13	+	1888.06i	−0.635113	+	0.186486i
$469$	10593.8	+	6808.21i	1.04302	+	0.670307i
$470$	197.144	+	1371.17i	0.0193480	+	0.134569i
$471$	−199.226	−	436.244i	−0.0194901	−	0.0426774i
$472$	−1652.75	−	3619.01i	−0.161173	−	0.352920i
$473$	−448.631	−	3120.30i	−0.0436111	−	0.303322i
$474$	−23.9175	−	15.3709i	−0.00231766	−	0.00148947i
$475$	1633.36	−	479.598i	0.157776	−	0.0463273i
$476$	−1167.18	+	8117.90i	−0.112390	+	0.781687i
$477$	604.314	−	697.415i	0.0580076	−	0.0669444i
$478$	3425.44	−	2201.39i	0.327774	−	0.210647i
$479$	−2599.76	−	3000.29i	−0.247988	−	0.286193i	0.618085	−	0.786111i	$-0.287909\pi$
$479$	−2599.76	−	3000.29i	−0.247988	−	0.286193i	−0.866073	+	0.499918i	$0.833363\pi$
$480$	490.514	+	144.028i	0.0466433	+	0.0136957i
$481$	−6162.95	+	13495.0i	−0.584213	+	1.27925i
$482$	490.943			0.0463938
$483$	−3172.50	+	229.128i	−0.298869	+	0.0215853i
$484$	−2640.42			−0.247973
$485$	2109.80	−	4619.82i	0.197528	−	0.432526i
$486$	1159.08	+	340.337i	0.108183	+	0.0317655i
$487$	−9286.68	−	10717.4i	−0.864106	−	0.997232i	−0.999979	−	0.00650563i	$-0.997929\pi$
$487$	−9286.68	−	10717.4i	−0.864106	−	0.997232i	0.135872	−	0.990726i	$-0.456616\pi$
$488$	6391.46	−	4107.54i	0.592885	−	0.381024i
$489$	1812.51	−	2091.75i	0.167617	−	0.193440i
$490$	−356.025	+	2476.21i	−0.0328237	+	0.228294i
$491$	8776.64	−	2577.05i	0.806689	−	0.236865i	0.147714	−	0.989030i	$-0.452808\pi$
$491$	8776.64	−	2577.05i	0.806689	−	0.236865i	0.658975	+	0.752165i	$0.270990\pi$
$492$	1183.19	+	760.390i	0.108419	+	0.0696769i
$493$	−1164.67	−	8100.47i	−0.106398	−	0.740014i
$494$	−630.261	−	1380.08i	−0.0574024	−	0.125694i
$495$	−2234.38	−	4892.62i	−0.202885	−	0.444256i
$496$	1073.07	+	7463.37i	0.0971417	+	0.675635i
$497$	−6639.93	−	4267.22i	−0.599279	−	0.385133i
$498$	−354.046	+	103.957i	−0.0318578	+	0.00935428i
$499$	−1072.58	+	7459.98i	−0.0962233	+	0.669248i	0.883432	+	0.468560i	$0.155227\pi$
$499$	−1072.58	+	7459.98i	−0.0962233	+	0.669248i	−0.979655	+	0.200688i	$0.935682\pi$
$500$	619.199	−	714.593i	0.0553828	−	0.0639152i
$501$	−1550.88	+	996.692i	−0.138300	+	0.0888801i
$502$	−2078.21	−	2398.39i	−0.184771	−	0.213238i
$503$	3974.35	+	1166.97i	0.352301	+	0.103445i	0.453095	−	0.891462i	$-0.350320\pi$
$503$	3974.35	+	1166.97i	0.352301	+	0.103445i	−0.100794	+	0.994907i	$0.532138\pi$
$504$	3716.46	−	8137.91i	0.328461	−	0.719229i
$505$	4080.77			0.359588
$506$	1432.00	+	2618.17i	0.125811	+	0.230023i
$507$	918.978			0.0804995
$508$	3470.03	−	7598.32i	0.303067	−	0.663624i
$509$	2581.14	+	757.890i	0.224768	+	0.0659978i	0.392177	−	0.919890i	$-0.371722\pi$
$509$	2581.14	+	757.890i	0.224768	+	0.0659978i	−0.167409	+	0.985887i	$0.553540\pi$
$510$	−61.3688	−	70.8234i	−0.00532834	−	0.00614924i
$511$	6808.04	−	4375.26i	0.589373	−	0.378767i
$512$	−7031.94	+	8115.29i	−0.606974	+	0.700485i
