LMFDB - Embedded newform 115.4.g.a.6.4

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			6.4
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13426 + 2.48368i) q^{2} +(-4.84173 - 1.42166i) q^{3} +(0.356777 + 0.411743i) q^{4} +(4.20627 - 2.70320i) q^{5} +(9.02270 - 10.4128i) q^{6} +(-3.26809 + 22.7301i) q^{7} +(-22.3859 + 6.57308i) q^{8} +(-1.29264 - 0.830727i) q^{9} +O(q^{10})$	\(q+(-1.13426 + 2.48368i) q^{2} +(-4.84173 - 1.42166i) q^{3} +(0.356777 + 0.411743i) q^{4} +(4.20627 - 2.70320i) q^{5} +(9.02270 - 10.4128i) q^{6} +(-3.26809 + 22.7301i) q^{7} +(-22.3859 + 6.57308i) q^{8} +(-1.29264 - 0.830727i) q^{9} +(1.94290 + 13.5131i) q^{10} +(-19.7103 - 43.1595i) q^{11} +(-1.14206 - 2.50076i) q^{12} +(3.63873 + 25.3079i) q^{13} +(-52.7473 - 33.8986i) q^{14} +(-24.2086 + 7.10830i) q^{15} +(8.44563 - 58.7406i) q^{16} +(56.7638 - 65.5090i) q^{17} +(3.52944 - 2.26823i) q^{18} +(-76.3911 - 88.1600i) q^{19} +(2.61372 + 0.767459i) q^{20} +(48.1377 - 105.407i) q^{21} +129.551 q^{22} +(-87.1373 - 67.6320i) q^{23} +117.731 q^{24} +(10.3854 - 22.7408i) q^{25} +(-66.9839 - 19.6682i) q^{26} +(94.2994 + 108.827i) q^{27} +(-10.5249 + 6.76396i) q^{28} +(-32.8084 + 37.8629i) q^{29} +(9.80411 - 68.1891i) q^{30} +(-149.245 + 43.8223i) q^{31} +(-20.7046 - 13.3060i) q^{32} +(34.0737 + 236.988i) q^{33} +(98.3183 + 215.287i) q^{34} +(47.6976 + 104.443i) q^{35} +(-0.119137 - 0.828618i) q^{36} +(-229.801 - 147.684i) q^{37} +(305.608 - 89.7346i) q^{38} +(18.3615 - 127.707i) q^{39} +(-76.3925 + 88.1617i) q^{40} +(20.7001 - 13.3032i) q^{41} +(207.196 + 239.117i) q^{42} +(-287.156 - 84.3167i) q^{43} +(10.7384 - 23.5139i) q^{44} -7.68280 q^{45} +(266.812 - 139.709i) q^{46} +249.467 q^{47} +(-124.401 + 272.399i) q^{48} +(-176.870 - 51.9338i) q^{49} +(44.7011 + 51.5878i) q^{50} +(-367.966 + 236.478i) q^{51} +(-9.12213 + 10.5275i) q^{52} +(-105.968 + 737.026i) q^{53} +(-377.252 + 110.771i) q^{54} +(-199.576 - 128.259i) q^{55} +(-76.2476 - 530.314i) q^{56} +(244.531 + 535.449i) q^{57} +(-56.8261 - 124.432i) q^{58} +(56.0769 + 390.023i) q^{59} +(-11.5639 - 7.43165i) q^{60} +(37.5544 - 11.0270i) q^{61} +(60.4418 - 420.382i) q^{62} +(23.1070 - 26.6669i) q^{63} +(455.923 - 293.004i) q^{64} +(83.7179 + 96.6156i) q^{65} +(-627.249 - 184.177i) q^{66} +(-330.724 + 724.184i) q^{67} +47.2249 q^{68} +(325.745 + 451.335i) q^{69} -313.504 q^{70} +(237.653 - 520.388i) q^{71} +(34.3972 + 10.0999i) q^{72} +(128.355 + 148.130i) q^{73} +(627.454 - 403.240i) q^{74} +(-82.6128 + 95.3403i) q^{75} +(9.04465 - 62.9069i) q^{76} +(1045.43 - 306.967i) q^{77} +(296.356 + 190.457i) q^{78} +(42.7517 + 297.344i) q^{79} +(-123.263 - 269.909i) q^{80} +(-284.622 - 623.236i) q^{81} +(9.56149 + 66.5016i) q^{82} +(-972.567 - 625.031i) q^{83} +(60.5749 - 17.7864i) q^{84} +(61.6798 - 428.992i) q^{85} +(535.124 - 617.566i) q^{86} +(212.678 - 136.680i) q^{87} +(724.922 + 836.605i) q^{88} +(871.852 + 255.999i) q^{89} +(8.71427 - 19.0816i) q^{90} -587.143 q^{91} +(-3.24161 - 60.0077i) q^{92} +784.904 q^{93} +(-282.959 + 619.594i) q^{94} +(-559.636 - 164.324i) q^{95} +(81.3292 + 93.8589i) q^{96} +(-1383.09 + 888.860i) q^{97} +(329.603 - 380.382i) q^{98} +(-10.3755 + 72.1634i) 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 $

$2$	−1.13426	+	2.48368i	−0.401020	+	0.878112i	0.596145	+	0.802876i	$0.296698\pi$
$2$	−1.13426	+	2.48368i	−0.401020	+	0.878112i	−0.997166	+	0.0752357i	$0.976029\pi$
$3$	−4.84173	−	1.42166i	−0.931791	−	0.273598i	−0.219605	−	0.975589i	$-0.570477\pi$
$3$	−4.84173	−	1.42166i	−0.931791	−	0.273598i	−0.712186	+	0.701990i	$0.752295\pi$
$4$	0.356777	+	0.411743i	0.0445971	+	0.0514678i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	9.02270	−	10.4128i	0.613917	−	0.708498i
$7$	−3.26809	+	22.7301i	−0.176460	+	1.22731i	0.688413	+	0.725319i	$0.258308\pi$
$7$	−3.26809	+	22.7301i	−0.176460	+	1.22731i	−0.864873	+	0.501990i	$0.832601\pi$
$8$	−22.3859	+	6.57308i	−0.989324	+	0.290492i
$9$	−1.29264	−	0.830727i	−0.0478754	−	0.0307677i
$10$	1.94290	+	13.5131i	0.0614398	+	0.427323i
$11$	−19.7103	−	43.1595i	−0.540261	−	1.18301i	−0.961183	−	0.275910i	$-0.911021\pi$
$11$	−19.7103	−	43.1595i	−0.540261	−	1.18301i	0.420922	−	0.907097i	$-0.361707\pi$
$12$	−1.14206	−	2.50076i	−0.0274737	−	0.0601590i
$13$	3.63873	+	25.3079i	0.0776309	+	0.539935i	0.991110	+	0.133048i	$0.0424765\pi$
$13$	3.63873	+	25.3079i	0.0776309	+	0.539935i	−0.913479	+	0.406887i	$0.866614\pi$
$14$	−52.7473	−	33.8986i	−1.00695	−	0.647128i
$15$	−24.2086	+	7.10830i	−0.416710	+	0.122357i
$16$	8.44563	−	58.7406i	0.131963	−	0.917822i
$17$	56.7638	−	65.5090i	0.809838	−	0.934603i	−0.189039	−	0.981970i	$-0.560537\pi$
$17$	56.7638	−	65.5090i	0.809838	−	0.934603i	0.998878	+	0.0473663i	$0.0150828\pi$
$18$	3.52944	−	2.26823i	0.0462165	−	0.0297015i
$19$	−76.3911	−	88.1600i	−0.922385	−	1.06449i	−0.997731	−	0.0673316i	$-0.978551\pi$
$19$	−76.3911	−	88.1600i	−0.922385	−	1.06449i	0.0753457	−	0.997157i	$-0.475994\pi$
$20$	2.61372	+	0.767459i	0.0292223	+	0.00858045i
$21$	48.1377	−	105.407i	0.500214	−	1.09532i
$22$	129.551			1.25547
$23$	−87.1373	−	67.6320i	−0.789973	−	0.613141i
$23$	−87.1373	−	67.6320i	−0.789973	−	0.613141i
$24$	117.731			1.00132
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	−66.9839	−	19.6682i	−0.505255	−	0.148356i
$27$	94.2994	+	108.827i	0.672146	+	0.775698i
$28$	−10.5249	+	6.76396i	−0.0710366	+	0.0456524i
$29$	−32.8084	+	37.8629i	−0.210082	+	0.242447i	−0.851005	−	0.525158i	$-0.824006\pi$
$29$	−32.8084	+	37.8629i	−0.210082	+	0.242447i	0.640923	+	0.767605i	$0.278552\pi$
$30$	9.80411	−	68.1891i	0.0596659	−	0.414985i
$31$	−149.245	+	43.8223i	−0.864684	+	0.253894i	−0.683853	−	0.729620i	$-0.739697\pi$
$31$	−149.245	+	43.8223i	−0.864684	+	0.253894i	−0.180831	+	0.983514i	$0.557879\pi$
$32$	−20.7046	−	13.3060i	−0.114378	−	0.0735060i
$33$	34.0737	+	236.988i	0.179742	+	1.25013i
$34$	98.3183	+	215.287i	0.495925	+	1.08592i
$35$	47.6976	+	104.443i	0.230353	+	0.504403i
$36$	−0.119137	−	0.828618i	−0.000551562	−	0.00383620i
$37$	−229.801	−	147.684i	−1.02106	−	0.656193i	−0.0808246	−	0.996728i	$-0.525755\pi$
$37$	−229.801	−	147.684i	−1.02106	−	0.656193i	−0.940232	+	0.340535i	$0.889392\pi$
$38$	305.608	−	89.7346i	1.30464	−	0.383076i
$39$	18.3615	−	127.707i	0.0753896	−	0.524346i
$40$	−76.3925	+	88.1617i	−0.301968	+	0.348490i
$41$	20.7001	−	13.3032i	0.0788492	−	0.0506733i	−0.500622	−	0.865666i	$-0.666895\pi$
$41$	20.7001	−	13.3032i	0.0788492	−	0.0506733i	0.579471	+	0.814993i	$0.303259\pi$
$42$	207.196	+	239.117i	0.761215	+	0.878488i
$43$	−287.156	−	84.3167i	−1.01839	−	0.299027i	−0.270410	−	0.962745i	$-0.587159\pi$
$43$	−287.156	−	84.3167i	−1.01839	−	0.299027i	−0.747983	+	0.663718i	$0.768978\pi$
$44$	10.7384	−	23.5139i	0.0367927	−	0.0805648i
$45$	−7.68280			−0.0254508
$46$	266.812	−	139.709i	0.855202	−	0.447803i
$47$	249.467			0.774222			0.387111	−	0.922033i	$-0.373473\pi$
$47$	249.467			0.774222			0.387111	+	0.922033i	$0.373473\pi$
$48$	−124.401	+	272.399i	−0.374077	+	0.819114i
$49$	−176.870	−	51.9338i	−0.515657	−	0.151411i
$50$	44.7011	+	51.5878i	0.126434	+	0.145912i
$51$	−367.966	+	236.478i	−1.01031	+	0.649284i
$52$	−9.12213	+	10.5275i	−0.0243272	+	0.0280750i
