LMFDB - Embedded newform 115.4.g.a.16.9

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			16.9
Character	$\chi$	$=$	115.16
Dual form			115.4.g.a.36.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11818 - 2.44451i) q^{2} +(-0.807164 + 0.518733i) q^{3} +(-0.350419 - 2.43722i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.441670 + 3.07188i) q^{6} +(31.6351 - 9.28890i) q^{7} +(15.0685 + 9.68396i) q^{8} +(-10.8338 + 23.7227i) q^{9} +O(q^{10})$	\(q+(2.11818 - 2.44451i) q^{2} +(-0.807164 + 0.518733i) q^{3} +(-0.350419 - 2.43722i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.441670 + 3.07188i) q^{6} +(31.6351 - 9.28890i) q^{7} +(15.0685 + 9.68396i) q^{8} +(-10.8338 + 23.7227i) q^{9} +(15.5176 + 4.55638i) q^{10} +(-43.6869 - 50.4173i) q^{11} +(1.54711 + 1.78546i) q^{12} +(74.3430 + 21.8291i) q^{13} +(44.3019 - 97.0077i) q^{14} +(-4.03582 - 2.59366i) q^{15} +(74.4906 - 21.8724i) q^{16} +(7.85142 - 54.6078i) q^{17} +(35.0423 + 76.7320i) q^{18} +(2.28138 + 15.8673i) q^{19} +(10.3570 - 6.65605i) q^{20} +(-20.7162 + 23.9078i) q^{21} -215.782 q^{22} +(-107.980 - 22.5249i) q^{23} -17.1862 q^{24} +(-16.3715 + 18.8937i) q^{25} +(210.833 - 135.494i) q^{26} +(-7.24788 - 50.4101i) q^{27} +(-33.7246 - 73.8466i) q^{28} +(-35.9668 + 250.154i) q^{29} +(-14.8888 + 4.37175i) q^{30} +(-70.7442 - 45.4645i) q^{31} +(44.7898 - 98.0759i) q^{32} +(61.4156 + 18.0332i) q^{33} +(-116.859 - 134.862i) q^{34} +(107.956 + 124.588i) q^{35} +(61.6137 + 18.0914i) q^{36} +(41.4347 - 90.7294i) q^{37} +(43.6202 + 28.0330i) q^{38} +(-71.3304 + 20.9445i) q^{39} +(-12.7457 + 88.6484i) q^{40} +(48.6556 + 106.541i) q^{41} +(14.5621 + 101.282i) q^{42} +(-215.405 + 138.432i) q^{43} +(-107.569 + 124.142i) q^{44} -130.397 q^{45} +(-283.782 + 216.245i) q^{46} -255.532 q^{47} +(-48.7802 + 56.2954i) q^{48} +(625.945 - 402.270i) q^{49} +(11.5081 + 80.0406i) q^{50} +(21.9895 + 48.1503i) q^{51} +(27.1510 - 188.839i) q^{52} +(-121.070 + 35.5492i) q^{53} +(-138.580 - 89.0600i) q^{54} +(138.565 - 303.415i) q^{55} +(566.648 + 166.383i) q^{56} +(-10.0724 - 11.6241i) q^{57} +(535.320 + 617.792i) q^{58} +(-652.592 - 191.618i) q^{59} +(-4.90710 + 10.7450i) q^{60} +(-189.119 - 121.540i) q^{61} +(-260.987 + 76.6327i) q^{62} +(-122.370 + 851.102i) q^{63} +(113.133 + 247.726i) q^{64} +(55.1338 + 383.464i) q^{65} +(174.171 - 111.933i) q^{66} +(133.508 - 154.077i) q^{67} -135.843 q^{68} +(98.8417 - 37.8313i) q^{69} +533.225 q^{70} +(273.764 - 315.941i) q^{71} +(-392.978 + 252.552i) q^{72} +(-16.3078 - 113.423i) q^{73} +(-134.023 - 293.468i) q^{74} +(3.41370 - 23.7428i) q^{75} +(37.8728 - 11.1204i) q^{76} +(-1850.36 - 1189.15i) q^{77} +(-99.8914 + 218.732i) q^{78} +(-1044.42 - 306.669i) q^{79} +(254.202 + 293.365i) q^{80} +(-429.117 - 495.227i) q^{81} +(363.501 + 106.733i) q^{82} +(121.099 - 265.170i) q^{83} +(65.5280 + 42.1123i) q^{84} +(264.673 - 77.7151i) q^{85} +(-117.867 + 819.782i) q^{86} +(-100.732 - 220.573i) q^{87} +(-170.058 - 1182.78i) q^{88} +(-450.737 + 289.671i) q^{89} +(-276.204 + 318.756i) q^{90} +2554.61 q^{91} +(-17.0599 + 271.064i) q^{92} +80.6860 q^{93} +(-541.261 + 624.649i) q^{94} +(-67.4286 + 43.3338i) q^{95} +(14.7225 + 102.397i) q^{96} +(122.812 + 268.921i) q^{97} +(342.509 - 2382.21i) q^{98} +(1669.33 - 490.159i) 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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	2.11818	−	2.44451i	0.748889	−	0.864263i	−0.245572	−	0.969378i	$-0.578976\pi$
$2$	2.11818	−	2.44451i	0.748889	−	0.864263i	0.994460	+	0.105115i	$0.0335211\pi$
$3$	−0.807164	+	0.518733i	−0.155339	+	0.0998301i	−0.616001	−	0.787745i	$-0.711248\pi$
$3$	−0.807164	+	0.518733i	−0.155339	+	0.0998301i	0.460662	+	0.887575i	$0.347612\pi$
$4$	−0.350419	−	2.43722i	−0.0438024	−	0.304652i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$5$	2.07708	+	4.54816i	0.185779	+	0.406800i
$6$	−0.441670	+	3.07188i	−0.0300519	+	0.209015i