$513$	448.402	−	3118.70i	0.0385914	−	0.268409i
$514$	1499.66	−	440.341i	0.128691	−	0.0377872i
$515$	3234.93	+	2078.97i	0.276793	+	0.177884i
$516$	−71.9510	−	500.430i	−0.00613850	−	0.0426942i
$517$	−7147.18	−	15650.1i	−0.607994	−	1.33132i
$518$	−3998.51	−	8755.52i	−0.339159	−	0.742655i
$519$	−62.0053	−	431.256i	−0.00524418	−	0.0364741i
$520$	−1458.70	−	937.448i	−0.123016	−	0.0790573i
$521$	−15100.7	+	4433.97i	−1.26982	+	0.372852i	−0.846139	−	0.532962i	$-0.821079\pi$
$521$	−15100.7	+	4433.97i	−1.26982	+	0.372852i	−0.423677	+	0.905813i	$0.639261\pi$
$522$	−617.454	+	4294.49i	−0.0517725	+	0.360085i
$523$	−14493.9	+	16726.9i	−1.21181	+	1.39850i	−0.319189	+	0.947691i	$0.603410\pi$
$523$	−14493.9	+	16726.9i	−1.21181	+	1.39850i	−0.892620	+	0.450811i	$0.851135\pi$
$524$	1610.67	−	1035.11i	0.134279	−	0.0862961i
$525$	472.094	+	544.825i	0.0392455	+	0.0452917i
$526$	−106.268	−	31.2032i	−0.00880897	−	0.00258655i
$527$	1904.70	−	4170.71i	0.157438	−	0.344742i
$528$	−1914.04			−0.157761
$529$	−6563.68	+	10244.7i	−0.539466	+	0.842008i
$530$	116.042			0.00951044
$531$	−4222.25	+	9245.45i	−0.345066	+	0.755590i
$532$	−16398.8	−	4815.14i	−1.33643	−	0.392411i
$533$	−4729.66	−	5458.32i	−0.384361	−	0.443576i
$534$	576.312	−	370.373i	0.0467031	−	0.0300143i
$535$	−1659.03	+	1914.62i	−0.134067	+	0.154722i
$536$	554.854	−	3859.10i	0.0447128	−	0.310984i
$537$	−1082.88	+	317.962i	−0.0870200	+	0.0255514i
$538$	161.061	+	103.508i	0.0129067	+	0.00829466i
$539$	−4421.81	−	30754.4i	−0.353360	−	2.45767i
$540$	−727.009	−	1591.93i	−0.0579361	−	0.126862i
$541$	−907.998	−	1988.24i	−0.0721587	−	0.158006i	0.870115	−	0.492848i	$-0.164044\pi$
$541$	−907.998	−	1988.24i	−0.0721587	−	0.158006i	−0.942274	+	0.334843i	$0.891317\pi$
$542$	159.793	+	1111.38i	0.0126636	+	0.0880775i
$543$	3299.90	+	2120.72i	0.260796	+	0.167604i
$544$	3688.56	−	1083.06i	0.290709	−	0.0853600i
$545$	−217.972	+	1516.03i	−0.0171319	+	0.119155i
$546$	420.752	−	485.573i	0.0329789	−	0.0380597i
$547$	−5650.05	+	3631.06i	−0.441643	+	0.283826i	−0.742504	−	0.669841i	$-0.766362\pi$
$547$	−5650.05	+	3631.06i	−0.441643	+	0.283826i	0.300862	+	0.953668i	$0.402726\pi$
$548$	11710.6	+	13514.7i	0.912865	+	1.05350i
$549$	−18623.2	−	5468.25i	−1.44775	−	0.425099i
$550$	280.969	−	615.236i	0.0217828	−	0.0476977i
$551$	17054.5			1.31859
$552$	472.554	+	863.983i	0.0364370	+	0.0666188i
$553$	1644.66			0.126470
$554$	−1517.19	+	3322.18i	−0.116352	+	0.254776i
$555$	−1832.29	−	538.009i	−0.140138	−	0.0411481i
$556$	−15141.4	−	17474.1i	−1.15493	−	1.33286i
$557$	4917.31	−	3160.16i	0.374063	−	0.240396i	−0.340079	−	0.940397i	$-0.610454\pi$
$557$	4917.31	−	3160.16i	0.374063	−	0.240396i	0.714142	+	0.700001i	$0.246817\pi$
$558$	−1591.82	+	1837.06i	−0.120766	+	0.139371i