$53$	−105.968	+	737.026i	−0.274639	+	1.91016i	0.122628	+	0.992453i	$0.460868\pi$
$53$	−105.968	+	737.026i	−0.274639	+	1.91016i	−0.397267	+	0.917703i	$0.630041\pi$
$54$	−377.252	+	110.771i	−0.950694	+	0.279149i
$55$	−199.576	−	128.259i	−0.489287	−	0.314446i
$56$	−76.2476	−	530.314i	−0.181947	−	1.26547i
$57$	244.531	+	535.449i	0.568227	+	1.24424i
$58$	−56.8261	−	124.432i	−0.128649	−	0.281702i
$59$	56.0769	+	390.023i	0.123739	+	0.860622i	0.953261	+	0.302148i	$0.0977038\pi$
$59$	56.0769	+	390.023i	0.123739	+	0.860622i	−0.829522	+	0.558474i	$0.811387\pi$
$60$	−11.5639	−	7.43165i	−0.0248815	−	0.0159904i
$61$	37.5544	−	11.0270i	0.0788254	−	0.0231452i	−0.242082	−	0.970256i	$-0.577830\pi$
$61$	37.5544	−	11.0270i	0.0788254	−	0.0231452i	0.320907	+	0.947111i	$0.396012\pi$
$62$	60.4418	−	420.382i	0.123808	−	0.861106i
$63$	23.1070	−	26.6669i	0.0462096	−	0.0533287i
$64$	455.923	−	293.004i	0.890475	−	0.572274i
$65$	83.7179	+	96.6156i	0.159753	+	0.184364i
$66$	−627.249	−	184.177i	−1.16983	−	0.343494i
$67$	−330.724	+	724.184i	−0.603050	+	1.32049i	0.324178	+	0.945996i	$0.394912\pi$
$67$	−330.724	+	724.184i	−0.603050	+	1.32049i	−0.927227	+	0.374499i	$0.877815\pi$
$68$	47.2249			0.0842185
$69$	325.745	+	451.335i	0.568335	+	0.787455i
$70$	−313.504			−0.535299
$71$	237.653	−	520.388i	0.397243	−	0.869841i	−0.600299	−	0.799775i	$-0.704952\pi$
$71$	237.653	−	520.388i	0.397243	−	0.869841i	0.997542	−	0.0700655i	$-0.0223208\pi$
$72$	34.3972	+	10.0999i	0.0563021	+	0.0165318i
$73$	128.355	+	148.130i	0.205793	+	0.237497i	0.849258	−	0.527978i	$-0.177050\pi$
$73$	128.355	+	148.130i	0.205793	+	0.237497i	−0.643466	+	0.765475i	$0.722504\pi$
$74$	627.454	−	403.240i	0.985676	−	0.633455i
$75$	−82.6128	+	95.3403i	−0.127191	+	0.146786i
$76$	9.04465	−	62.9069i	0.0136512	−	0.0949463i
$77$	1045.43	−	306.967i	1.54725	−	0.454314i
$78$	296.356	+	190.457i	0.430202	+	0.276474i
$79$	42.7517	+	297.344i	0.0608853	+	0.423466i	0.997353	+	0.0727125i	$0.0231655\pi$
$79$	42.7517	+	297.344i	0.0608853	+	0.423466i	−0.936468	+	0.350754i	$0.885925\pi$
$80$	−123.263	−	269.909i	−0.172266	−	0.377209i
$81$	−284.622	−	623.236i	−0.390428	−	0.854919i
$82$	9.56149	+	66.5016i	0.0128767	+	0.0895594i
$83$	−972.567	−	625.031i	−1.28618	−	0.826579i	−0.294545	−	0.955638i	$-0.595168\pi$
$83$	−972.567	−	625.031i	−1.28618	−	0.826579i	−0.991637	+	0.129059i	$0.958804\pi$
$84$	60.5749	−	17.7864i	0.0786817	−	0.0231030i
$85$	61.6798	−	428.992i	0.0787072	−	0.547421i
$86$	535.124	−	617.566i	0.670976	−	0.774348i
$87$	212.678	−	136.680i	0.262085	−	0.168432i
$88$	724.922	+	836.605i	0.878147	+	1.01344i
$89$	871.852	+	255.999i	1.03838	+	0.304897i	0.756115	−	0.654438i	$-0.227095\pi$
$89$	871.852	+	255.999i	1.03838	+	0.304897i	0.282269	+	0.959335i	$0.408913\pi$
$90$	8.71427	−	19.0816i	0.0102063	−	0.0223486i
$91$	−587.143			−0.676366
$92$	−3.24161	−	60.0077i	−0.00367350	−	0.0680026i
$93$	784.904			0.875170
$94$	−282.959	+	619.594i	−0.310479	+	0.679854i
$95$	−559.636	−	164.324i	−0.604394	−	0.177466i
$96$	81.3292	+	93.8589i	0.0864649	+	0.0997858i
$97$	−1383.09	+	888.860i	−1.44775	+	0.930413i	−0.448420	+	0.893823i	$0.648013\pi$
$97$	−1383.09	+	888.860i	−1.44775	+	0.930413i	−0.999330	+	0.0365902i	$0.988350\pi$
$98$	329.603	−	380.382i	0.339744	−	0.392086i
$99$	−10.3755	+	72.1634i	−0.0105331	+	0.0732596i
$100$	13.0686	−	3.83729i	0.0130686	−	0.00383729i
$101$	−622.474	−	400.040i	−0.613253	−	0.394113i	0.196823	−	0.980439i	$-0.436938\pi$
$101$	−622.474	−	400.040i	−0.613253	−	0.394113i	−0.810076	+	0.586326i	$0.800574\pi$
$102$	−169.965	−	1182.14i	−0.164991	−	1.14754i
$103$	−445.005	−	974.426i	−0.425706	−	0.932165i	−0.994004	−	0.109343i	$-0.965125\pi$
$103$	−445.005	−	974.426i	−0.425706	−	0.932165i	0.568299	−	0.822822i	$-0.307602\pi$
$104$	−247.807	−	542.621i	−0.233649	−	0.511619i
$105$	−82.4561	−	573.495i	−0.0766371	−	0.533023i
$106$	−1710.34	−	1099.17i	−1.56720	−	1.00718i
$107$	−1412.64	+	414.788i	−1.27631	+	0.374758i	−0.848540	−	0.529131i	$-0.822518\pi$
$107$	−1412.64	+	414.788i	−1.27631	+	0.374758i	−0.427767	+	0.903889i	$0.640700\pi$
$108$	−11.1650	+	77.6542i	−0.00994770	+	0.0691878i
$109$	445.084	−	513.654i	0.391113	−	0.451369i	−0.525709	−	0.850664i	$-0.676200\pi$
$109$	445.084	−	513.654i	0.391113	−	0.451369i	0.916822	+	0.399296i	$0.130745\pi$
$110$	544.925	−	350.202i	0.472332	−	0.303550i
$111$	902.678	+	1041.75i	0.771878	+	0.890794i
$112$	1307.58	+	383.940i	1.10317	+	0.323919i
$113$	971.877	−	2128.11i	0.809084	−	1.77165i	0.197786	−	0.980245i	$-0.436625\pi$
$113$	971.877	−	2128.11i	0.809084	−	1.77165i	0.611297	−	0.791401i	$-0.290648\pi$
$114$	−1607.24			−1.32046
$115$	−549.346	−	48.9284i	−0.445450	−	0.0396747i
$116$	−27.2951			−0.0218473
$117$	16.3204	−	35.7367i	0.0128959	−	0.0282381i
$118$	−1032.30	−	303.110i	−0.805345	−	0.236470i
$119$	1303.51	+	1504.34i	1.00414	+	1.15884i
$120$	495.208	−	318.251i	0.376717	−	0.242101i
$121$	−602.627	+	695.469i	−0.452763	+	0.522516i
$122$	−15.2089	+	105.780i	−0.0112865	+	0.0784992i
$123$	−119.137	+	34.9818i	−0.0873351	+	0.0256439i
$124$	−71.2907	−	45.8158i	−0.0516298	−	0.0331805i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	40.0226	+	87.6373i	0.0282976	+	0.0619631i
$127$	64.2460	+	140.679i	0.0448890	+	0.0982933i	0.930748	−	0.365662i	$-0.119157\pi$
$127$	64.2460	+	140.679i	0.0448890	+	0.0982933i	−0.885859	+	0.463955i	$0.846430\pi$
$128$	182.573	+	1269.82i	0.126073	+	0.876854i
$129$	1270.46	+	816.477i	0.867116	+	0.557262i
$130$	−334.920	+	98.3412i	−0.225957	+	0.0663469i
$131$	−192.228	+	1336.98i	−0.128206	+	0.891696i	0.819620	+	0.572908i	$0.194185\pi$
$131$	−192.228	+	1336.98i	−0.128206	+	0.891696i	−0.947826	+	0.318788i	$0.896724\pi$
$132$	−85.4213	+	98.5814i	−0.0563255	+	0.0650031i
$133$	2253.54	−	1448.26i	1.46922	−	0.944212i
$134$	−1423.51	−	1642.82i	−0.917707	−	1.05909i
$135$	690.831	+	202.846i	0.440424	+	0.129320i
$136$	−840.111	+	1839.59i	−0.529698	+	1.15988i
$137$	−421.788			−0.263035			−0.131517	−	0.991314i	$-0.541985\pi$
$137$	−421.788			−0.263035			−0.131517	+	0.991314i	$0.541985\pi$
$138$	−1490.45	+	297.116i	−0.919388	+	0.183277i
$139$	−2015.05			−1.22960			−0.614800	−	0.788683i	$-0.710763\pi$
$139$	−2015.05			−1.22960			−0.614800	+	0.788683i	$0.710763\pi$
$140$	−25.9863	+	56.9021i	−0.0156874	+	0.0343507i
$141$	−1207.85	−	354.657i	−0.721413	−	0.211826i
$142$	1022.92	+	1180.51i	0.604515	+	0.697648i
$143$	1020.56	−	655.872i	0.596806	−	0.383544i
$144$	−59.7146	+	68.9143i	−0.0345570	+	0.0398810i
$145$	−35.6498	+	247.950i	−0.0204176	+	0.142008i
$146$	−513.495	+	150.776i	−0.291076	+	0.0854677i
$147$	782.526	+	502.899i	0.439059	+	0.282166i
$148$	−21.1799	−	147.309i	−0.0117633	−	0.0818159i
$149$	−315.363	−	690.548i	−0.173393	−	0.379677i	0.802906	−	0.596106i	$-0.203286\pi$
$149$	−315.363	−	690.548i	−0.173393	−	0.379677i	−0.976298	+	0.216429i	$0.930559\pi$
$150$	−143.090	−	313.324i	−0.0778885	−	0.170552i
$151$	294.525	+	2048.46i	0.158729	+	1.10398i	0.900979	+	0.433862i	$0.142849\pi$
$151$	294.525	+	2048.46i	0.158729	+	1.10398i	−0.742250	+	0.670123i	$0.766241\pi$
$152$	2289.56	+	1471.41i	1.22176	+	0.785180i
$153$	−127.795	+	37.5240i	−0.0675269	+	0.0198277i
$154$	−423.384	+	2944.70i	−0.221541	+	1.54085i
$155$	−509.304	+	587.768i	−0.263924	+	0.304585i