$7$	31.6351	−	9.28890i	1.70813	−	0.501553i	0.725676	−	0.688037i	$-0.241527\pi$
$7$	31.6351	−	9.28890i	1.70813	−	0.501553i	0.982458	+	0.186484i	$0.0597091\pi$
$8$	15.0685	+	9.68396i	0.665941	+	0.427974i
$9$	−10.8338	+	23.7227i	−0.401251	+	0.878617i
$10$	15.5176	+	4.55638i	0.490710	+	0.144085i
$11$	−43.6869	−	50.4173i	−1.19746	−	1.38195i	−0.904859	−	0.425711i	$-0.860024\pi$
$11$	−43.6869	−	50.4173i	−1.19746	−	1.38195i	−0.292603	−	0.956234i	$-0.594522\pi$
$12$	1.54711	+	1.78546i	0.0372177	+	0.0429515i
$13$	74.3430	+	21.8291i	1.58608	+	0.465715i	0.951629	−	0.307249i	$-0.0994086\pi$
$13$	74.3430	+	21.8291i	1.58608	+	0.465715i	0.634450	+	0.772964i	$0.281227\pi$
$14$	44.3019	−	97.0077i	0.845728	−	1.85189i
$15$	−4.03582	−	2.59366i	−0.0694696	−	0.0446454i
$16$	74.4906	−	21.8724i	1.16392	−	0.341757i
$17$	7.85142	−	54.6078i	0.112015	−	0.779079i	−0.853941	−	0.520370i	$-0.825794\pi$
$17$	7.85142	−	54.6078i	0.112015	−	0.779079i	0.965955	−	0.258709i	$-0.0832970\pi$
$18$	35.0423	+	76.7320i	0.458864	+	1.00477i
$19$	2.28138	+	15.8673i	0.0275466	+	0.191590i	0.998948	−	0.0458515i	$-0.0146001\pi$
$19$	2.28138	+	15.8673i	0.0275466	+	0.191590i	−0.971402	+	0.237442i	$0.923691\pi$
$20$	10.3570	−	6.65605i	0.115795	−	0.0744169i
$21$	−20.7162	+	23.9078i	−0.215269	+	0.248434i
$22$	−215.782			−2.09113
$23$	−107.980	−	22.5249i	−0.978928	−	0.204207i
$23$	−107.980	−	22.5249i	−0.978928	−	0.204207i
$24$	−17.1862			−0.146171
$25$	−16.3715	+	18.8937i	−0.130972	+	0.151150i
$26$	210.833	−	135.494i	1.59030	−	1.02202i
$27$	−7.24788	−	50.4101i	−0.0516613	−	0.359312i
$28$	−33.7246	−	73.8466i	−0.227620	−	0.498418i
$29$	−35.9668	+	250.154i	−0.230305	+	1.60181i	0.466481	+	0.884531i	$0.345522\pi$
$29$	−35.9668	+	250.154i	−0.230305	+	1.60181i	−0.696787	+	0.717279i	$0.745388\pi$
$30$	−14.8888	+	4.37175i	−0.0906104	+	0.0266056i
$31$	−70.7442	−	45.4645i	−0.409872	−	0.263409i	0.319417	−	0.947614i	$-0.396513\pi$
$31$	−70.7442	−	45.4645i	−0.409872	−	0.263409i	−0.729289	+	0.684205i	$0.760149\pi$
$32$	44.7898	−	98.0759i	0.247431	−	0.541798i
$33$	61.4156	+	18.0332i	0.323972	+	0.0951268i
$34$	−116.859	−	134.862i	−0.589443	−	0.680254i
$35$	107.956	+	124.588i	0.521368	+	0.601690i
$36$	61.6137	+	18.0914i	0.285249	+	0.0837566i
$37$	41.4347	−	90.7294i	0.184103	−	0.403130i	−0.794967	−	0.606653i	$-0.792512\pi$
$37$	41.4347	−	90.7294i	0.184103	−	0.403130i	0.979070	+	0.203523i	$0.0652390\pi$
$38$	43.6202	+	28.0330i	0.186214	+	0.119672i
$39$	−71.3304	+	20.9445i	−0.292872	+	0.0859949i
$40$	−12.7457	+	88.6484i	−0.0503819	+	0.350414i
$41$	48.6556	+	106.541i	0.185335	+	0.405827i	0.979378	−	0.202034i	$-0.0647552\pi$
$41$	48.6556	+	106.541i	0.185335	+	0.405827i	−0.794044	+	0.607861i	$0.792028\pi$
$42$	14.5621	+	101.282i	0.0534997	+	0.372099i
$43$	−215.405	+	138.432i	−0.763928	+	0.490947i	−0.863664	−	0.504067i	$-0.831836\pi$
$43$	−215.405	+	138.432i	−0.763928	+	0.490947i	0.0997364	+	0.995014i	$0.468200\pi$
$44$	−107.569	+	124.142i	−0.368561	+	0.425342i
$45$	−130.397			−0.431965
$46$	−283.782	+	216.245i	−0.909597	+	0.693123i
$47$	−255.532			−0.793045			−0.396523	−	0.918025i	$-0.629783\pi$
$47$	−255.532			−0.793045			−0.396523	+	0.918025i	$0.629783\pi$
$48$	−48.7802	+	56.2954i	−0.146684	+	0.169282i
$49$	625.945	−	402.270i	1.82491	−	1.17280i
$50$	11.5081	+	80.0406i	0.0325498	+	0.226389i
$51$	21.9895	+	48.1503i	0.0603754	+	0.132204i
$52$	27.1510	−	188.839i	0.0724071	−	0.503602i
$53$	−121.070	+	35.5492i	−0.313777	+	0.0921333i	−0.434829	−	0.900513i	$-0.643191\pi$
$53$	−121.070	+	35.5492i	−0.313777	+	0.0921333i	0.121052	+	0.992646i	$0.461373\pi$
$54$	−138.580	−	89.0600i	−0.349229	−	0.224436i
$55$	138.565	−	303.415i	0.339711	−	0.743864i
$56$	566.648	+	166.383i	1.35217	+	0.397033i
$57$	−10.0724	−	11.6241i	−0.0234055	−	0.0270114i
$58$	535.320	+	617.792i	1.21191	+	1.39862i
$59$	−652.592	−	191.618i	−1.44000	−	0.422823i	−0.533781	−	0.845623i	$-0.679229\pi$
$59$	−652.592	−	191.618i	−1.44000	−	0.422823i	−0.906223	+	0.422799i	$0.861047\pi$