$559$	−369.480	+	2569.79i	−0.0279558	+	0.194437i
$560$	−8553.83	+	2511.63i	−0.645474	+	0.189528i
$561$	979.139	+	629.255i	0.0736886	+	0.0473568i
$562$	572.232	+	3979.96i	0.0429504	+	0.298727i
$563$	−4189.98	−	9174.77i	−0.313653	−	0.686803i	0.685495	−	0.728077i	$-0.259586\pi$
$563$	−4189.98	−	9174.77i	−0.313653	−	0.686803i	−0.999148	+	0.0412737i	$0.986858\pi$
$564$	−1146.26	−	2509.96i	−0.0855784	−	0.187391i
$565$	855.107	+	5947.40i	0.0636719	+	0.442848i
$566$	1613.66	+	1037.04i	0.119836	+	0.0770142i
$567$	−21280.2	+	6248.44i	−1.57616	+	0.462804i
$568$	−347.769	+	2418.79i	−0.0256903	+	0.178680i
$569$	9870.44	−	11391.1i	0.727224	−	0.839261i	−0.264932	−	0.964267i	$-0.585350\pi$
$569$	9870.44	−	11391.1i	0.727224	−	0.839261i	0.992156	+	0.125006i	$0.0398950\pi$
$570$	164.290	−	105.583i	0.0120725	−	0.00775854i
$571$	9395.13	+	10842.6i	0.688571	+	0.794653i	0.987161	−	0.159728i	$-0.0510619\pi$
$571$	9395.13	+	10842.6i	0.688571	+	0.794653i	−0.298590	+	0.954381i	$0.596516\pi$
$572$	10042.4	+	2948.73i	0.734083	+	0.215546i
$573$	−796.509	+	1744.11i	−0.0580709	+	0.127158i
$574$	4685.87			0.340740
$575$	2750.44	−	198.646i	0.199480	−	0.0144071i
$576$	9243.83			0.668680
$577$	8209.48	−	17976.3i	0.592314	−	1.29699i	−0.341720	−	0.939802i	$-0.611009\pi$
$577$	8209.48	−	17976.3i	0.592314	−	1.29699i	0.934034	−	0.357185i	$-0.116263\pi$
$578$	2435.29	+	715.065i	0.175250	+	0.0514581i
$579$	−1474.07	−	1701.17i	−0.105803	−	0.122104i
$580$	7969.04	−	5121.39i	0.570511	−	0.366645i
$581$	13978.3	−	16131.8i	0.998135	−	1.15191i
$582$	82.9187	−	576.712i	0.00590566	−	0.0410747i
$583$	−1382.85	+	406.042i	−0.0982364	+	0.0288448i
$584$	−2107.78	−	1354.59i	−0.149351	−	0.0959818i
$585$	630.415	+	4384.64i	0.0445547	+	0.309884i
$586$	−1202.13	−	2632.30i	−0.0847434	−	0.185562i
$587$	2079.98	+	4554.52i	0.146252	+	0.320247i	0.968554	−	0.248805i	$-0.0800377\pi$
$587$	2079.98	+	4554.52i	0.146252	+	0.320247i	−0.822302	+	0.569052i	$0.807310\pi$
$588$	−709.166	−	4932.36i	−0.0497373	−	0.345930i
$589$	8038.16	+	5165.81i	0.562320	+	0.361381i
$590$	−1226.32	+	360.081i	−0.0855710	+	0.0251259i
$591$	−236.149	+	1642.45i	−0.0164363	+	0.114317i
$592$	15464.7	−	17847.2i	1.07364	−	1.23905i
$593$	7915.45	−	5086.95i	0.548143	−	0.352270i	−0.237073	−	0.971492i	$-0.576188\pi$
$593$	7915.45	−	5086.95i	0.548143	−	0.352270i	0.785216	+	0.619222i	$0.212552\pi$
$594$	−819.788	−	946.086i	−0.0566268	−	0.0653508i
$595$	5201.48	+	1527.29i	0.358387	+	0.105232i
$596$	9991.47	−	21878.3i	0.686689	−	1.50364i
$597$	−1353.90			−0.0928163
$598$	−524.099	−	2401.17i	−0.0358395	−	0.164199i
$599$	8690.04			0.592764			0.296382	−	0.955070i	$-0.404220\pi$
$599$	8690.04			0.592764			0.296382	+	0.955070i	$0.404220\pi$
$600$	92.7184	−	203.025i	0.00630869	−	0.0138141i