$156$	59.1334	−	38.0027i	0.0303491	−	0.0195042i
$157$	1108.89	+	1279.72i	0.563687	+	0.650530i	0.964017	−	0.265842i	$-0.0856498\pi$
$157$	1108.89	+	1279.72i	0.563687	+	0.650530i	−0.400330	+	0.916371i	$0.631104\pi$
$158$	−786.998	−	231.084i	−0.396267	−	0.116355i
$159$	1560.87	−	3417.83i	0.778522	−	1.70472i
$160$	−123.058			−0.0608036
$161$	1822.05	−	1759.61i	0.891913	−	0.861347i
$162$	1870.75			0.907285
$163$	72.8879	−	159.602i	0.0350247	−	0.0766933i	−0.891311	−	0.453392i	$-0.850214\pi$
$163$	72.8879	−	159.602i	0.0350247	−	0.0766933i	0.926336	+	0.376699i	$0.122941\pi$
$164$	12.8628	+	3.77686i	0.00612449	+	0.00179831i
$165$	783.950	+	904.726i	0.369881	+	0.426866i
$166$	2655.51	−	1706.60i	1.24161	−	0.797937i
$167$	−527.466	+	608.728i	−0.244411	+	0.282065i	−0.864679	−	0.502325i	$-0.832478\pi$
$167$	−527.466	+	608.728i	−0.244411	+	0.282065i	0.620269	+	0.784390i	$0.287024\pi$
$168$	−384.755	+	2676.03i	−0.176694	+	1.22893i
$169$	1480.76	−	434.789i	0.673990	−	0.197901i
$170$	995.518	+	639.780i	0.449134	+	0.288641i
$171$	25.5090	+	177.419i	0.0114077	+	0.0793425i
$172$	−67.7340	−	148.317i	−0.0300271	−	0.0657503i
$173$	−898.855	−	1968.22i	−0.395021	−	0.864976i	−0.997751	−	0.0670306i	$-0.978647\pi$
$173$	−898.855	−	1968.22i	−0.395021	−	0.864976i	0.602730	−	0.797946i	$-0.294080\pi$
$174$	98.2368	+	683.252i	0.0428007	+	0.297685i
$175$	482.960	+	310.380i	0.208619	+	0.134071i
$176$	−2701.68	+	793.285i	−1.15708	+	0.339751i
$177$	282.971	−	1968.11i	0.120166	−	0.835775i
$178$	−1624.72	+	1875.03i	−0.684147	+	0.789548i
$179$	562.106	−	361.244i	0.234714	−	0.150842i	−0.417997	−	0.908448i	$-0.637268\pi$
$179$	562.106	−	361.244i	0.234714	−	0.150842i	0.652711	+	0.757607i	$0.273631\pi$
$180$	−2.74105	−	3.16334i	−0.00113503	−	0.00130990i
$181$	927.612	+	272.371i	0.380933	+	0.111852i	0.466592	−	0.884473i	$-0.345482\pi$
$181$	927.612	+	272.371i	0.380933	+	0.111852i	−0.0856595	+	0.996324i	$0.527300\pi$
$182$	665.971	−	1458.27i	0.271236	−	0.593925i
$183$	−197.505			−0.0797812
$184$	2395.19	+	941.240i	0.959652	+	0.377115i
$185$	−1365.83			−0.542797
$186$	−890.283	+	1949.45i	−0.350961	+	0.768497i
$187$	−3946.16	−	1158.70i	−1.54317	−	0.453115i
$188$	89.0040	+	102.716i	0.0345281	+	0.0398475i
$189$	−2781.83	+	1787.78i	−1.07063	+	0.688051i
$190$	1042.90	−	1203.57i	0.398209	−	0.459558i
$191$	369.474	−	2569.75i	0.139970	−	0.973511i	−0.791883	−	0.610673i	$-0.790899\pi$
$191$	369.474	−	2569.75i	0.139970	−	0.973511i	0.931852	−	0.362837i	$-0.118192\pi$
$192$	−2624.01	+	770.479i	−0.986310	+	0.289607i
$193$	1487.46	+	955.932i	0.554765	+	0.356526i	0.787789	−	0.615945i	$-0.211226\pi$
$193$	1487.46	+	955.932i	0.554765	+	0.356526i	−0.233024	+	0.972471i	$0.574862\pi$
$194$	−638.857	−	4443.35i	−0.236429	−	1.64440i
$195$	−267.985	−	586.805i	−0.0984143	−	0.215497i
$196$	−41.7199	−	91.3539i	−0.0152041	−	0.0332922i
$197$	357.824	+	2488.72i	0.129411	+	0.900072i	0.946303	+	0.323281i	$0.104786\pi$
$197$	357.824	+	2488.72i	0.129411	+	0.900072i	−0.816892	+	0.576790i	$0.804305\pi$
$198$	−167.462	−	107.621i	−0.0601061	−	0.0386279i
$199$	−4795.10	+	1407.97i	−1.70812	+	0.501549i	−0.982455	−	0.186502i	$-0.940285\pi$
$199$	−4795.10	+	1407.97i	−1.70812	+	0.501549i	−0.725663	+	0.688050i	$0.758467\pi$
$200$	−83.0084	+	577.336i	−0.0293479	+	0.204119i
$201$	2630.82	−	3036.12i	0.923202	−	1.06543i
$202$	1699.62	−	1092.28i	0.592003	−	0.380457i
$203$	−753.407	−	869.478i	−0.260487	−	0.300618i
$204$	−228.650	−	67.1377i	−0.0784740	−	0.0230420i
$205$	51.1091	−	111.913i	0.0174128	−	0.0381286i
$206$	2924.91			0.989262
$207$	56.4532	+	159.811i	0.0189554	+	0.0536601i
$208$	1517.33			0.505808
$209$	−2299.25	+	5034.66i	−0.760969	+	1.66629i
$210$	1517.90	+	445.696i	0.498787	+	0.146457i
$211$	2783.75	+	3212.62i	0.908253	+	1.04818i	0.998633	+	0.0522728i	$0.0166465\pi$
$211$	2783.75	+	3212.62i	0.908253	+	1.04818i	−0.0903795	+	0.995907i	$0.528808\pi$
$212$	−341.272	+	219.322i	−0.110560	+	0.0710524i
$213$	−1890.47	+	2181.72i	−0.608135	+	0.701825i
$214$	572.095	−	3979.01i	0.182746	−	1.27103i
$215$	−1435.78	+	421.583i	−0.455439	+	0.133729i
$216$	−2826.30	−	1816.36i	−0.890304	−	0.572164i
$217$	−508.338	−	3535.57i	−0.159024	−	1.10604i
$218$	770.912	+	1688.06i	0.239508	+	0.524449i
$219$	−410.871	−	899.683i	−0.126777	−	0.277602i
$220$	−18.3941	−	127.934i	−0.00563696	−	0.0392059i
$221$	1864.44	+	1198.20i	0.567493	+	0.364706i
$222$	−3611.23	+	1060.35i	−1.09176	+	0.320568i
$223$	627.492	−	4364.30i	0.188430	−	1.31056i	−0.647643	−	0.761944i	$-0.724245\pi$
$223$	627.492	−	4364.30i	0.188430	−	1.31056i	0.836073	−	0.548618i	$-0.184846\pi$
$224$	370.111	−	427.131i	0.110398	−	0.127406i
$225$	−32.3159	+	20.7682i	−0.00957509	+	0.00615354i
$226$	4183.19	+	4827.65i	1.23124	+	1.42093i
$227$	−2338.72	−	686.709i	−0.683815	−	0.200786i	−0.0786690	−	0.996901i	$-0.525067\pi$
$227$	−2338.72	−	686.709i	−0.683815	−	0.200786i	−0.605146	+	0.796115i	$0.706885\pi$
$228$	−133.224	+	291.720i	−0.0386972	+	0.0847352i
$229$	−314.612			−0.0907866			−0.0453933	−	0.998969i	$-0.514454\pi$
$229$	−314.612			−0.0907866			−0.0453933	+	0.998969i	$0.514454\pi$
$230$	744.622	−	1308.90i	0.213473	−	0.375245i
$231$	−5498.11			−1.56601
$232$	485.568	−	1063.25i	0.137410	−	0.300886i
$233$	2114.77	+	620.953i	0.594606	+	0.174592i	0.565170	−	0.824974i	$-0.308811\pi$
$233$	2114.77	+	620.953i	0.594606	+	0.174592i	0.0294364	+	0.999567i	$0.490629\pi$
$234$	70.2469	+	81.0693i	0.0196247	+	0.0226481i
$235$	1049.32	−	674.359i	0.291278	−	0.187193i
$236$	−140.582	+	162.241i	−0.0387760	+	0.0447498i
$237$	215.730	−	1500.44i	0.0591274	−	0.411240i
$238$	−5214.80	+	1531.20i	−1.42028	+	0.417031i
$239$	2461.29	+	1581.78i	0.666141	+	0.428103i	0.829532	−	0.558459i	$-0.188607\pi$
$239$	2461.29	+	1581.78i	0.666141	+	0.428103i	−0.163392	+	0.986561i	$0.552243\pi$
$240$	213.089	+	1482.06i	0.0573117	+	0.398612i
$241$	−1352.75	−	2962.11i	−0.361570	−	0.791727i	−0.999761	−	0.0218494i	$-0.993045\pi$
$241$	−1352.75	−	2962.11i	−0.361570	−	0.791727i	0.638192	−	0.769877i	$-0.279683\pi$
$242$	−1043.79	−	2285.57i	−0.277261	−	0.607116i
$243$	−61.2826	−	426.230i	−0.0161781	−	0.112521i
$244$	17.9388	+	11.5286i	0.00470662	+	0.00302476i
$245$	−884.352	+	259.669i	−0.230609	+	0.0677129i
$246$	48.2485	−	335.576i	0.0125049	−	0.0869737i
$247$	1953.18	−	2254.09i	0.503149	−	0.580665i
$248$	3052.93	−	1962.00i	0.781699	−	0.502367i
$249$	3820.32	+	4408.89i	0.972302	+	1.12210i
$250$	327.477	+	96.1560i	0.0828459	+	0.0243258i
$251$	2408.08	−	5272.97i	0.605565	−	1.32600i	−0.320001	−	0.947417i	$-0.603683\pi$
$251$	2408.08	−	5272.97i	0.605565	−	1.32600i	0.925566	−	0.378586i	$-0.123589\pi$
$252$	19.2239			0.00480553
$253$	−1201.46	+	5093.85i	−0.298558	+	1.26580i
$254$	−422.273			−0.104314
$255$	−908.518	+	1989.38i	−0.223112	+	0.488547i
$256$	799.128	+	234.645i	0.195100	+	0.0572864i
$257$	−1057.70	−	1220.65i	−0.256721	−	0.296272i	0.612729	−	0.790293i	$-0.290072\pi$
$257$	−1057.70	−	1220.65i	−0.256721	−	0.296272i	−0.869450	+	0.494022i	$0.835526\pi$
$258$	−3468.90	+	2229.32i	−0.837070	+	0.537952i
$259$	4107.89	−	4740.76i	0.985528	−	1.13736i
$260$	−9.91214	+	68.9405i	−0.00236433	+	0.0164443i
$261$	73.8632	−	21.6882i	0.0175173	−	0.00514354i
$262$	−3102.58	−	1993.91i	−0.731595	−	0.470168i