$60$	−4.90710	+	10.7450i	−0.0105584	+	0.0231197i
$61$	−189.119	−	121.540i	−0.396955	−	0.255108i	0.326901	−	0.945059i	$-0.393996\pi$
$61$	−189.119	−	121.540i	−0.396955	−	0.255108i	−0.723856	+	0.689951i	$0.757632\pi$
$62$	−260.987	+	76.6327i	−0.534603	+	0.156974i
$63$	−122.370	+	851.102i	−0.244717	+	1.70204i
$64$	113.133	+	247.726i	0.220963	+	0.483841i
$65$	55.1338	+	383.464i	0.105208	+	0.731737i
$66$	174.171	−	111.933i	0.324834	−	0.208758i
$67$	133.508	−	154.077i	0.243442	−	0.280947i	−0.620859	−	0.783923i	$-0.713216\pi$
$67$	133.508	−	154.077i	0.243442	−	0.280947i	0.864301	+	0.502975i	$0.167761\pi$
$68$	−135.843			−0.242255
$69$	98.8417	−	37.8313i	0.172451	−	0.0660052i
$70$	533.225			0.910465
$71$	273.764	−	315.941i	0.457603	−	0.528102i	−0.479319	−	0.877641i	$-0.659116\pi$
$71$	273.764	−	315.941i	0.457603	−	0.528102i	0.936922	+	0.349539i	$0.113662\pi$
$72$	−392.978	+	252.552i	−0.643235	+	0.413382i
$73$	−16.3078	−	113.423i	−0.0261463	−	0.181852i	0.972563	−	0.232639i	$-0.0747360\pi$
$73$	−16.3078	−	113.423i	−0.0261463	−	0.181852i	−0.998709	+	0.0507873i	$0.983827\pi$
$74$	−134.023	−	293.468i	−0.210538	−	0.461014i
$75$	3.41370	−	23.7428i	0.00525573	−	0.0365544i
$76$	37.8728	−	11.1204i	0.0571619	−	0.0167843i
$77$	−1850.36	−	1189.15i	−2.73855	−	1.75996i
$78$	−99.8914	+	218.732i	−0.145006	+	0.317519i
$79$	−1044.42	−	306.669i	−1.48742	−	0.436746i	−0.565704	−	0.824608i	$-0.691396\pi$
$79$	−1044.42	−	306.669i	−1.48742	−	0.436746i	−0.921718	+	0.387862i	$0.873214\pi$
$80$	254.202	+	293.365i	0.355258	+	0.409990i
$81$	−429.117	−	495.227i	−0.588637	−	0.679324i
$82$	363.501	+	106.733i	0.489536	+	0.143741i
$83$	121.099	−	265.170i	0.160149	−	0.350677i	−0.812499	−	0.582963i	$-0.801893\pi$
$83$	121.099	−	265.170i	0.160149	−	0.350677i	0.972648	+	0.232286i	$0.0746205\pi$
$84$	65.5280	+	42.1123i	0.0851153	+	0.0547003i
$85$	264.673	−	77.7151i	0.337739	−	0.0991692i
$86$	−117.867	+	819.782i	−0.147790	+	1.02790i
$87$	−100.732	−	220.573i	−0.124134	−	0.271815i
$88$	−170.058	−	1182.78i	−0.206002	−	1.43278i
$89$	−450.737	+	289.671i	−0.536832	+	0.345001i	−0.780799	−	0.624783i	$-0.785188\pi$
$89$	−450.737	+	289.671i	−0.536832	+	0.345001i	0.243967	+	0.969784i	$0.421551\pi$
$90$	−276.204	+	318.756i	−0.323494	+	0.373332i
$91$	2554.61			2.94282
$92$	−17.0599	+	271.064i	−0.0193329	+	0.307178i
$93$	80.6860			0.0899651
$94$	−541.261	+	624.649i	−0.593903	+	0.685400i
$95$	−67.4286	+	43.3338i	−0.0728214	+	0.0467995i
$96$	14.7225	+	102.397i	0.0156522	+	0.108863i
$97$	122.812	+	268.921i	0.128553	+	0.281492i	0.962954	−	0.269666i	$-0.0869133\pi$
$97$	122.812	+	268.921i	0.128553	+	0.281492i	−0.834401	+	0.551158i	$0.814186\pi$
$98$	342.509	−	2382.21i	0.353048	−	2.45550i
$99$	1669.33	−	490.159i	1.69468	−	0.497604i
$100$	51.7851	+	33.2803i	0.0517851	+	0.0332803i
$101$	−88.7561	+	194.349i	−0.0874412	+	0.191470i	−0.948301	−	0.317373i	$-0.897199\pi$
$101$	−88.7561	+	194.349i	−0.0874412	+	0.191470i	0.860860	+	0.508843i	$0.169927\pi$
$102$	164.281	+	48.2373i	0.159473	+	0.0468256i
$103$	−174.315	−	201.171i	−0.166755	−	0.192446i	0.666221	−	0.745754i	$-0.267911\pi$
$103$	−174.315	−	201.171i	−0.166755	−	0.192446i	−0.832977	+	0.553308i	$0.813365\pi$
$104$	908.847	+	1048.87i	0.856921	+	0.988940i
$105$	−151.766	−	44.5624i	−0.141055	−	0.0414176i
$106$	−169.546	+	371.255i	−0.155357	+	0.340184i
$107$	1248.35	+	802.267i	1.12788	+	0.724842i	0.965116	−	0.261823i	$-0.0843238\pi$
$107$	1248.35	+	802.267i	1.12788	+	0.724842i	0.162761	+	0.986666i	$0.447960\pi$
$108$	−120.321	+	35.3294i	−0.107202	+	0.0314775i
$109$	120.961	−	841.301i	0.106293	−	0.739284i	−0.865064	−	0.501661i	$-0.832723\pi$
$109$	120.961	−	841.301i	0.106293	−	0.739284i	0.971357	−	0.237623i	$-0.0763684\pi$
$110$	−448.195	−	981.411i	−0.388489	−	0.850671i
$111$	13.6197	+	94.7270i	0.0116462	+	0.0810008i
$112$	2153.35	−	1383.87i	1.81672	−	1.16753i
$113$	628.595	−	725.437i	0.523303	−	0.603923i	−0.431152	−	0.902279i	$-0.641893\pi$