$601$	−9111.47	−	2675.37i	−0.618410	−	0.181582i	−0.0425027	−	0.999096i	$-0.513533\pi$
$601$	−9111.47	−	2675.37i	−0.618410	−	0.181582i	−0.575908	+	0.817515i	$0.695351\pi$
$602$	−1103.06	−	1273.00i	−0.0746799	−	0.0861853i
$603$	−8379.04	+	5384.88i	−0.565872	+	0.363664i
$604$	−6792.00	+	7838.39i	−0.457554	+	0.528046i
$605$	−248.383	+	1727.54i	−0.0166912	+	0.116090i
$606$	449.187	−	131.893i	0.0301105	−	0.00884125i
$607$	−1114.57	−	716.293i	−0.0745291	−	0.0478969i	0.502846	−	0.864376i	$-0.332286\pi$
$607$	−1114.57	−	716.293i	−0.0745291	−	0.0478969i	−0.577375	+	0.816479i	$0.695923\pi$
$608$	1140.12	+	7929.71i	0.0760493	+	0.528935i
$609$	3000.26	+	6569.66i	0.199634	+	0.437137i
$610$	−1013.90	−	2220.13i	−0.0672976	−	0.147361i
$611$	2016.53	+	14025.3i	0.133519	+	0.928644i
$612$	−5457.03	−	3507.02i	−0.360437	−	0.231639i
$613$	−17865.8	+	5245.88i	−1.17715	+	0.345643i	−0.811075	−	0.584942i	$-0.801117\pi$
$613$	−17865.8	+	5245.88i	−1.17715	+	0.345643i	−0.366077	+	0.930585i	$0.619299\pi$
$614$	−721.857	+	5020.63i	−0.0474459	+	0.329993i
$615$	608.801	−	702.594i	0.0399175	−	0.0460672i
$616$	−11754.2	+	7553.98i	−0.768816	+	0.494088i
$617$	−16604.3	−	19162.3i	−1.08341	−	1.25032i	−0.966360	−	0.257192i	$-0.917203\pi$
$617$	−16604.3	−	19162.3i	−1.08341	−	1.25032i	−0.117047	−	0.993126i	$-0.537343\pi$
$618$	423.276	+	124.285i	0.0275512	+	0.00808976i
$619$	−1843.88	+	4037.54i	−0.119729	+	0.262169i	−0.960002	−	0.279994i	$-0.909667\pi$
$619$	−1843.88	+	4037.54i	−0.119729	+	0.262169i	0.840273	+	0.542163i	$0.182395\pi$
$620$	5307.26			0.343781
$621$	1780.32	−	4783.41i	0.115043	−	0.309101i
$622$	−2521.84			−0.162567
$623$	−16462.7	+	36048.2i	−1.05869	+	2.31820i
$624$	1512.50	+	444.109i	0.0970325	+	0.0284913i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	−4676.76	+	3005.57i	−0.298596	+	0.191896i
$627$	−1588.37	+	1833.08i	−0.101170	+	0.116756i
$628$	594.081	−	4131.92i	0.0377491	−	0.262550i
$629$	−13778.4	+	4045.72i	−0.873422	+	0.256460i
$630$	−2417.76	−	1553.80i	−0.152898	−	0.0982617i
$631$	−4107.91	−	28571.1i	−0.259165	−	1.80253i	−0.538808	−	0.842429i	$-0.681125\pi$
$631$	−4107.91	−	28571.1i	−0.259165	−	1.80253i	0.279643	−	0.960104i	$-0.409784\pi$
$632$	−211.526	−	463.177i	−0.0133134	−	0.0291522i
$633$	−967.178	−	2117.82i	−0.0607297	−	0.132979i
$634$	−646.070	−	4493.51i	−0.0404712	−	0.281483i
$635$	−4644.91	−	2985.10i	−0.290280	−	0.186552i
$636$	−221.780	+	65.1206i	−0.0138273	+	0.00406006i
$637$	−3641.68	+	25328.4i	−0.226513	+	1.57543i
$638$	4437.34	−	5120.97i	0.275354	−	0.317776i
$639$	5251.78	−	3375.11i	0.325129	−	0.208947i
$640$	3843.04	+	4435.10i	0.237358	+	0.273926i
$641$	−7961.25	−	2337.63i	−0.490562	−	0.144042i	0.0270904	−	0.999633i	$-0.491376\pi$
$641$	−7961.25	−	2337.63i	−0.490562	−	0.144042i	−0.517653	+	0.855591i	$0.673194\pi$