$263$	−1013.18	−	7046.85i	−0.237550	−	1.65219i	−0.664036	−	0.747701i	$-0.731158\pi$
$263$	−1013.18	−	7046.85i	−0.237550	−	1.65219i	0.426486	−	0.904494i	$-0.359751\pi$
$264$	−2320.51	−	5081.21i	−0.540975	−	1.18457i
$265$	1546.60	+	3386.58i	0.358516	+	0.785042i
$266$	1040.92	+	7239.76i	0.239936	+	1.66879i
$267$	−3857.33	−	2478.95i	−0.884137	−	0.568200i
$268$	−416.172	+	122.199i	−0.0948573	+	0.0278526i
$269$	967.484	−	6729.00i	0.219288	−	1.52518i	−0.521387	−	0.853320i	$-0.674585\pi$
$269$	967.484	−	6729.00i	0.219288	−	1.52518i	0.740675	−	0.671863i	$-0.234506\pi$
$270$	−1287.38	+	1485.72i	−0.290177	+	0.334882i
$271$	−1231.45	+	791.404i	−0.276034	+	0.177396i	−0.671332	−	0.741157i	$-0.734278\pi$
$271$	−1231.45	+	791.404i	−0.276034	+	0.177396i	0.395298	+	0.918553i	$0.370641\pi$
$272$	−3368.63	−	3887.61i	−0.750931	−	0.866621i
$273$	2842.78	+	834.717i	0.630231	+	0.185053i
$274$	478.415	−	1047.58i	0.105482	−	0.230974i
$275$	−1186.18			−0.260107
$276$	−69.6155	+	295.149i	−0.0151825	+	0.0643692i
$277$	2701.71			0.586030			0.293015	−	0.956108i	$-0.405341\pi$
$277$	2701.71			0.586030			0.293015	+	0.956108i	$0.405341\pi$
$278$	2285.59	−	5004.74i	0.493095	−	1.07973i
$279$	229.324	+	67.3356i	0.0492089	+	0.0144490i
$280$	−1754.26	−	2024.53i	−0.374419	−	0.432103i
$281$	−3658.31	+	2351.06i	−0.776643	+	0.499118i	−0.867918	−	0.496707i	$-0.834542\pi$
$281$	−3658.31	+	2351.06i	−0.776643	+	0.499118i	0.0912748	+	0.995826i	$0.470906\pi$
$282$	2250.86	−	2597.63i	0.475308	−	0.548535i
$283$	−1079.12	+	7505.43i	−0.226668	+	1.57651i	0.485333	+	0.874329i	$0.338698\pi$
$283$	−1079.12	+	7505.43i	−0.226668	+	1.57651i	−0.712001	+	0.702179i	$0.752211\pi$
$284$	299.055	−	87.8105i	0.0624847	−	0.0183472i
$285$	2475.99	+	1591.22i	0.514614	+	0.330723i
$286$	471.400	+	3278.66i	0.0974631	+	0.677871i
$287$	234.732	+	513.992i	0.0482780	+	0.105714i
$288$	15.7098	+	34.3997i	0.00321427	+	0.00703827i
$289$	−370.098	−	2574.09i	−0.0753303	−	0.523934i
$290$	−575.390	−	369.781i	−0.116511	−	0.0748768i
$291$	7960.22	−	2337.33i	1.60356	−	0.470848i
$292$	−15.1972	+	105.699i	−0.00304571	+	0.0211834i
$293$	1353.06	−	1561.51i	0.269783	−	0.311347i	−0.604651	−	0.796491i	$-0.706687\pi$
$293$	1353.06	−	1561.51i	0.269783	−	0.311347i	0.874434	+	0.485144i	$0.161233\pi$
$294$	−2136.62	+	1373.12i	−0.423845	+	0.272389i
$295$	1290.19	+	1488.96i	0.254636	+	0.293865i
$296$	6115.04	+	1795.54i	1.20077	+	0.352579i
$297$	2838.27	−	6214.93i	0.554521	−	1.21423i
$298$	2072.80			0.402933
$299$	1394.56	−	2451.36i	0.269730	−	0.474133i
$300$	−68.7300			−0.0132271
$301$	2854.98	−	6251.53i	0.546705	−	1.19712i
$302$	−5421.79	−	1591.98i	−1.03308	−	0.303338i
$303$	2445.13	+	2821.83i	0.463594	+	0.535016i
$304$	−5823.74	+	3742.69i	−1.09873	+	0.706112i
$305$	128.156	−	147.900i	0.0240596	−	0.0277662i
$306$	51.7549	−	359.964i	0.00966874	−	0.0672475i
$307$	2216.38	−	650.787i	0.412037	−	0.120985i	−0.0691431	−	0.997607i	$-0.522027\pi$
$307$	2216.38	−	650.787i	0.412037	−	0.120985i	0.481180	+	0.876622i	$0.340208\pi$
$308$	499.378	+	320.931i	0.0923855	+	0.0593725i
$309$	769.293	+	5350.55i	0.141630	+	0.985055i
$310$	−882.144	−	1931.63i	−0.161621	−	0.353900i
$311$	2707.95	+	5929.59i	0.493743	+	1.08115i	0.978453	+	0.206471i	$0.0661979\pi$
$311$	2707.95	+	5929.59i	0.493743	+	1.08115i	−0.484710	+	0.874675i	$0.661075\pi$
$312$	428.391	+	2979.52i	0.0777335	+	0.540648i
$313$	−4766.49	−	3063.24i	−0.860760	−	0.553177i	0.0341533	−	0.999417i	$-0.489127\pi$
$313$	−4766.49	−	3063.24i	−0.860760	−	0.553177i	−0.894914	+	0.446240i	$0.852763\pi$
$314$	−4436.19	+	1302.58i	−0.797288	+	0.234105i
$315$	25.1081	−	174.631i	0.00449105	−	0.0312360i
$316$	−107.177	+	123.688i	−0.0190796	+	0.0220190i
$317$	−6555.03	+	4212.66i	−1.16141	+	0.746393i	−0.971879	−	0.235482i	$-0.924333\pi$
$317$	−6555.03	+	4212.66i	−1.16141	+	0.746393i	−0.189531	+	0.981875i	$0.560697\pi$
$318$	6718.35	+	7753.39i	1.18474	+	1.36726i
$319$	2280.81	+	669.706i	0.400316	+	0.117543i
$320$	1125.69	−	2464.91i	0.196649	−	0.430602i
$321$	7429.29			1.29178
$322$	2303.63	+	6521.24i	0.398684	+	1.12862i
$323$	−10111.5			−1.74186
$324$	155.066	−	339.547i	0.0265888	−	0.0582214i
$325$	613.312	+	180.085i	0.104678	+	0.0307363i
$326$	313.727	+	362.060i	0.0532997	+	0.0615112i
$327$	−2885.22	+	1854.22i	−0.487929	+	0.313573i
$328$	−375.947	+	433.866i	−0.0632872	+	0.0730374i
$329$	−815.280	+	5670.40i	−0.136620	+	0.950210i
$330$	−3136.25	+	920.885i	−0.523166	+	0.153615i
$331$	−5532.54	−	3555.55i	−0.918719	−	0.590425i	−0.00643344	−	0.999979i	$-0.502048\pi$
$331$	−5532.54	−	3555.55i	−0.918719	−	0.590425i	−0.912286	+	0.409554i	$0.865684\pi$
$332$	−89.6377	−	623.444i	−0.0148178	−	0.103060i
$333$	174.364	+	381.804i	0.0286940	+	0.0628311i
$334$	−913.602	−	2000.51i	−0.149671	−	0.327734i
$335$	566.504	+	3940.13i	0.0923924	+	0.642603i
$336$	−5785.11	−	3717.86i	−0.939296	−	0.603649i
$337$	3486.28	−	1023.66i	0.563530	−	0.165467i	0.0124539	−	0.999922i	$-0.496036\pi$
$337$	3486.28	−	1023.66i	0.563530	−	0.165467i	0.551076	+	0.834455i	$0.314218\pi$
$338$	−599.682	+	4170.88i	−0.0965042	+	0.671201i
$339$	−7731.01	+	8922.06i	−1.23862	+	1.42944i
$340$	198.640	−	127.658i	0.0316847	−	0.0203625i
$341$	4833.01	+	5577.59i	0.767514	+	0.885758i
$342$	−469.585	−	137.883i	−0.0742464	−	0.0218007i
$343$	−1513.57	+	3314.25i	−0.238265	+	0.521727i
$344$	6982.46			1.09439
$345$	2590.22	+	1017.88i	0.404212	+	0.158843i
$346$	5907.95			0.917958
$347$	−3917.32	+	8577.74i	−0.606031	+	1.32702i	0.319225	+	0.947679i	$0.396578\pi$
$347$	−3917.32	+	8577.74i	−0.606031	+	1.32702i	−0.925256	+	0.379344i	$0.876150\pi$
$348$	132.155	+	38.8043i	0.0203571	+	0.00597738i
$349$	−1514.40	−	1747.71i	−0.232275	−	0.268059i	0.627632	−	0.778510i	$-0.284024\pi$
$349$	−1514.40	−	1747.71i	−0.232275	−	0.268059i	−0.859907	+	0.510450i	$0.829479\pi$
$350$	−1318.68	+	847.466i	−0.201390	+	0.129426i
$351$	−2411.06	+	2782.51i	−0.366647	+	0.423133i
$352$	−166.188	+	1155.86i	−0.0251644	+	0.175022i
$353$	−4290.05	+	1259.67i	−0.646846	+	0.189931i	−0.588668	−	0.808375i	$-0.700347\pi$
$353$	−4290.05	+	1259.67i	−0.646846	+	0.189931i	−0.0581781	+	0.998306i	$0.518529\pi$
$354$	4567.18	+	2935.15i	0.685715	+	0.440682i
$355$	−407.082	−	2831.32i	−0.0608610	−	0.423298i
$356$	205.651	+	450.313i	0.0306166	+	0.0670409i
$357$	−4172.61	−	9136.74i	−0.618594	−	1.35453i
$358$	259.640	+	1805.83i	0.0383307	+	0.266596i
$359$	7127.40	+	4580.50i	1.04783	+	0.673398i	0.946911	−	0.321497i	$-0.104186\pi$
$359$	7127.40	+	4580.50i	1.04783	+	0.673398i	0.100917	+	0.994895i	$0.467822\pi$
$360$	171.986	−	50.4997i	0.0251791	−	0.00739324i
$361$	−960.452	+	6680.09i	−0.140028	+	0.973916i
$362$	−1728.63	+	1994.95i	−0.250980	+	0.289647i
$363$	3906.48	−	2510.54i	0.564840	−	0.363000i
$364$	−209.479	−	241.752i	−0.0301640	−	0.0348111i
$365$	940.323	+	276.104i	0.134846	+	0.0395943i
$366$	224.021	−	490.538i	0.0319939	−	0.0700569i
$367$	7381.32			1.04987			0.524934	−	0.851143i	$-0.324090\pi$
$367$	7381.32			1.04987			0.524934	+	0.851143i	$0.324090\pi$
$368$	−4708.68	+	4547.31i	−0.667002	+	0.644143i
$369$	−37.8090			−0.00533404
$370$	1549.20	−	3392.27i	0.217673	−	0.476637i
$371$	−16406.3	−	4817.34i	−2.29589	−	0.674134i
$372$	280.036	+	323.179i	0.0390301	+	0.0450431i