$113$	628.595	−	725.437i	0.523303	−	0.603923i	0.954455	+	0.298356i	$0.0964382\pi$
$114$	−49.7503			−0.0408732
$115$	−121.835	−	537.895i	−0.0987930	−	0.436165i
$116$	622.284			0.498083
$117$	−1323.26	+	1527.12i	−1.04560	+	1.20669i
$118$	−1850.72	+	1189.38i	−1.44383	+	0.927895i
$119$	−258.866	−	1800.45i	−0.199414	−	1.38695i
$120$	−35.6969	−	78.1654i	−0.0271556	−	0.0594624i
$121$	−443.944	+	3087.70i	−0.333542	+	2.31983i
$122$	−697.693	+	204.861i	−0.517755	+	0.152027i
$123$	−94.5392	−	60.7567i	−0.0693034	−	0.0445386i
$124$	−86.0169	+	188.351i	−0.0622947	+	0.136406i
$125$	−119.937	−	35.2166i	−0.0858197	−	0.0251989i
$126$	1821.32	+	2101.92i	1.28775	+	1.48614i
$127$	−1189.27	−	1372.49i	−0.830951	−	0.958968i	0.168693	−	0.985669i	$-0.446045\pi$
$127$	−1189.27	−	1372.49i	−0.830951	−	0.958968i	−0.999643	+	0.0267006i	$0.991500\pi$
$128$	1672.82	+	491.184i	1.15514	+	0.339179i
$129$	102.058	−	223.475i	0.0696563	−	0.152526i
$130$	1054.16	+	677.470i	0.711202	+	0.457062i
$131$	893.722	−	262.421i	0.596068	−	0.175021i	0.0302371	−	0.999543i	$-0.490374\pi$
$131$	893.722	−	262.421i	0.596068	−	0.175021i	0.565831	+	0.824521i	$0.308556\pi$
$132$	22.4298	−	156.002i	0.0147899	−	0.102866i
$133$	219.562	+	480.773i	0.143146	+	0.313446i
$134$	−93.8475	−	652.724i	−0.0605014	−	0.420797i
$135$	214.219	−	137.670i	0.136571	−	0.0877686i
$136$	647.129	−	746.827i	0.408021	−	0.470882i
$137$	−490.412			−0.305830			−0.152915	−	0.988239i	$-0.548866\pi$
$137$	−490.412			−0.305830			−0.152915	+	0.988239i	$0.548866\pi$
$138$	116.885	−	321.753i	0.0721010	−	0.198474i
$139$	1210.77			0.738822			0.369411	−	0.929266i	$-0.379560\pi$
$139$	1210.77			0.738822			0.369411	+	0.929266i	$0.379560\pi$
$140$	265.818	−	306.770i	0.160469	−	0.185191i
$141$	206.256	−	132.553i	0.123191	−	0.0791698i
$142$	−192.438	−	1338.44i	−0.113726	−	0.790979i
$143$	−2147.25	−	4701.82i	−1.25568	−	2.74955i
$144$	−288.143	+	2004.08i	−0.166749	+	1.15977i
$145$	−1212.45	+	356.007i	−0.694402	+	0.203895i
$146$	−311.806	−	200.386i	−0.176748	−	0.113589i
$147$	−296.569	+	649.396i	−0.166399	+	0.364362i
$148$	−235.647	−	69.1922i	−0.130879	−	0.0384295i
$149$	119.076	+	137.421i	0.0654705	+	0.0755569i	0.787540	−	0.616264i	$-0.211354\pi$
$149$	119.076	+	137.421i	0.0654705	+	0.0755569i	−0.722070	+	0.691821i	$0.756809\pi$
$150$	−50.8086	−	58.6362i	−0.0276567	−	0.0319175i
$151$	1383.36	+	406.192i	0.745540	+	0.218910i	0.632371	−	0.774665i	$-0.282082\pi$
$151$	1383.36	+	406.192i	0.745540	+	0.218910i	0.113169	+	0.993576i	$0.463900\pi$
$152$	−119.282	+	261.190i	−0.0636514	+	0.139377i
$153$	1210.38	+	777.866i	0.639566	+	0.411024i
$154$	−6826.28	+	2004.38i	−3.57193	+	1.04881i
$155$	59.8389	−	416.189i	0.0310089	−	0.215672i
$156$	76.0419	+	166.508i	0.0390271	+	0.0854574i
$157$	220.377	+	1532.76i	0.112026	+	0.779155i	0.965945	+	0.258749i	$0.0833102\pi$
$157$	220.377	+	1532.76i	0.112026	+	0.779155i	−0.853919	+	0.520406i	$0.825781\pi$
$158$	−2961.92	+	1903.51i	−1.49138	+	0.958450i
$159$	79.2824	−	91.4968i	0.0395441	−	0.0456363i
$160$	539.097			0.266371
$161$	−3625.18	+	290.436i	−1.77456	+	0.142171i
$162$	−2119.53			−1.02794
$163$	1209.06	−	1395.33i	0.580985	−	0.670493i	−0.386831	−	0.922151i	$-0.626430\pi$
$163$	1209.06	−	1395.33i	0.580985	−	0.670493i	0.967816	+	0.251658i	$0.0809757\pi$
$164$	242.614	−	155.918i	0.115518	−	0.0742389i
$165$	45.5467	+	316.784i	0.0214897	+	0.149464i
$166$	−391.700	−	857.704i	−0.183144	−	0.401029i
$167$	−574.070	+	3992.74i	−0.266005	+	1.85011i	0.219168	+	0.975687i	$0.429666\pi$
$167$	−574.070	+	3992.74i	−0.266005	+	1.85011i	−0.485173	+	0.874418i	$0.661243\pi$
$168$	−543.685	+	159.640i	−0.249680	+	0.0733127i
$169$	3202.13	+	2057.89i	1.45750	+	0.936680i
$170$	370.650	−	811.610i	0.167221	−	0.366162i
$171$	−401.132	−	117.783i	−0.179388	−	0.0526730i
$172$	412.872	+	476.479i	0.183030	+	0.211228i
$173$	455.491	+	525.664i	0.200175	+	0.231015i	0.846958	−	0.531660i	$-0.178431\pi$