$642$	−120.734	+	264.371i	−0.00742211	+	0.0162521i
$643$	−4066.93			−0.249431			−0.124715	−	0.992193i	$-0.539802\pi$
$643$	−4066.93			−0.249431			−0.124715	+	0.992193i	$0.539802\pi$
$644$	−24308.8	−	13251.6i	−1.48743	−	0.810848i
$645$	−334.184			−0.0204008
$646$	610.059	−	1335.84i	0.0371555	−	0.0813592i
$647$	−7034.42	−	2065.49i	−0.427437	−	0.125507i	0.0609364	−	0.998142i	$-0.480591\pi$
$647$	−7034.42	−	2065.49i	−0.427437	−	0.125507i	−0.488373	+	0.872635i	$0.662409\pi$
$648$	4496.63	+	5189.39i	0.272600	+	0.314597i
$649$	13353.9	−	8582.04i	0.807685	−	0.519067i
$650$	−364.776	+	420.974i	−0.0220118	+	0.0254030i
$651$	−575.862	+	4005.21i	−0.0346695	+	0.241131i
$652$	23115.6	−	6787.36i	1.38846	−	0.407690i
$653$	26333.9	+	16923.8i	1.57814	+	1.01421i	0.976519	+	0.215429i	$0.0691150\pi$
$653$	26333.9	+	16923.8i	1.57814	+	1.01421i	0.601622	+	0.798781i	$0.294521\pi$
$654$	25.0059	+	173.920i	0.00149512	+	0.0103988i
$655$	−525.727	−	1151.18i	−0.0313616	−	0.0686723i
$656$	4775.82	+	10457.6i	0.284245	+	0.622409i
$657$	910.936	+	6335.70i	0.0540929	+	0.376224i
$658$	−7733.76	−	4970.18i	−0.458196	−	0.294465i
$659$	5549.54	−	1629.49i	0.328041	−	0.0963217i	−0.113565	−	0.993531i	$-0.536227\pi$
$659$	5549.54	−	1629.49i	0.328041	−	0.0963217i	0.441606	+	0.897209i	$0.354409\pi$
$660$	−191.731	+	1333.52i	−0.0113078	+	0.0786473i
$661$	1187.97	−	1370.99i	0.0699042	−	0.0806738i	−0.719720	−	0.694264i	$-0.755730\pi$
$661$	1187.97	−	1370.99i	0.0699042	−	0.0806738i	0.789624	+	0.613590i	$0.210275\pi$
$662$	−2594.23	+	1667.21i	−0.152308	+	0.0978822i
$663$	−627.723	−	724.431i	−0.0367703	−	0.0424352i
$664$	−6340.90	−	1861.86i	−0.370594	−	0.108816i
$665$	−4693.02	+	10276.3i	−0.273666	+	0.599244i
$666$	7613.06			0.442943
$667$	26999.5	+	5853.64i	1.56735	+	0.339811i
$668$	−16046.6			−0.929435
$669$	−1365.33	+	2989.66i	−0.0789040	+	0.172776i
$670$	−1201.74	−	352.862i	−0.0692943	−	0.0203466i
$671$	19850.9	+	22909.2i	1.14208	+	1.31803i
$672$	−2854.08	+	1834.21i	−0.163837	+	0.105292i
$673$	8404.56	−	9699.38i	0.481385	−	0.555548i	−0.462158	−	0.886797i	$-0.652925\pi$
$673$	8404.56	−	9699.38i	0.481385	−	0.555548i	0.943543	+	0.331250i	$0.107470\pi$
$674$	−412.703	+	2870.41i	−0.0235856	+	0.164042i
$675$	−1109.94	+	325.907i	−0.0632911	+	0.0185839i
$676$	6729.21	+	4324.60i	0.382863	+	0.246051i
$677$	3759.03	+	26144.7i	0.213399	+	1.48423i	0.761692	+	0.647939i	$0.224369\pi$
$677$	3759.03	+	26144.7i	0.213399	+	1.48423i	−0.548292	+	0.836287i	$0.684722\pi$
$678$	286.349	+	627.016i	0.0162200	+	0.0355168i
$679$	14001.4	+	30658.8i	0.791347	+	1.73281i
$680$	−238.858	−	1661.29i	−0.0134703	−	0.0936879i
$681$	2415.63	+	1552.43i	0.135928	+	0.0873557i
$682$	3642.56	−	1069.55i	0.204517	−	0.0600517i
$683$	3683.76	−	25621.1i	0.206377	−	1.43538i	−0.578476	−	0.815699i	$-0.696353\pi$