$373$	4763.75	−	3061.48i	0.661281	−	0.424979i	−0.166492	−	0.986043i	$-0.553244\pi$
$373$	4763.75	−	3061.48i	0.661281	−	0.424979i	0.827773	+	0.561064i	$0.189608\pi$
$374$	7353.80	−	8486.73i	1.01673	−	1.17337i
$375$	−89.7674	+	624.346i	−0.0123615	+	0.0859763i
$376$	−5584.52	+	1639.76i	−0.765957	+	0.224905i
$377$	−1077.61	−	692.540i	−0.147215	−	0.0946090i
$378$	−1284.94	−	8936.97i	−0.174842	−	1.21605i
$379$	−577.092	−	1263.66i	−0.0782144	−	0.171266i	0.866485	−	0.499203i	$-0.166374\pi$
$379$	−577.092	−	1263.66i	−0.0782144	−	0.171266i	−0.944699	+	0.327937i	$0.893647\pi$
$380$	−132.006	−	289.053i	−0.0178204	−	0.0390213i
$381$	−111.064	−	772.466i	−0.0149343	−	0.103870i
$382$	5963.35	+	3832.41i	0.798721	+	0.513307i
$383$	11805.1	−	3466.30i	1.57497	−	0.462453i	0.626527	−	0.779400i	$-0.284476\pi$
$383$	11805.1	−	3466.30i	1.57497	−	0.462453i	0.948443	+	0.316947i	$0.102658\pi$
$384$	921.285	−	6407.68i	0.122433	−	0.851538i
$385$	3567.58	−	4117.21i	0.472262	−	0.545019i
$386$	−4061.39	+	2610.09i	−0.535542	+	0.344172i
$387$	301.145	+	347.539i	0.0395557	+	0.0456497i
$388$	−859.437	−	252.354i	−0.112452	−	0.0330188i
$389$	447.007	−	978.809i	0.0582626	−	0.127577i	−0.878261	−	0.478181i	$-0.841296\pi$
$389$	447.007	−	978.809i	0.0582626	−	0.127577i	0.936524	+	0.350604i	$0.114024\pi$
$390$	1761.40			0.228697
$391$	−9376.75	+	1869.22i	−1.21279	+	0.241766i
$392$	4300.76			0.554136
$393$	2831.44	−	6199.99i	0.363428	−	0.795797i
$394$	−6587.05	−	1934.13i	−0.842260	−	0.247310i
$395$	983.607	+	1135.14i	0.125293	+	0.144596i
$396$	−33.4145	+	21.4742i	−0.00424026	+	0.00272505i
$397$	7319.23	−	8446.84i	0.925294	−	1.06785i	−0.0722210	−	0.997389i	$-0.523009\pi$
$397$	7319.23	−	8446.84i	0.925294	−	1.06785i	0.997515	−	0.0704573i	$-0.0224459\pi$
$398$	1941.94	−	13506.5i	0.244574	−	1.70105i
$399$	−12969.9	+	3808.32i	−1.62734	+	0.477831i
$400$	−1248.10	−	802.104i	−0.156012	−	0.100263i
$401$	527.387	+	3668.06i	0.0656769	+	0.456793i	0.995949	+	0.0899221i	$0.0286618\pi$
$401$	527.387	+	3668.06i	0.0656769	+	0.456793i	−0.930272	+	0.366871i	$0.880429\pi$
$402$	4556.73	+	9977.84i	0.565346	+	1.23793i
$403$	−1652.11	−	3617.62i	−0.204212	−	0.447163i
$404$	−57.3710	−	399.024i	−0.00706514	−	0.0491391i
$405$	−2881.93	−	1852.11i	−0.353591	−	0.227239i
$406$	3014.06	−	885.008i	0.368437	−	0.108183i
$407$	−1844.53	+	12829.0i	−0.224644	+	1.56243i
$408$	6682.86	−	7712.43i	0.810908	−	0.935838i
$409$	−9357.73	+	6013.85i	−1.13132	+	0.727055i	−0.965835	−	0.259157i	$-0.916555\pi$
$409$	−9357.73	+	6013.85i	−1.13132	+	0.727055i	−0.165485	+	0.986212i	$0.552919\pi$
$410$	219.986	+	253.877i	0.0264983	+	0.0305807i
$411$	2042.18	+	599.638i	0.245093	+	0.0719659i
$412$	242.445	−	530.880i	0.0289913	−	0.0634820i
$413$	−9048.53			−1.07808
$414$	−460.951	−	41.0553i	−0.0547210	−	0.00487382i
$415$	−5780.46			−0.683739
$416$	261.409	−	572.406i	0.0308092	−	0.0674628i
$417$	9756.33	+	2864.72i	1.14573	+	0.336417i
$418$	−9896.52	−	11421.2i	−1.15803	−	1.33643i
$419$	1548.26	−	995.004i	0.180519	−	0.116012i	−0.447261	−	0.894404i	$-0.647600\pi$
$419$	1548.26	−	995.004i	0.180519	−	0.116012i	0.627779	+	0.778391i	$0.283964\pi$
$420$	206.714	−	238.561i	0.0240157	−	0.0277156i
$421$	−165.116	+	1148.41i	−0.0191146	+	0.132945i	−0.997144	−	0.0755210i	$-0.975938\pi$
$421$	−165.116	+	1148.41i	−0.0191146	+	0.132945i	0.978030	+	0.208466i	$0.0668471\pi$
$422$	−11136.6	+	3270.00i	−1.28465	+	0.377207i
$423$	−322.470	−	207.239i	−0.0370662	−	0.0238210i
$424$	−2472.34	−	17195.5i	−0.283178	−	1.96954i
$425$	−900.212	−	1971.19i	−0.102745	−	0.224981i
$426$	−3274.40	−	7169.93i	−0.372406	−	0.815456i
$427$	127.913	+	889.652i	0.0144968	+	0.100827i
$428$	−674.783	−	433.656i	−0.0762076	−	0.0489756i
$429$	−5873.68	+	1724.67i	−0.661035	+	0.194097i
$430$	581.468	−	4044.20i	0.0652114	−	0.453555i
$431$	9768.32	−	11273.2i	1.09170	−	1.25989i	0.128326	−	0.991732i	$-0.459039\pi$
$431$	9768.32	−	11273.2i	1.09170	−	1.25989i	0.963375	−	0.268158i	$-0.0864151\pi$
$432$	7189.00	−	4620.09i	0.800651	−	0.514547i
$433$	7601.36	+	8772.43i	0.843644	+	0.973617i	0.999901	−	0.0140995i	$-0.00448815\pi$
$433$	7601.36	+	8772.43i	0.843644	+	0.973617i	−0.156257	+	0.987716i	$0.549943\pi$
$434$	9357.79	+	2747.70i	1.03500	+	0.303902i
$435$	525.106	−	1149.82i	0.0578780	−	0.126735i
$436$	370.289			0.0406735
$437$	694.076	+	12848.5i	0.0759775	+	1.40647i
$438$	2700.55			0.294606
$439$	−195.316	+	427.683i	−0.0212345	+	0.0464970i	−0.919952	−	0.392031i	$-0.871773\pi$
$439$	−195.316	+	427.683i	−0.0212345	+	0.0464970i	0.898718	+	0.438528i	$0.144500\pi$
$440$	5310.73	+	1559.37i	0.575407	+	0.168955i
$441$	185.486	+	214.063i	0.0200288	+	0.0231144i
$442$	−5090.71	+	3271.60i	−0.547829	+	0.352068i
$443$	8140.49	−	9394.62i	0.873061	−	1.00757i	−0.126816	−	0.991926i	$-0.540476\pi$
$443$	8140.49	−	9394.62i	0.873061	−	1.00757i	0.999878	−	0.0156403i	$-0.00497867\pi$
$444$	−106.876	+	743.342i	−0.0114237	+	0.0794537i
$445$	4359.26	−	1279.99i	0.464379	−	0.136354i
$446$	10127.8	+	6508.73i	1.07526	+	0.691025i
$447$	545.176	+	3791.78i	0.0576867	+	0.401220i
$448$	5170.01	+	11320.7i	0.545223	+	1.19387i
$449$	1966.23	+	4305.44i	0.206664	+	0.452531i	0.984374	−	0.176093i	$-0.0563459\pi$
$449$	1966.23	+	4305.44i	0.206664	+	0.452531i	−0.777710	+	0.628624i	$0.783619\pi$
$450$	−14.9269	−	103.819i	−0.00156369	−	0.0108757i
$451$	−982.163	−	631.198i	−0.102546	−	0.0659023i
$452$	1222.98	−	359.099i	0.127266	−	0.0373686i
$453$	1486.21	−	10336.8i	0.154146	−	1.07211i
$454$	4358.27	−	5029.71i	0.450536	−	0.519947i
$455$	−2469.68	+	1587.17i	−0.254462	+	0.163533i
$456$	−8993.59	−	10379.2i	−0.923604	−	1.06590i
$457$	−3345.11	−	982.214i	−0.342402	−	0.100538i	0.106010	−	0.994365i	$-0.466192\pi$
$457$	−3345.11	−	982.214i	−0.342402	−	0.100538i	−0.448413	+	0.893827i	$0.648010\pi$
$458$	356.851	−	781.394i	0.0364073	−	0.0797208i
$459$	12482.0			1.26930
$460$	−175.848	−	243.646i	−0.0178238	−	0.0246957i
$461$	−13653.3			−1.37939			−0.689693	−	0.724102i	$-0.742254\pi$
$461$	−13653.3			−1.37939			−0.689693	+	0.724102i	$0.742254\pi$
$462$	6236.27	−	13655.5i	0.628003	−	1.37514i
$463$	−2702.08	−	793.401i	−0.271223	−	0.0796382i	0.143293	−	0.989680i	$-0.454231\pi$
$463$	−2702.08	−	793.401i	−0.271223	−	0.0796382i	−0.414516	+	0.910042i	$0.636049\pi$
$464$	1947.01	+	2246.96i	0.194801	+	0.224812i
$465$	3301.52	−	2121.76i	0.329256	−	0.211600i
$466$	−3940.94	+	4548.09i	−0.391761	+	0.452116i
$467$	1261.83	−	8776.22i	0.125033	−	0.869625i	−0.826688	−	0.562661i	$-0.809778\pi$
$467$	1261.83	−	8776.22i	0.125033	−	0.869625i	0.951721	−	0.306964i	$-0.0993132\pi$
$468$	20.5371	−	6.03023i	0.00202848	−	0.000595615i
$469$	−15379.9	−	9884.08i	−1.51424	−	0.973144i
$470$	484.688	+	3371.08i	0.0475680	+	0.330843i
$471$	−3549.60	−	7772.54i	−0.347255	−	0.760381i
$472$	−3818.98	−	8362.41i	−0.372421	−	0.815489i
$473$	2020.87	+	14055.4i	0.196447	+	1.36632i
$474$	3481.91	+	2237.69i	0.337404	+	0.216836i
$475$	−2798.18	+	821.619i	−0.270293	+	0.0793652i
$476$	−154.335	+	1073.43i	−0.0148612	+	0.103362i
$477$	749.246	−	864.676i	0.0719195	−	0.0829996i
$478$	−6720.35	+	4318.91i	−0.643058	+	0.413268i
$479$	−4065.54	−	4691.88i	−0.387806	−	0.447552i	0.527957	−	0.849271i	$-0.322958\pi$
$479$	−4065.54	−	4691.88i	−0.387806	−	0.447552i	−0.915763	+	0.401719i	$0.868413\pi$