$173$	455.491	+	525.664i	0.200175	+	0.231015i	−0.646783	+	0.762674i	$0.723886\pi$
$174$	−752.559	−	220.971i	−0.327882	−	0.0962747i
$175$	−342.412	+	749.778i	−0.147908	+	0.323874i
$176$	−4357.01	−	2800.08i	−1.86603	−	1.19923i
$177$	626.147	−	183.853i	0.265899	−	0.0780750i
$178$	−246.638	+	1715.40i	−0.103856	+	0.722332i
$179$	−104.685	−	229.228i	−0.0437124	−	0.0957167i	0.886516	−	0.462698i	$-0.153119\pi$
$179$	−104.685	−	229.228i	−0.0437124	−	0.0957167i	−0.930228	+	0.366981i	$0.880391\pi$
$180$	45.6936	+	317.806i	0.0189211	+	0.131599i
$181$	−950.291	+	610.715i	−0.390246	+	0.250796i	−0.721020	−	0.692914i	$-0.756327\pi$
$181$	−950.291	+	610.715i	−0.390246	+	0.250796i	0.330774	+	0.943710i	$0.392690\pi$
$182$	5411.12	−	6244.77i	2.20384	−	2.54337i
$183$	215.697			0.0871299
$184$	−1408.97	−	1385.09i	−0.564513	−	0.554946i
$185$	498.715			0.198196
$186$	170.907	−	197.238i	0.0673738	−	0.0777535i
$187$	−3096.19	+	1989.80i	−1.21078	+	0.778120i
$188$	89.5433	+	622.787i	0.0347373	+	0.241603i
$189$	−697.542	−	1527.40i	−0.268459	−	0.587842i
$190$	−36.8961	+	256.618i	−0.0140880	+	0.0979844i
$191$	−125.141	+	36.7448i	−0.0474078	+	0.0139202i	−0.305350	−	0.952240i	$-0.598774\pi$
$191$	−125.141	+	36.7448i	−0.0474078	+	0.0139202i	0.257943	+	0.966160i	$0.416955\pi$
$192$	−219.821	−	141.270i	−0.0826259	−	0.0531005i
$193$	−1097.31	+	2402.77i	−0.409253	+	0.896140i	0.586994	+	0.809591i	$0.300311\pi$
$193$	−1097.31	+	2402.77i	−0.409253	+	0.896140i	−0.996248	+	0.0865486i	$0.972416\pi$
$194$	917.515	+	269.407i	0.339556	+	0.0997025i
$195$	−243.417	−	280.919i	−0.0893922	−	0.103164i
$196$	−1199.76	−	1384.60i	−0.437232	−	0.504593i
$197$	882.559	+	259.143i	0.319186	+	0.0937216i	0.437401	−	0.899266i	$-0.355899\pi$
$197$	882.559	+	259.143i	0.319186	+	0.0937216i	−0.118215	+	0.992988i	$0.537717\pi$
$198$	2337.73	−	5118.92i	0.839068	−	1.83730i
$199$	2639.60	+	1696.37i	0.940283	+	0.604283i	0.918475	−	0.395479i	$-0.129421\pi$
$199$	2639.60	+	1696.37i	0.940283	+	0.604283i	0.0218077	+	0.999762i	$0.493058\pi$
$200$	−429.661	+	126.160i	−0.151908	+	0.0446042i
$201$	−27.8384	+	193.620i	−0.00976900	+	0.0679449i
$202$	287.086	+	628.630i	0.0999964	+	0.218962i
$203$	1185.85	+	8247.74i	0.410000	+	2.85162i
$204$	109.647	−	70.4660i	0.0376316	−	0.0241843i
$205$	−383.504	+	442.587i	−0.130659	+	0.150788i
$206$	−860.993			−0.291205
$207$	1704.18	−	2317.54i	0.572216	−	0.778164i
$208$	6015.31			2.00522
$209$	700.323	−	808.216i	0.231782	−	0.267490i
$210$	−430.400	+	276.601i	−0.141430	+	0.0908919i
$211$	483.510	+	3362.89i	0.157754	+	1.09721i	0.902759	+	0.430147i	$0.141538\pi$
$211$	483.510	+	3362.89i	0.157754	+	1.09721i	−0.745004	+	0.667060i	$0.767553\pi$
$212$	129.066	+	282.616i	0.0418128	+	0.0915573i
$213$	−57.0837	+	397.026i	−0.0183630	+	0.127717i
$214$	4605.38	−	1352.26i	1.47111	−	0.431956i
$215$	−1077.02	−	692.161i	−0.341639	−	0.219558i
$216$	378.954	−	829.794i	0.119373	−	0.261391i
$217$	−2660.31	−	781.138i	−0.832229	−	0.244365i
$218$	−1800.35	−	2077.71i	−0.559335	−	0.645507i
$219$	71.9993	+	83.0916i	0.0222158	+	0.0256384i
$220$	−788.046	−	231.391i	−0.241500	−	0.0709109i
$221$	1775.74	−	3888.32i	0.540493	−	1.18351i
$222$	260.410	+	167.355i	0.0787277	+	0.0505952i
$223$	−4641.13	+	1362.76i	−1.39369	+	0.409224i	−0.890513	−	0.454958i	$-0.849654\pi$
$223$	−4641.13	+	1362.76i	−1.39369	+	0.409224i	−0.503178	+	0.864183i	$0.667836\pi$
$224$	505.911	−	3518.69i	0.150904	−	1.04956i
$225$	−270.844	−	593.066i	−0.0802502	−	0.175723i
$226$	−441.860	−	3073.21i	−0.130054	−	0.904543i
$227$	3370.84	−	2166.31i	0.985596	−	0.633404i	0.0546290	−	0.998507i	$-0.482602\pi$
$227$	3370.84	−	2166.31i	0.985596	−	0.633404i	0.930967	+	0.365102i	$0.118966\pi$
$228$	−24.8010	+	28.6219i	−0.00720388	+	0.00831373i
$229$	4616.72			1.33223			0.666117	−	0.745848i	$-0.267955\pi$
$229$	4616.72			1.33223			0.666117	+	0.745848i	$0.267955\pi$
$230$	−1572.96	−	841.530i	−0.450946	−	0.241256i