$683$	3683.76	−	25621.1i	0.206377	−	1.43538i	0.784853	−	0.619682i	$-0.212738\pi$
$684$	8852.45	−	10216.3i	0.494856	−	0.571095i
$685$	9943.84	−	6390.52i	0.554649	−	0.356451i
$686$	−5952.56	−	6869.62i	−0.331297	−	0.382337i
$687$	−3910.70	−	1148.29i	−0.217180	−	0.0637698i
$688$	1716.75	−	3759.16i	0.0951316	−	0.208309i
$689$	1186.96			0.0656305
$690$	296.331	−	110.762i	0.0163495	−	0.00611105i
$691$	−28074.0			−1.54557			−0.772783	−	0.634671i	$-0.781136\pi$
$691$	−28074.0			−1.54557			−0.772783	+	0.634671i	$0.781136\pi$
$692$	1575.41	−	3449.66i	0.0865433	−	0.189503i
$693$	34248.9	+	10056.4i	1.87736	+	0.551242i
$694$	−37.6415	−	43.4407i	−0.00205887	−	0.00237606i
$695$	−12857.1	+	8262.77i	−0.701724	+	0.450971i
$696$	1464.30	−	1689.89i	0.0797474	−	0.0920335i
$697$	994.908	−	6919.74i	0.0540672	−	0.376045i
$698$	2136.78	−	627.417i	0.115872	−	0.0340230i
$699$	1131.46	+	727.146i	0.0612243	+	0.0393465i
$700$	893.020	+	6211.09i	0.0482185	+	0.335367i
$701$	−1715.17	−	3755.71i	−0.0924126	−	0.202355i	0.857781	−	0.514015i	$-0.171842\pi$
$701$	−1715.17	−	3755.71i	−0.0924126	−	0.202355i	−0.950194	+	0.311660i	$0.899115\pi$
$702$	428.288	+	937.820i	0.0230266	+	0.0504213i
$703$	−4258.86	−	29621.0i	−0.228486	−	1.58916i
$704$	−12145.0	−	7805.14i	−0.650189	−	0.417851i
$705$	−1750.01	+	513.850i	−0.0934884	+	0.0274507i
$706$	−403.870	+	2808.98i	−0.0215295	+	0.149741i
$707$	−17734.6	+	20466.8i	−0.943392	+	1.08873i
$708$	2141.69	−	1376.38i	0.113686	−	0.0730615i
$709$	22897.2	+	26424.7i	1.21287	+	1.39972i	0.891656	+	0.452713i	$0.149544\pi$
$709$	22897.2	+	26424.7i	1.21287	+	1.39972i	0.321209	+	0.947008i	$0.395911\pi$
$710$	753.220	+	221.165i	0.0398139	+	0.0116904i
$711$	−540.383	+	1183.27i	−0.0285034	+	0.0624138i
$712$	12269.4			0.645806
$713$	10952.4	+	10937.1i	0.575274	+	0.574471i
$714$	621.911			0.0325973
$715$	2873.95	−	6293.06i	0.150321	−	0.329157i
$716$	−9425.67	−	2767.63i	−0.491975	−	0.144457i
$717$	3510.78	+	4051.66i	0.182863	+	0.211035i
$718$	−5233.34	+	3363.26i	−0.272015	+	0.174813i
$719$	−16771.2	+	19355.0i	−0.869902	+	1.00392i	0.130021	+	0.991511i	$0.458496\pi$
$719$	−16771.2	+	19355.0i	−0.869902	+	1.00392i	−0.999923	+	0.0124094i	$0.996050\pi$
$720$	1003.49	−	6979.41i	0.0519413	−	0.361260i
$721$	−24485.6	+	7189.61i	−1.26476	+	0.371366i
$722$	−1234.01	−	793.052i	−0.0636083	−	0.0408786i
$723$	91.9913	+	639.814i	0.00473194	+	0.0329114i
$724$	14183.7	+	31057.9i	0.728082	+	1.59428i
$725$	−2601.12	−	5695.66i	−0.133246	−	0.291767i
$726$	28.4947	+	198.185i	0.00145667	+	0.0101313i
$727$	20770.3	+	13348.3i	1.05960	+	0.680962i	0.949757	−	0.312987i	$-0.101330\pi$
$727$	20770.3	+	13348.3i	1.05960	+	0.680962i	0.109841	+	0.993949i	$0.464966\pi$
$728$	11041.0	−	3241.94i	0.562099	−	0.165047i
$729$	2341.96	−	16288.7i	0.118984	−	0.827551i