$480$	595.812	+	174.946i	0.0566562	+	0.0166358i
$481$	2901.40	−	6353.17i	0.275036	−	0.602245i
$482$	8891.28			0.840222
$483$	−11323.5	+	5929.22i	−1.06674	+	0.558569i
$484$	−501.358			−0.0470847
$485$	−3414.89	+	7477.57i	−0.319716	+	0.700080i
$486$	1128.13	+	331.248i	0.105294	+	0.0309171i
$487$	−2273.28	−	2623.51i	−0.211524	−	0.244112i	0.640066	−	0.768320i	$-0.278907\pi$
$487$	−2273.28	−	2623.51i	−0.211524	−	0.244112i	−0.851590	+	0.524208i	$0.824361\pi$
$488$	−768.206	+	493.696i	−0.0712603	+	0.0457962i
$489$	−579.803	+	669.129i	−0.0536188	+	0.0618794i
$490$	358.148	−	2490.98i	0.0330194	−	0.229655i
$491$	−6157.83	+	1808.10i	−0.565986	+	0.166188i	−0.552193	−	0.833716i	$-0.686209\pi$
$491$	−6157.83	+	1808.10i	−0.565986	+	0.166188i	−0.0137930	+	0.999905i	$0.504391\pi$
$492$	−56.9088	−	36.5731i	−0.00521473	−	0.00335130i
$493$	618.030	+	4298.49i	0.0564598	+	0.392686i
$494$	3383.02	+	7407.78i	0.308116	+	0.674680i
$495$	151.430	+	331.586i	0.0137501	+	0.0301084i
$496$	1313.68	+	9136.86i	0.118923	+	0.827131i
$497$	11051.8	+	7102.56i	0.997466	+	0.641033i
$498$	−15283.5	+	4487.63i	−1.37524	+	0.403807i
$499$	−1112.32	+	7736.34i	−0.0997879	+	0.694040i	0.877103	+	0.480302i	$0.159473\pi$
$499$	−1112.32	+	7736.34i	−0.0997879	+	0.694040i	−0.976891	+	0.213738i	$0.931436\pi$
$500$	44.5971	−	51.4678i	0.00398889	−	0.00460342i
$501$	3419.25	−	2197.42i	0.304912	−	0.195955i
$502$	10365.0	+	11961.8i	0.921535	+	1.06351i
$503$	−10465.3	−	3072.90i	−0.927688	−	0.272394i	−0.217219	−	0.976123i	$-0.569699\pi$
$503$	−10465.3	−	3072.90i	−0.927688	−	0.272394i	−0.710468	+	0.703729i	$0.751517\pi$
$504$	−341.986	+	748.844i	−0.0302247	+	0.0661829i
$505$	−3699.68			−0.326007
$506$	−11288.7	−	8761.78i	−0.991787	−	0.769780i
$507$	−7787.54			−0.682163
$508$	−35.0021	+	76.6439i	−0.00305702	+	0.00669394i
$509$	17282.1	+	5074.50i	1.50495	+	0.441892i	0.927276	−	0.374378i	$-0.122144\pi$
$509$	17282.1	+	5074.50i	1.50495	+	0.441892i	0.577670	+	0.816270i	$0.303962\pi$
$510$	−3910.47	−	4512.93i	−0.339527	−	0.391835i
$511$	−3786.48	+	2433.43i	−0.327797	+	0.210662i
$512$	−8210.05	+	9474.90i	−0.708665	+	0.817843i
$513$	2390.58	−	16626.9i	0.205744	−	1.43098i
$514$	4231.39	−	1242.45i	0.363110	−	0.106619i
$515$	−4505.88	−	2895.75i	−0.385540	−	0.247771i
$516$	117.094	+	814.404i	0.00998984	+	0.0694809i
$517$	−4917.06	−	10766.9i	−0.418282	−	0.915910i
$518$	7115.10	+	15579.9i	0.603513	+	1.32151i
$519$	1553.88	+	10807.4i	0.131421	+	0.914054i
$520$	−2509.16	−	1612.54i	−0.211604	−	0.135989i
$521$	−15733.3	+	4619.71i	−1.32301	+	0.388470i	−0.865577	−	0.500775i	$-0.833048\pi$
$521$	−15733.3	+	4619.71i	−1.32301	+	0.388470i	−0.457431	+	0.889245i	$0.651230\pi$
$522$	−29.9134	+	208.052i	−0.00250819	+	0.0174448i
$523$	−1522.29	+	1756.81i	−0.127275	+	0.146883i	−0.815810	−	0.578320i	$-0.803709\pi$
$523$	−1522.29	+	1756.81i	−0.127275	+	0.146883i	0.688535	+	0.725203i	$0.258254\pi$
$524$	−619.073	+	397.854i	−0.0516113	+	0.0331686i
$525$	−1897.11	−	2189.38i	−0.157708	−	0.182004i
$526$	18651.3	+	5476.52i	1.54607	+	0.453968i
$527$	−5600.97	+	12264.4i	−0.462964	+	1.01375i
$528$	14208.6			1.17112
$529$	3018.82	+	11786.5i	0.248116	+	0.968730i
$530$	−10165.4			−0.833127
$531$	251.516	−	550.743i	0.0205553	−	0.0450098i
$532$	1400.32	+	411.171i	0.114120	+	0.0335085i
$533$	411.997	+	475.470i	0.0334814	+	0.0386396i
$534$	10532.1	−	6768.58i	0.853501	−	0.548512i
$535$	−4820.68	+	5563.36i	−0.389563	+	0.449579i
$536$	2643.41	−	18385.3i	0.213019	−	1.48158i
$537$	−3235.13	+	949.920i	−0.259974	+	0.0763354i
$538$	15615.3	+	10035.3i	1.25134	+	0.804189i
$539$	1244.73	+	8657.27i	0.0994697	+	0.691827i
$540$	162.952	+	356.816i	0.0129858	+	0.0284350i
$541$	−6248.81	−	13683.0i	−0.496594	−	1.08739i	−0.977561	−	0.210651i	$-0.932442\pi$
$541$	−6248.81	−	13683.0i	−0.496594	−	1.08739i	0.480967	−	0.876739i	$-0.340286\pi$
$542$	−568.812	−	3956.18i	−0.0450786	−	0.313528i
$543$	−4104.02	−	2637.50i	−0.324347	−	0.208445i
$544$	−2046.93	+	601.034i	−0.161326	+	0.0473697i
$545$	483.630	−	3363.72i	0.0380118	−	0.264378i
$546$	−5297.61	+	6113.77i	−0.415233	+	0.479204i
$547$	5186.77	−	3333.33i	0.405430	−	0.260554i	−0.321995	−	0.946741i	$-0.604353\pi$
$547$	5186.77	−	3333.33i	0.405430	−	0.260554i	0.727425	+	0.686187i	$0.240717\pi$
$548$	−150.484	−	173.668i	−0.0117306	−	0.0135378i
$549$	−57.7046	−	16.9436i	−0.00448592	−	0.00131719i
$550$	1345.43	−	2946.09i	0.104308	−	0.228403i
$551$	5844.27			0.451859
$552$	−10258.8	−	7962.38i	−0.791017	−	0.613951i
$553$	−6898.38			−0.530468
$554$	−3064.44	+	6710.18i	−0.235010	+	0.514600i
$555$	6612.96	+	1941.74i	0.505774	+	0.148509i
$556$	−718.924	−	829.683i	−0.0548367	−	0.0632849i
$557$	2792.26	−	1794.47i	0.212409	−	0.136507i	−0.430111	−	0.902776i	$-0.641525\pi$
$557$	2792.26	−	1794.47i	0.212409	−	0.136507i	0.642520	+	0.766269i	$0.277889\pi$
$558$	−427.352	+	493.191i	−0.0324216	+	0.0374165i
$559$	1089.00	−	7574.13i	0.0823964	−	0.573080i
$560$	6537.89	−	1919.70i	0.493351	−	0.144861i
$561$	17459.0	+	11220.2i	1.31394	+	0.844416i
$562$	−1689.79	−	11752.8i	−0.126832	−	0.882136i
$563$	4042.05	+	8850.85i	0.302579	+	0.662555i	0.998453	−	0.0556087i	$-0.0177099\pi$
$563$	4042.05	+	8850.85i	0.302579	+	0.662555i	−0.695874	+	0.718164i	$0.744983\pi$
$564$	−284.906	−	623.856i	−0.0212707	−	0.0465764i
$565$	−1664.75	−	11578.6i	−0.123959	−	0.862151i
$566$	−17417.1	−	11193.3i	−1.29345	−	0.831251i
$567$	15096.4	−	4432.70i	1.11815	−	0.328317i
$568$	−1899.52	+	13211.4i	−0.140321	+	0.975951i
$569$	−3982.47	+	4596.01i	−0.293416	+	0.338620i	−0.883248	−	0.468906i	$-0.844648\pi$
$569$	−3982.47	+	4596.01i	−0.293416	+	0.338620i	0.589832	+	0.807526i	$0.299194\pi$
$570$	−6760.49	+	4344.71i	−0.496782	+	0.319263i
$571$	−9218.18	−	10638.3i	−0.675602	−	0.779686i	0.309640	−	0.950854i	$-0.399792\pi$
$571$	−9218.18	−	10638.3i	−0.675602	−	0.779686i	−0.985242	+	0.171168i	$0.945246\pi$
$572$	634.161	+	186.207i	0.0463560	+	0.0136113i
$573$	−5442.20	+	11916.8i	−0.396773	+	0.868813i
$574$	−1542.84			−0.112189
$575$	−2442.96	+	1279.19i	−0.177180	+	0.0927754i
$576$	−832.750			−0.0602394
$577$	−8770.36	+	19204.4i	−0.632781	+	1.38560i	0.273067	+	0.961995i	$0.411962\pi$
$577$	−8770.36	+	19204.4i	−0.632781	+	1.38560i	−0.905848	+	0.423603i	$0.860765\pi$
$578$	6812.98	+	2000.47i	0.490281	+	0.143960i
$579$	−5842.86	−	6743.02i	−0.419380	−	0.483990i
$580$	−114.810	+	73.7842i	−0.00821938	+	0.00528228i
$581$	17385.4	−	20063.9i	1.24143	−	1.43268i
$582$	−3223.76	+	22421.7i	−0.229603	+	1.59693i
$583$	33898.3	−	9953.44i	2.40810	−	0.707083i
$584$	−3847.01	−	2472.33i	−0.272587	−	0.175181i
$585$	−27.9556	−	194.436i	−0.00197577	−	0.0137418i
$586$	2343.58	+	5131.72i	0.165209	+	0.361757i
$587$	−3465.68	−	7588.79i	−0.243687	−	0.533599i	0.747782	−	0.663944i	$-0.231119\pi$
$587$	−3465.68	−	7588.79i	−0.243687	−	0.533599i	−0.991469	+	0.130345i	$0.958392\pi$
$588$	72.1224	+	501.622i	0.00505829	+	0.0351812i
$589$	15264.4	+	9809.81i	1.06784	+	0.686259i
$590$	−5161.49	+	1515.55i	−0.360161	+	0.105753i
$591$	1805.63	−	12558.4i	0.125674	−	0.874085i
$592$	−10615.9	+	12251.4i	−0.737010	+	0.850555i
$593$	−596.124	+	383.106i	−0.0412814	+	0.0265300i	−0.561119	−	0.827735i	$-0.689629\pi$