$231$	2110.40			0.601099
$232$	−2964.45	+	3421.16i	−0.838904	+	0.968146i
$233$	3228.90	−	2075.09i	0.907864	−	0.583449i	−0.00124851	−	0.999999i	$-0.500397\pi$
$233$	3228.90	−	2075.09i	0.907864	−	0.583449i	0.909113	+	0.416550i	$0.136761\pi$
$234$	930.163	+	6469.43i	0.259858	+	1.80735i
$235$	−530.759	−	1162.20i	−0.147331	−	0.322611i
$236$	−238.335	+	1657.66i	−0.0657385	+	0.457222i
$237$	1002.10	−	294.242i	0.274655	−	0.0806459i
$238$	−4949.55	−	3180.88i	−1.34803	−	0.866327i
$239$	1527.52	−	3344.81i	0.413419	−	0.905261i	−0.582313	−	0.812965i	$-0.697852\pi$
$239$	1527.52	−	3344.81i	0.413419	−	0.905261i	0.995732	−	0.0922964i	$-0.0294207\pi$
$240$	−357.360	−	104.930i	−0.0961147	−	0.0282218i
$241$	−1417.69	−	1636.10i	−0.378926	−	0.437304i	0.533965	−	0.845506i	$-0.320701\pi$
$241$	−1417.69	−	1636.10i	−0.378926	−	0.437304i	−0.912892	+	0.408202i	$0.866156\pi$
$242$	6607.54	+	7625.51i	1.75516	+	2.02556i
$243$	1922.63	+	564.534i	0.507558	+	0.149032i
$244$	−229.948	+	503.516i	−0.0603316	+	0.132108i
$245$	3129.72	+	2011.35i	0.816125	+	0.524492i
$246$	−348.771	+	102.408i	−0.0903936	+	0.0265419i
$247$	−176.765	+	1229.43i	−0.0455355	+	0.316706i
$248$	−625.734	−	1370.17i	−0.160218	−	0.350829i
$249$	39.8055	+	276.854i	0.0101308	+	0.0704614i
$250$	−340.134	+	218.591i	−0.0860479	+	0.0552996i
$251$	1708.10	−	1971.26i	0.429540	−	0.495716i	−0.499179	−	0.866499i	$-0.666365\pi$
$251$	1708.10	−	1971.26i	0.429540	−	0.495716i	0.928720	+	0.370783i	$0.120911\pi$
$252$	2117.20			0.529251
$253$	3581.65	+	6428.09i	0.890026	+	1.59735i
$254$	−5874.15			−1.45109
$255$	−173.321	+	200.023i	−0.0425639	+	0.0491214i
$256$	2911.19	−	1870.91i	0.710741	−	0.456765i
$257$	−238.982	−	1662.15i	−0.0580049	−	0.403433i	−0.998052	−	0.0623883i	$-0.980128\pi$
$257$	−238.982	−	1662.15i	−0.0580049	−	0.403433i	0.940047	−	0.341045i	$-0.110781\pi$
$258$	−330.110	−	722.840i	−0.0796579	−	0.174426i
$259$	468.015	−	3255.12i	0.112282	−	0.780938i
$260$	915.267	−	268.747i	0.218317	−	0.0641037i
$261$	−5544.67	−	3563.34i	−1.31497	−	0.845078i
$262$	1251.57	−	2740.56i	0.295124	−	0.646231i
$263$	219.611	+	64.4836i	0.0514897	+	0.0151188i	0.307376	−	0.951588i	$-0.400549\pi$
$263$	219.611	+	64.4836i	0.0514897	+	0.0151188i	−0.255886	+	0.966707i	$0.582367\pi$
$264$	750.809	+	866.480i	0.175035	+	0.202001i
$265$	−413.154	−	476.805i	−0.0957731	−	0.110528i
$266$	1640.32	+	481.643i	0.378100	+	0.111020i
$267$	213.557	−	467.624i	0.0489493	−	0.107184i
$268$	−422.303	−	271.398i	−0.0962547	−	0.0618591i
$269$	−7802.96	+	2291.16i	−1.76861	+	0.519310i	−0.993631	−	0.112682i	$-0.964056\pi$
$269$	−7802.96	+	2291.16i	−1.76861	+	0.519310i	−0.774975	+	0.631992i	$0.782238\pi$
$270$	117.218	−	815.269i	0.0264210	−	0.183762i
$271$	−414.043	−	906.628i	−0.0928094	−	0.203224i	0.857534	−	0.514427i	$-0.171995\pi$
$271$	−414.043	−	906.628i	−0.0928094	−	0.203224i	−0.950343	+	0.311203i	$0.899268\pi$
$272$	−609.549	−	4239.50i	−0.135880	−	0.945065i
$273$	−2061.99	+	1325.16i	−0.457133	+	0.293782i
$274$	−1038.78	+	1198.81i	−0.229033	+	0.264318i
$275$	1667.79			0.365715
$276$	−126.839	−	227.642i	−0.0276624	−	0.0496466i
$277$	6282.89			1.36282			0.681412	−	0.731900i	$-0.261366\pi$
$277$	6282.89			1.36282			0.681412	+	0.731900i	$0.261366\pi$
$278$	2564.63	−	2959.74i	0.553295	−	0.638537i
$279$	1844.97	−	1185.69i	0.395897	−	0.254427i
$280$	420.234	+	2922.79i	0.0896921	+	0.623822i
$281$	−2232.21	−	4887.85i	−0.473887	−	1.03767i	−0.984099	−	0.177620i	$-0.943160\pi$
$281$	−2232.21	−	4887.85i	−0.473887	−	1.03767i	0.510212	−	0.860049i	$-0.329567\pi$
$282$	112.861	−	784.964i	0.0238325	−	0.165759i
$283$	−1245.05	+	365.579i	−0.261521	+	0.0767895i	−0.409865	−	0.912146i	$-0.634424\pi$
$283$	−1245.05	+	365.579i	−0.261521	+	0.0767895i	0.148343	+	0.988936i	$0.452606\pi$
$284$	−865.949	−	556.512i	−0.180932	−	0.116278i
$285$	31.9473	−	69.9549i	0.00663998	−	0.0145395i
$286$	−16041.9	−	4710.32i	−3.31670	−	0.973870i
$287$	2528.87	+	2918.47i	0.520120	+	0.600251i