$730$	−527.093	+	608.298i	−0.0267241	+	0.0308413i
$731$	−2114.07	+	1358.63i	−0.106965	+	0.0687424i
$732$	3183.67	+	3674.15i	0.160754	+	0.185520i
$733$	8367.19	+	2456.83i	0.421622	+	0.123799i	0.485660	−	0.874148i	$-0.338579\pi$
$733$	8367.19	+	2456.83i	0.421622	+	0.123799i	−0.0640373	+	0.997948i	$0.520398\pi$
$734$	1674.15	−	3665.89i	0.0841882	−	0.184346i
$735$	−3293.80			−0.165297
$736$	−916.767	+	12945.1i	−0.0459137	+	0.648319i
$737$	15555.6			0.777474
$738$	−1539.63	+	3371.31i	−0.0767947	+	0.168157i
$739$	−24886.5	−	7307.35i	−1.23879	−	0.363742i	−0.404230	−	0.914657i	$-0.632460\pi$
$739$	−24886.5	−	7307.35i	−1.23879	−	0.363742i	−0.834561	+	0.550916i	$0.814279\pi$
$740$	−10885.1	−	12562.1i	−0.540736	−	0.624043i
$741$	1680.47	−	1079.97i	0.0833112	−	0.0535409i
$742$	−504.305	+	581.999i	−0.0249510	+	0.0287950i
$743$	3241.53	−	22545.3i	0.160054	−	1.11320i	−0.738474	−	0.674282i	$-0.764453\pi$
$743$	3241.53	−	22545.3i	0.160054	−	1.11320i	0.898528	−	0.438917i	$-0.144638\pi$
$744$	1202.03	−	352.947i	0.0592318	−	0.0173920i
$745$	−13374.4	−	8595.18i	−0.657716	−	0.422689i
$746$	712.647	+	4956.57i	0.0349757	+	0.243261i
$747$	7013.42	+	15357.2i	0.343517	+	0.752198i
$748$	4208.54	+	9215.42i	0.205721	+	0.450467i
$749$	−2392.68	−	16641.5i	−0.116725	−	0.811837i
$750$	−60.3184	−	38.7643i	−0.00293669	−	0.00188730i
$751$	6839.10	−	2008.14i	0.332307	−	0.0975740i	−0.111323	−	0.993784i	$-0.535509\pi$
$751$	6839.10	−	2008.14i	0.332307	−	0.0975740i	0.443630	+	0.896210i	$0.353691\pi$
$752$	3209.88	−	22325.2i	0.155655	−	1.08260i
$753$	2736.25	−	3157.80i	0.132423	−	0.152824i
$754$	−4694.64	+	3017.06i	−0.226749	+	0.145723i
$755$	4489.49	+	5181.15i	0.216410	+	0.249750i
$756$	11143.7	+	3272.08i	0.536101	+	0.157413i
$757$	2293.96	−	5023.06i	0.110139	−	0.241171i	−0.846534	−	0.532334i	$-0.821315\pi$
$757$	2293.96	−	5023.06i	0.110139	−	0.241171i	0.956673	+	0.291163i	$0.0940423\pi$
$758$	−6842.30			−0.327867
$759$	−3143.77	+	2356.82i	−0.150345	+	0.112710i
$760$	3497.64			0.166938
$761$	−10600.5	+	23211.8i	−0.504950	+	1.10569i	0.469879	+	0.882731i	$0.344298\pi$
$761$	−10600.5	+	23211.8i	−0.504950	+	1.10569i	−0.974829	+	0.222955i	$0.928430\pi$
$762$	−607.764	−	178.456i	−0.0288937	−	0.00848395i
$763$	−6656.24	−	7681.71i	−0.315822	−	0.364478i
$764$	−14040.0	+	9022.96i	−0.664855	+	0.427276i

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)