$593$	−596.124	+	383.106i	−0.0412814	+	0.0265300i	0.519837	+	0.854265i	$0.325993\pi$
$594$	12216.6	+	14098.7i	0.843858	+	0.973864i
$595$	9549.46	+	2803.97i	0.657966	+	0.193196i
$596$	171.814	−	376.220i	0.0118083	−	0.0258567i
$597$	25218.2			1.72883
$598$	4506.59	+	6244.09i	0.308174	+	0.426990i
$599$	6804.52			0.464149			0.232075	−	0.972698i	$-0.425449\pi$
$599$	6804.52			0.464149			0.232075	+	0.972698i	$0.425449\pi$
$600$	1222.68	−	2677.29i	0.0831928	−	0.182167i
$601$	6065.57	+	1781.01i	0.411680	+	0.120880i	0.481013	−	0.876713i	$-0.340269\pi$
$601$	6065.57	+	1781.01i	0.411680	+	0.120880i	−0.0693331	+	0.997594i	$0.522087\pi$
$602$	12288.5	+	14181.7i	0.831963	+	0.960137i
$603$	1029.11	−	661.366i	0.0694998	−	0.0446648i
$604$	−738.361	+	852.114i	−0.0497408	+	0.0574040i
$605$	−654.817	+	4554.35i	−0.0440035	+	0.306051i
$606$	−9781.92	+	2872.23i	−0.655715	+	0.192535i
$607$	7289.93	+	4684.95i	0.487461	+	0.313272i	0.761184	−	0.648536i	$-0.224619\pi$
$607$	7289.93	+	4684.95i	0.487461	+	0.313272i	−0.273722	+	0.961809i	$0.588255\pi$
$608$	408.585	+	2841.77i	0.0272538	+	0.189555i
$609$	2411.69	+	5280.86i	0.160471	+	0.351382i
$610$	221.973	+	486.053i	0.0147335	+	0.0322618i
$611$	907.741	+	6313.48i	0.0601036	+	0.418029i
$612$	−61.0446	−	39.2310i	−0.00403200	−	0.00259121i
$613$	−9912.49	+	2910.57i	−0.653118	+	0.191773i	−0.591472	−	0.806325i	$-0.701453\pi$
$613$	−9912.49	+	2910.57i	−0.653118	+	0.191773i	−0.0616459	+	0.998098i	$0.519635\pi$
$614$	−897.597	+	6242.92i	−0.0589968	+	0.410332i
$615$	−406.559	+	469.194i	−0.0266570	+	0.0307638i
$616$	−21385.2	+	13743.4i	−1.39876	+	0.898927i
$617$	−10207.7	−	11780.3i	−0.666039	−	0.768650i	0.317712	−	0.948187i	$-0.397086\pi$
$617$	−10207.7	−	11780.3i	−0.666039	−	0.768650i	−0.983751	+	0.179537i	$0.942540\pi$
$618$	−14161.6	−	4158.22i	−0.921785	−	0.270661i
$619$	8288.12	−	18148.4i	0.538171	−	1.17843i	−0.423920	−	0.905700i	$-0.639346\pi$
$619$	8288.12	−	18148.4i	0.538171	−	1.17843i	0.962091	−	0.272730i	$-0.0879265\pi$
$620$	−423.717			−0.0274466
$621$	−856.788	−	15860.6i	−0.0553651	−	1.02490i
$622$	−17798.7			−1.14737
$623$	−8668.17	+	18980.7i	−0.557437	+	1.22062i
$624$	−7346.52	−	2157.13i	−0.471308	−	0.138388i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	13014.5	−	8363.92i	0.830934	−	0.534009i
$627$	18289.9	−	21107.7i	1.16496	−	1.34443i
$628$	−131.292	+	913.153i	−0.00834252	+	0.0580235i
$629$	−22719.0	+	6670.91i	−1.44017	+	0.422872i
$630$	405.247	+	260.437i	0.0256277	+	0.0164699i
$631$	3119.78	+	21698.5i	0.196825	+	1.36895i	0.813425	+	0.581670i	$0.197600\pi$
$631$	3119.78	+	21698.5i	0.196825	+	1.36895i	−0.616600	+	0.787276i	$0.711491\pi$
$632$	−2911.50	−	6375.30i	−0.183249	−	0.401259i
$633$	−8910.92	−	19512.2i	−0.559522	−	1.22518i
$634$	−3027.80	−	21058.8i	−0.189668	−	1.31917i
$635$	650.520	+	418.064i	0.0406537	+	0.0261265i
$636$	1964.15	−	576.726i	0.122458	−	0.0359570i
$637$	670.753	−	4665.19i	0.0417209	−	0.290175i
$638$	−4250.36	+	4905.17i	−0.263751	+	0.304385i
$639$	−739.500	+	475.248i	−0.0457812	+	0.0294218i
$640$	4200.53	+	4847.67i	0.259438	+	0.299408i
$641$	6011.23	+	1765.06i	0.370404	+	0.108761i	0.461637	−	0.887069i	$-0.347262\pi$
$641$	6011.23	+	1765.06i	0.370404	+	0.108761i	−0.0912323	+	0.995830i	$0.529081\pi$
$642$	−8426.73	+	18452.0i	−0.518032	+	1.13433i
$643$	3690.87			0.226367			0.113183	−	0.993574i	$-0.463895\pi$
$643$	3690.87			0.226367			0.113183	+	0.993574i	$0.463895\pi$
$644$	1374.57	+	122.429i	0.0841084	+	0.00749125i
$645$	7551.01			0.460962
$646$	11469.1	−	25113.7i	0.698520	−	1.52955i
$647$	−5360.65	−	1574.03i	−0.325732	−	0.0956436i	0.114778	−	0.993391i	$-0.463384\pi$
$647$	−5360.65	−	1574.03i	−0.325732	−	0.0956436i	−0.440510	+	0.897748i	$0.645202\pi$
$648$	10468.1	+	12080.8i	0.634607	+	0.732376i
$649$	15727.9	−	10107.7i	0.951271	−	0.611345i
$650$	−1142.92	+	1319.01i	−0.0689680	+	0.0795933i
$651$	−2565.14	+	17840.9i	−0.154433	+	1.07410i
$652$	91.7198	−	26.9314i	0.00550924	−	0.00161766i
$653$	−13521.9	−	8689.98i	−0.810340	−	0.520774i	0.0686351	−	0.997642i	$-0.478136\pi$
$653$	−13521.9	−	8689.98i	−0.810340	−	0.520774i	−0.878975	+	0.476868i	$0.841772\pi$
$654$	−1332.70	−	9269.11i	−0.0796828	−	0.554206i
$655$	2805.56	+	6143.31i	0.167362	+	0.366472i
$656$	−606.611	−	1328.29i	−0.0361039	−	0.0790565i
$657$	−42.8613	−	298.107i	−0.00254517	−	0.0177021i
$658$	−13158.7	−	8456.58i	−0.779604	−	0.501021i
$659$	−6576.44	+	1931.02i	−0.388743	+	0.114145i	−0.470263	−	0.882526i	$-0.655841\pi$
$659$	−6576.44	+	1931.02i	−0.388743	+	0.114145i	0.0815197	+	0.996672i	$0.474023\pi$
$660$	−92.8191	+	645.571i	−0.00547421	+	0.0380740i
$661$	5233.37	−	6039.64i	0.307950	−	0.355393i	−0.580587	−	0.814198i	$-0.697177\pi$
$661$	5233.37	−	6039.64i	0.307950	−	0.355393i	0.888537	+	0.458805i	$0.151722\pi$
$662$	15106.2	−	9708.14i	0.886884	−	0.569966i
$663$	−7323.68	−	8451.98i	−0.429002	−	0.495095i
$664$	25880.1	+	7599.09i	1.51257	+	0.444129i
$665$	5564.04	−	12183.5i	0.324457	−	0.710463i
$666$	−1146.05			−0.0666796
$667$	5419.58	−	1080.38i	0.314613	−	0.0627171i
$668$	−438.827			−0.0254173
$669$	−9242.70	+	20238.7i	−0.534145	+	1.16962i
$670$	−10428.6	−	3062.10i	−0.601329	−	0.176566i
$671$	−1216.13	−	1403.48i	−0.0699672	−	0.0807465i
$672$	−2399.21	+	1541.88i	−0.137726	+	0.0885109i
$673$	16908.7	−	19513.7i	0.968474	−	1.11768i	−0.0245417	−	0.999699i	$-0.507813\pi$
$673$	16908.7	−	19513.7i	0.968474	−	1.11768i	0.993016	−	0.117980i	$-0.0376419\pi$
$674$	−1411.88	+	9819.88i	−0.0806881	+	0.561198i
$675$	3454.16	−	1014.23i	0.196964	−	0.0578338i
$676$	707.321	+	454.568i	0.0402436	+	0.0258630i
$677$	−1252.37	−	8710.43i	−0.0710968	−	0.494489i	−0.993993	−	0.109441i	$-0.965094\pi$
$677$	−1252.37	−	8710.43i	−0.0710968	−	0.494489i	0.922897	−	0.385048i	$-0.125815\pi$
$678$	−13390.6	−	29321.2i	−0.758498	−	1.66088i
$679$	−15683.8	−	34342.7i	−0.886434	−	1.94102i
$680$	1439.05	+	10008.8i	0.0811543	+	0.564440i
$681$	10347.2	+	6649.71i	0.582238	+	0.374181i
$682$	−19334.8	+	5677.21i	−1.08558	+	0.318756i
$683$	932.636	−	6486.63i	0.0522494	−	0.363403i	−0.946876	−	0.321598i	$-0.895780\pi$
$683$	932.636	−	6486.63i	0.0522494	−	0.363403i	0.999126	−	0.0418048i	$-0.0133108\pi$
$684$	−63.9500	+	73.8022i	−0.00357484	+	0.00412558i
$685$	−1774.15	+	1140.18i	−0.0989589	+	0.0635970i
$686$	−6514.74	−	7518.41i	−0.362586	−	0.418447i
$687$	1523.26	+	447.271i	0.0845941	+	0.0248391i
$688$	−7378.03	+	16155.6i	−0.408844	+	0.895244i
$689$	−19038.2			−1.05268
$690$	−5466.07	+	5278.74i	−0.301579	+	0.291244i
$691$	−20490.1			−1.12805			−0.564024	−	0.825758i	$-0.690748\pi$
$691$	−20490.1			−1.12805			−0.564024	+	0.825758i	$0.690748\pi$
$692$	489.709	−	1072.31i	0.0269016	−	0.0589063i
$693$	−1606.37	−	471.674i	−0.0880535	−	0.0258548i
$694$	−16861.1	−	19458.7i	−0.922244	−	1.06433i
$695$	−8475.85	+	5447.10i	−0.462600	+	0.297295i
$696$	−3862.56	+	4457.64i	−0.210359	+	0.242768i
$697$	303.542	−	2111.18i	0.0164957	−	0.114730i
$698$	6058.46	−	1778.92i	0.328533	−	0.0964660i
$699$	−9356.36	−	6012.97i	−0.506281	−	0.325367i
$700$	44.5125	+	309.592i	0.00240345	+	0.0167164i
$701$	421.064	+	922.001i	0.0226867	+	0.0496769i	0.920636	−	0.390422i	$-0.127671\pi$
$701$	421.064	+	922.001i	0.0226867	+	0.0496769i	−0.897949	+	0.440099i	$0.854943\pi$