$288$	1841.38	+	2125.06i	0.376751	+	0.434794i
$289$	1793.62	+	526.653i	0.365076	+	0.107196i
$290$	−1697.92	+	3717.92i	−0.343811	+	0.752841i
$291$	−238.627	−	153.356i	−0.0480707	−	0.0308932i
$292$	−270.722	+	79.4912i	−0.0542563	+	0.0159311i
$293$	−994.122	+	6914.27i	−0.198216	+	1.37862i	0.611242	+	0.791444i	$0.290670\pi$
$293$	−994.122	+	6914.27i	−0.198216	+	1.37862i	−0.809458	+	0.587178i	$0.800239\pi$
$294$	959.266	+	2100.50i	0.190291	+	0.416679i
$295$	−483.972	−	3366.10i	−0.0955184	−	0.664345i
$296$	1502.98	−	965.907i	0.295132	−	0.189670i
$297$	−2224.91	+	2567.68i	−0.434687	+	0.501656i
$298$	588.151			0.114331
$299$	−7535.84	−	4031.66i	−1.45755	−	0.779790i
$300$	−59.0626			−0.0113666
$301$	−5528.46	+	6380.19i	−1.05866	+	1.22175i
$302$	3923.15	−	2521.25i	0.747522	−	0.480404i
$303$	−29.1743	−	202.912i	−0.00553143	−	0.0384719i
$304$	516.999	+	1132.07i	0.0975392	+	0.213581i
$305$	159.967	−	1112.59i	0.0300317	−	0.208875i
$306$	4465.30	−	1311.13i	0.834197	−	0.244942i
$307$	−4321.05	−	2776.97i	−0.803308	−	0.516255i	0.0733857	−	0.997304i	$-0.476620\pi$
$307$	−4321.05	−	2776.97i	−0.803308	−	0.516255i	−0.876694	+	0.481049i	$0.840256\pi$
$308$	−2249.83	+	4926.43i	−0.416220	+	0.911395i
$309$	245.055	+	71.9546i	0.0451155	+	0.0132471i
$310$	−890.627	−	1027.84i	−0.163175	−	0.188314i
$311$	−1568.30	−	1809.91i	−0.285949	−	0.330002i	0.594543	−	0.804064i	$-0.297333\pi$
$311$	−1568.30	−	1809.91i	−0.285949	−	0.330002i	−0.880492	+	0.474061i	$0.842787\pi$
$312$	−1277.67	−	375.158i	−0.231839	−	0.0680741i
$313$	−588.970	+	1289.66i	−0.106360	+	0.232895i	−0.955327	−	0.295549i	$-0.904497\pi$
$313$	−588.970	+	1289.66i	−0.106360	+	0.232895i	0.848968	+	0.528445i	$0.177225\pi$
$314$	4213.63	+	2707.94i	0.757289	+	0.486680i
$315$	−4125.12	+	1211.24i	−0.737855	+	0.216654i
$316$	−381.435	+	2652.94i	−0.0679032	+	0.472277i
$317$	−586.167	−	1283.53i	−0.103856	−	0.227413i	0.850569	−	0.525863i	$-0.176258\pi$
$317$	−586.167	−	1283.53i	−0.103856	−	0.227413i	−0.954425	+	0.298450i	$0.903530\pi$
$318$	−55.7303	−	387.613i	−0.00982767	−	0.0683530i
$319$	14183.4	−	9115.11i	2.48940	−	1.59984i
$320$	−891.714	+	1029.09i	−0.155776	+	0.179775i
$321$	−1423.79			−0.247564
$322$	−6968.80	+	9476.97i	−1.20607	+	1.64016i
$323$	884.394			0.152350
$324$	−1056.61	+	1219.39i	−0.181174	+	0.209086i
$325$	−1629.54	+	1047.24i	−0.278125	+	0.178740i
$326$	−849.887	−	5911.09i	−0.144389	−	1.00425i
$327$	338.775	+	741.814i	0.0572914	+	0.125451i
$328$	−298.569	+	2076.59i	−0.0502613	+	0.349575i
$329$	−8083.77	+	2373.61i	−1.35463	+	0.397755i
$330$	870.857	+	559.666i	0.145270	+	0.0933593i
$331$	−2446.72	+	5357.57i	−0.406296	+	0.889664i	0.590297	+	0.807186i	$0.299011\pi$
$331$	−2446.72	+	5357.57i	−0.406296	+	0.889664i	−0.996593	+	0.0824780i	$0.973717\pi$
$332$	−688.713	−	202.224i	−0.113849	−	0.0334292i
$333$	1703.45	+	1965.88i	0.280326	+	0.323513i
$334$	8544.30	+	9860.65i	1.39977	+	1.61542i
$335$	978.073	+	287.188i	0.159516	+	0.0468381i
$336$	−1020.24	+	2234.02i	−0.165651	+	0.362726i
$337$	481.591	+	309.499i	0.0778454	+	0.0500282i	0.578985	−	0.815339i	$-0.303449\pi$
$337$	481.591	+	309.499i	0.0778454	+	0.0500282i	−0.501139	+	0.865367i	$0.667086\pi$
$338$	11813.2	−	3468.67i	1.90104	−	0.558197i
$339$	−131.071	+	911.619i	−0.0209994	+	0.146054i
$340$	−282.155	−	617.834i	−0.0450059	−	0.0985493i
$341$	798.391	+	5552.93i	0.126790	+	0.881842i
$342$	−1137.59	+	731.084i	−0.179865	+	0.115592i
$343$	8659.40	−	9993.48i	1.36316	−	1.57317i
$344$	−4586.40			−0.718844
$345$	377.365	+	370.970i	0.0588888	+	0.0578908i
$346$	2249.80			0.349566
$347$	7945.87	−	9170.03i	1.22927	−	1.41865i	0.353843	−	0.935305i	$-0.384875\pi$
$347$	7945.87	−	9170.03i	1.22927	−	1.41865i	0.875428	−	0.483349i	$-0.160580\pi$
$348$	−502.285	+	322.799i	−0.0773716	+	0.0497237i
$349$	744.988	+	5181.51i	0.114265	+	0.794727i	0.963691	+	0.267020i	$0.0860390\pi$
$349$	744.988	+	5181.51i	0.114265	+	0.794727i	−0.849426	+	0.527707i	$0.823052\pi$