\(f(q)\)	\(=\)	\(q+(0.274193 - 0.600398i) q^{2} +(0.833837 + 0.244837i) q^{3} +(4.95359 + 5.71675i) q^{4} +(4.20627 - 2.70320i) q^{5} +(0.375631 - 0.433502i) q^{6} +(-4.72226 + 32.8441i) q^{7} +(9.85703 - 2.89429i) q^{8} +(-22.0785 - 14.1890i) q^{9} +O(q^{10})\)	\(q+(0.274193 - 0.600398i) q^{2} +(0.833837 + 0.244837i) q^{3} +(4.95359 + 5.71675i) q^{4} +(4.20627 - 2.70320i) q^{5} +(0.375631 - 0.433502i) q^{6} +(-4.72226 + 32.8441i) q^{7} +(9.85703 - 2.89429i) q^{8} +(-22.0785 - 14.1890i) q^{9} +(-0.469671 - 3.26663i) q^{10} +(17.0273 + 37.2845i) q^{11} +(2.73082 + 5.97966i) q^{12} +(-4.80412 - 33.4134i) q^{13} +(18.4247 + 11.8408i) q^{14} +(4.16919 - 1.22418i) q^{15} +(-7.64714 + 53.1870i) q^{16} +(21.3976 - 24.6941i) q^{17} +(-14.5728 + 9.36537i) q^{18} +(44.5912 + 51.4610i) q^{19} +(36.2897 + 10.6556i) q^{20} +(-11.9790 + 26.2304i) q^{21} +27.0543 q^{22} +(52.9307 + 96.7747i) q^{23} +8.92778 q^{24} +(10.3854 - 22.7408i) q^{25} +(-21.3786 - 6.27732i) q^{26} +(-30.3016 - 34.9699i) q^{27} +(-211.153 + 135.700i) q^{28} +(164.016 - 189.285i) q^{29} +(0.408163 - 2.83883i) q^{30} +(134.639 - 39.5336i) q^{31} +(98.9753 + 63.6076i) q^{32} +(5.06935 + 35.2581i) q^{33} +(-8.95924 - 19.6180i) q^{34} +(68.9211 + 150.916i) q^{35} +(-28.2530 - 196.504i) q^{36} +(-369.717 - 237.603i) q^{37} +(43.1237 - 12.6623i) q^{38} +(4.17497 - 29.0376i) q^{39} +(33.6375 - 38.8197i) q^{40} +(179.988 - 115.671i) q^{41} +(12.4641 + 14.3844i) q^{42} +(-73.7935 - 21.6677i) q^{43} +(-128.800 + 282.033i) q^{44} -131.224 q^{45} +(72.6165 - 5.24460i) q^{46} -419.749 q^{47} +(-19.3986 + 42.4770i) q^{48} +(-727.326 - 213.562i) q^{49} +(-10.8059 - 12.4707i) q^{50} +(23.8881 - 15.3520i) q^{51} +(167.218 - 192.980i) q^{52} +(-5.00404 + 34.8039i) q^{53} +(-29.3043 + 8.60453i) q^{54} +(172.409 + 110.800i) q^{55} +(48.5126 + 337.412i) q^{56} +(24.5823 + 53.8277i) q^{57} +(-68.6742 - 150.376i) q^{58} +(-55.1150 - 383.333i) q^{59} +(27.6508 + 17.7701i) q^{60} +(709.595 - 208.356i) q^{61} +(13.1811 - 91.6768i) q^{62} +(570.285 - 658.144i) q^{63} +(-296.303 + 190.422i) q^{64} +(-110.531 - 127.559i) q^{65} +(22.5589 + 6.62388i) q^{66} +(157.655 - 345.215i) q^{67} +247.165 q^{68} +(20.4416 + 93.6537i) q^{69} +109.507 q^{70} +(-98.8141 + 216.373i) q^{71} +(-258.695 - 75.9598i) q^{72} +(-159.714 - 184.320i) q^{73} +(-244.030 + 156.829i) q^{74} +(14.2275 - 16.4194i) q^{75} +(-73.3030 + 509.834i) q^{76} +(-1304.98 + 383.177i) q^{77} +(-16.2893 - 10.4685i) q^{78} +(-7.05386 - 49.0607i) q^{79} +(111.609 + 244.391i) q^{80} +(277.662 + 607.995i) q^{81} +(-20.0974 - 139.781i) q^{82} +(-541.167 - 347.787i) q^{83} +(-209.292 + 61.4536i) q^{84} +(23.2507 - 161.712i) q^{85} +(-33.2429 + 38.3643i) q^{86} +(183.107 - 117.676i) q^{87} +(275.750 + 318.233i) q^{88} +(1145.93 + 336.477i) q^{89} +(-35.9806 + 78.7865i) q^{90} +1120.12 q^{91} +(-291.039 + 781.974i) q^{92} +121.946 q^{93} +(-115.092 + 252.017i) q^{94} +(326.672 + 95.9197i) q^{95} +(66.9558 + 77.2711i) q^{96} +(854.509 - 549.159i) q^{97} +(-327.650 + 378.128i) q^{98} +(153.093 - 1064.79i) 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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