$702$	−4176.10	−	9144.39i	−0.224525	−	0.491642i
$703$	4534.92	+	31541.0i	0.243297	+	1.69217i
$704$	−21632.3	−	13902.2i	−1.15809	−	0.744261i
$705$	−6039.25	+	1773.28i	−0.322626	+	0.0947315i
$706$	1737.40	−	12083.9i	0.0926176	−	0.644169i
$707$	11127.2	−	12841.5i	0.591914	−	0.683105i
$708$	911.312	−	585.665i	0.0483746	−	0.0310885i
$709$	−6216.52	−	7174.25i	−0.329290	−	0.380021i	0.566829	−	0.823836i	$-0.308170\pi$
$709$	−6216.52	−	7174.25i	−0.329290	−	0.380021i	−0.896118	+	0.443815i	$0.853625\pi$
$710$	7493.81	+	2200.38i	0.396109	+	0.116308i
$711$	191.750	−	419.873i	0.0101142	−	0.0221469i
$712$	−21199.9			−1.11587
$713$	15968.6	+	6275.18i	0.838750	+	0.329604i
$714$	27425.5			1.43750
$715$	2519.78	−	5517.54i	0.131796	−	0.288594i
$716$	349.286	+	102.560i	0.0182311	+	0.00535312i
$717$	−9668.15	−	11157.6i	−0.503576	−	0.581157i
$718$	−19460.8	+	12506.7i	−1.01152	+	0.650064i
$719$	6919.05	−	7985.00i	0.358883	−	0.414173i	−0.547382	−	0.836883i	$-0.684376\pi$
$719$	6919.05	−	7985.00i	0.358883	−	0.414173i	0.906265	+	0.422710i	$0.138921\pi$
$720$	−64.8861	+	451.293i	−0.00335856	+	0.0233593i
$721$	23603.1	−	6930.49i	1.21918	−	0.357982i
$722$	−15501.8	−	9962.39i	−0.799053	−	0.513520i
$723$	2338.54	+	16264.9i	0.120292	+	0.836649i
$724$	218.804	+	479.113i	0.0112317	+	0.0245941i
$725$	520.306	+	1139.31i	0.0266533	+	0.0583627i
$726$	1804.42	+	12550.0i	0.0922429	+	0.641563i
$727$	10498.9	+	6747.24i	0.535602	+	0.344211i	0.780317	−	0.625385i	$-0.215058\pi$
$727$	10498.9	+	6747.24i	0.535602	+	0.344211i	−0.244715	+	0.969595i	$0.578694\pi$
$728$	13143.7	−	3859.34i	0.669145	−	0.196479i
$729$	−2941.94	+	20461.6i	−0.149466	+	1.03956i
$730$	−1752.32	+	2022.28i	−0.0888442	+	0.102532i
$731$	−21823.6	+	14025.2i	−1.10421	+	0.709630i
$732$	−70.4651	−	81.3211i	−0.00355801	−	0.00410617i
$733$	−13786.5	−	4048.07i	−0.694699	−	0.203982i	−0.0847260	−	0.996404i	$-0.527001\pi$
$733$	−13786.5	−	4048.07i	−0.694699	−	0.203982i	−0.609973	+	0.792422i	$0.708820\pi$
$734$	−8372.31	+	18332.8i	−0.421019	+	0.921902i
$735$	4650.95			0.233405
$736$	904.227	+	2559.74i	0.0452857	+	0.128197i
$737$	37774.1			1.88796
$738$	42.8852	−	93.9054i	0.00213906	−	0.00468388i
$739$	21395.7	+	6282.33i	1.06502	+	0.312719i	0.766872	−	0.641800i	$-0.221812\pi$
$739$	21395.7	+	6282.33i	1.06502	+	0.312719i	0.298151	+	0.954519i	$0.403630\pi$
$740$	−487.295	−	562.369i	−0.0242072	−	0.0279366i
$741$	−12661.3	+	8136.93i	−0.627699	+	0.403397i
$742$	30573.7	−	35283.9i	1.51266	−	1.74571i
$743$	5664.17	−	39395.2i	0.279675	−	1.94518i	−0.0440544	−	0.999029i	$-0.514027\pi$
$743$	5664.17	−	39395.2i	0.279675	−	1.94518i	0.323729	−	0.946150i	$-0.395063\pi$
$744$	−17570.8	+	5159.24i	−0.865827	+	0.254230i
$745$	−3193.19	−	2052.14i	−0.157033	−	0.100919i
$746$	2200.40	+	15304.1i	0.107992	+	0.751104i
$747$	737.946	+	1615.88i	0.0361446	+	0.0791457i
$748$	−930.815	−	2038.20i	−0.0455000	−	0.0996310i
$749$	−4811.53	−	33464.9i	−0.234726	−	1.63255i
$750$	−1448.85	−	931.122i	−0.0705396	−	0.0453330i
$751$	36807.5	−	10807.6i	1.78845	−	0.525135i	0.792089	−	0.610406i	$-0.208994\pi$
$751$	36807.5	−	10807.6i	1.78845	−	0.525135i	0.996358	+	0.0852707i	$0.0271755\pi$
$752$	2106.90	−	14653.8i	0.102169	−	0.710598i
$753$	−19155.6	+	22106.8i	−0.927053	+	1.06988i
$754$	2942.33	−	1890.92i	0.142113	−	0.0913307i
$755$	6776.27	+	7820.23i	0.326641	+	0.376963i
$756$	−1728.60	−	507.562i	−0.0831594	−	0.0244178i
$757$	−12968.7	+	28397.5i	−0.622663	+	1.36344i	0.290903	+	0.956753i	$0.406044\pi$
$757$	−12968.7	+	28397.5i	−0.622663	+	1.36344i	−0.913566	+	0.406690i	$0.866683\pi$
$758$	3793.08			0.181756
$759$	13058.9	−	22955.0i	0.624515	−	1.09778i
$760$	13608.0			0.649494
$761$	−3597.55	+	7877.53i	−0.171368	+	0.375243i	−0.975756	−	0.218861i	$-0.929766\pi$
$761$	−3597.55	+	7877.53i	−0.171368	+	0.375243i	0.804388	+	0.594104i	$0.202493\pi$
$762$	2044.53	+	600.328i	0.0971988	+	0.0285401i
$763$	10220.8	+	11795.5i	0.484953	+	0.559666i
$764$	1189.90	−	764.699i	0.0563467	−	0.0362118i

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)

\(f(q)\)	\(=\)	\(q+(-1.13426 + 2.48368i) q^{2} +(-4.84173 - 1.42166i) q^{3} +(0.356777 + 0.411743i) q^{4} +(4.20627 - 2.70320i) q^{5} +(9.02270 - 10.4128i) q^{6} +(-3.26809 + 22.7301i) q^{7} +(-22.3859 + 6.57308i) q^{8} +(-1.29264 - 0.830727i) q^{9} +O(q^{10})\)	\(q+(-1.13426 + 2.48368i) q^{2} +(-4.84173 - 1.42166i) q^{3} +(0.356777 + 0.411743i) q^{4} +(4.20627 - 2.70320i) q^{5} +(9.02270 - 10.4128i) q^{6} +(-3.26809 + 22.7301i) q^{7} +(-22.3859 + 6.57308i) q^{8} +(-1.29264 - 0.830727i) q^{9} +(1.94290 + 13.5131i) q^{10} +(-19.7103 - 43.1595i) q^{11} +(-1.14206 - 2.50076i) q^{12} +(3.63873 + 25.3079i) q^{13} +(-52.7473 - 33.8986i) q^{14} +(-24.2086 + 7.10830i) q^{15} +(8.44563 - 58.7406i) q^{16} +(56.7638 - 65.5090i) q^{17} +(3.52944 - 2.26823i) q^{18} +(-76.3911 - 88.1600i) q^{19} +(2.61372 + 0.767459i) q^{20} +(48.1377 - 105.407i) q^{21} +129.551 q^{22} +(-87.1373 - 67.6320i) q^{23} +117.731 q^{24} +(10.3854 - 22.7408i) q^{25} +(-66.9839 - 19.6682i) q^{26} +(94.2994 + 108.827i) q^{27} +(-10.5249 + 6.76396i) q^{28} +(-32.8084 + 37.8629i) q^{29} +(9.80411 - 68.1891i) q^{30} +(-149.245 + 43.8223i) q^{31} +(-20.7046 - 13.3060i) q^{32} +(34.0737 + 236.988i) q^{33} +(98.3183 + 215.287i) q^{34} +(47.6976 + 104.443i) q^{35} +(-0.119137 - 0.828618i) q^{36} +(-229.801 - 147.684i) q^{37} +(305.608 - 89.7346i) q^{38} +(18.3615 - 127.707i) q^{39} +(-76.3925 + 88.1617i) q^{40} +(20.7001 - 13.3032i) q^{41} +(207.196 + 239.117i) q^{42} +(-287.156 - 84.3167i) q^{43} +(10.7384 - 23.5139i) q^{44} -7.68280 q^{45} +(266.812 - 139.709i) q^{46} +249.467 q^{47} +(-124.401 + 272.399i) q^{48} +(-176.870 - 51.9338i) q^{49} +(44.7011 + 51.5878i) q^{50} +(-367.966 + 236.478i) q^{51} +(-9.12213 + 10.5275i) q^{52} +(-105.968 + 737.026i) q^{53} +(-377.252 + 110.771i) q^{54} +(-199.576 - 128.259i) q^{55} +(-76.2476 - 530.314i) q^{56} +(244.531 + 535.449i) q^{57} +(-56.8261 - 124.432i) q^{58} +(56.0769 + 390.023i) q^{59} +(-11.5639 - 7.43165i) q^{60} +(37.5544 - 11.0270i) q^{61} +(60.4418 - 420.382i) q^{62} +(23.1070 - 26.6669i) q^{63} +(455.923 - 293.004i) q^{64} +(83.7179 + 96.6156i) q^{65} +(-627.249 - 184.177i) q^{66} +(-330.724 + 724.184i) q^{67} +47.2249 q^{68} +(325.745 + 451.335i) q^{69} -313.504 q^{70} +(237.653 - 520.388i) q^{71} +(34.3972 + 10.0999i) q^{72} +(128.355 + 148.130i) q^{73} +(627.454 - 403.240i) q^{74} +(-82.6128 + 95.3403i) q^{75} +(9.04465 - 62.9069i) q^{76} +(1045.43 - 306.967i) q^{77} +(296.356 + 190.457i) q^{78} +(42.7517 + 297.344i) q^{79} +(-123.263 - 269.909i) q^{80} +(-284.622 - 623.236i) q^{81} +(9.56149 + 66.5016i) q^{82} +(-972.567 - 625.031i) q^{83} +(60.5749 - 17.7864i) q^{84} +(61.6798 - 428.992i) q^{85} +(535.124 - 617.566i) q^{86} +(212.678 - 136.680i) q^{87} +(724.922 + 836.605i) q^{88} +(871.852 + 255.999i) q^{89} +(8.71427 - 19.0816i) q^{90} -587.143 q^{91} +(-3.24161 - 60.0077i) q^{92} +784.904 q^{93} +(-282.959 + 619.594i) q^{94} +(-559.636 - 164.324i) q^{95} +(81.3292 + 93.8589i) q^{96} +(-1383.09 + 888.860i) q^{97} +(329.603 - 380.382i) q^{98} +(-10.3755 + 72.1634i) 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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