$350$	1107.55	+	2425.19i	0.169146	+	0.370377i
$351$	561.577	−	3905.85i	0.0853981	−	0.593957i
$352$	−6901.45	+	2026.45i	−1.04502	+	0.306847i
$353$	−8358.31	−	5371.56i	−1.26025	−	0.809912i	−0.271930	−	0.962317i	$-0.587662\pi$
$353$	−8358.31	−	5371.56i	−1.26025	−	0.809912i	−0.988318	+	0.152404i	$0.951298\pi$
$354$	876.860	−	1920.05i	0.131651	−	0.288276i
$355$	2005.58	+	588.891i	0.299845	+	0.0880424i
$356$	863.940	+	997.039i	0.128620	+	0.148435i
$357$	1142.90	+	1318.98i	0.169436	+	0.195540i
$358$	−782.090	−	229.642i	−0.115460	−	0.0339022i
$359$	−2213.87	+	4847.70i	−0.325470	+	0.712679i	−0.999665	−	0.0258738i	$-0.991763\pi$
$359$	−2213.87	+	4847.70i	−0.325470	+	0.712679i	0.674196	+	0.738553i	$0.264490\pi$
$360$	−1964.89	−	1262.76i	−0.287664	−	0.184870i
$361$	6334.59	−	1860.00i	0.923545	−	0.271177i
$362$	−519.988	+	3616.60i	−0.0754971	+	0.525094i
$363$	−1243.35	−	2722.57i	−0.179777	−	0.393657i
$364$	−895.186	−	6226.15i	−0.128902	−	0.896536i
$365$	481.994	−	309.759i	0.0691197	−	0.0444206i
$366$	456.884	−	527.273i	0.0652506	−	0.0753032i
$367$	2685.34			0.381944			0.190972	−	0.981595i	$-0.438836\pi$
$367$	2685.34			0.381944			0.190972	+	0.981595i	$0.438836\pi$
$368$	−8536.16	+	683.885i	−1.20918	+	0.0968749i
$369$	−3054.56			−0.430932
$370$	1056.37	−	1219.11i	0.148427	−	0.171294i
$371$	−3499.83	+	2249.21i	−0.489763	+	0.314752i
$372$	−28.2740	−	196.650i	−0.00394069	−	0.0274081i
$373$	3226.04	+	7064.05i	0.447824	+	0.980597i	0.990096	+	0.140394i	$0.0448370\pi$
$373$	3226.04	+	7064.05i	0.447824	+	0.980597i	−0.542272	+	0.840203i	$0.682436\pi$
$374$	−1694.20	+	11783.4i	−0.234237	+	1.62916i
$375$	115.076	−	33.7895i	0.0158467	−	0.00465302i
$376$	−3850.49	−	2474.56i	−0.528122	−	0.339403i
$377$	−8134.51	+	17812.1i	−1.11127	+	2.43334i
$378$	−5211.26	−	1530.16i	−0.709096	−	0.208209i
$379$	−3152.05	−	3637.65i	−0.427202	−	0.493018i	0.500815	−	0.865554i	$-0.333034\pi$
$379$	−3152.05	−	3637.65i	−0.427202	−	0.493018i	−0.928018	+	0.372536i	$0.878488\pi$
$380$	129.242	+	149.153i	0.0174473	+	0.0201353i
$381$	1671.89	+	490.912i	0.224813	+	0.0660110i
$382$	−175.248	+	383.740i	−0.0234725	+	0.0513975i
$383$	−7439.28	−	4780.94i	−0.992505	−	0.637844i	−0.0596967	−	0.998217i	$-0.519013\pi$
$383$	−7439.28	−	4780.94i	−0.992505	−	0.637844i	−0.932809	+	0.360372i	$0.882650\pi$
$384$	−1605.03	+	471.280i	−0.213298	+	0.0626300i
$385$	1565.13	−	10885.7i	0.207185	−	1.44100i
$386$	3549.29	+	7771.86i	0.468016	+	1.02481i
$387$	−950.334	−	6609.72i	−0.124827	−	0.868193i
$388$	612.383	−	393.555i	0.0801264	−	0.0514941i
$389$	6800.52	−	7848.22i	0.886375	−	1.02293i	−0.113194	−	0.993573i	$-0.536108\pi$
$389$	6800.52	−	7848.22i	0.886375	−	1.02293i	0.999569	−	0.0293587i	$-0.00934651\pi$
$390$	−1202.31			−0.156106
$391$	−2077.83	+	5719.69i	−0.268748	+	0.739788i
$392$	13327.6			1.71721
$393$	−585.254	+	675.419i	−0.0751200	+	0.0866931i
$394$	2502.89	−	1608.51i	0.320035	−	0.205674i
$395$	−774.557	−	5387.16i	−0.0986637	−	0.686221i
$396$	−1779.59	−	3896.76i	−0.225828	−	0.494493i
$397$	1012.32	−	7040.85i	0.127977	−	0.890102i	−0.820136	−	0.572169i	$-0.806102\pi$
$397$	1012.32	−	7040.85i	0.127977	−	0.890102i	0.948113	−	0.317933i	$-0.102989\pi$
$398$	9737.92	−	2859.31i	1.22643	−	0.360111i
$399$	−426.615	−	274.169i	−0.0535275	−	0.0344000i
$400$	−806.273	+	1765.49i	−0.100784	+	0.220686i
$401$	10744.2	+	3154.77i	1.33800	+	0.392872i	0.870955	−	0.491362i	$-0.163501\pi$
$401$	10744.2	+	3154.77i	1.33800	+	0.392872i	0.467044	+	0.884234i	$0.345319\pi$
$402$	414.339	+	478.173i	0.0514064	+	0.0593261i
$403$	−4266.88	−	4924.24i	−0.527416	−	0.608670i
$404$	504.773	+	148.215i	0.0621618	+	0.0182524i
$405$	1361.06	−	2980.31i	0.166992	−	0.365662i
$406$	22673.5	+	14571.4i	2.77159	+	1.78119i
$407$	−6384.49	+	1874.65i	−0.777561	+	0.228313i
$408$	−134.936	+	938.499i	−0.0163733	+	0.113879i
$409$	−6039.85	−	13225.4i	−0.730199	−	1.59891i	−0.799034	−	0.601285i	$-0.794656\pi$
$409$	−6039.85	−	13225.4i	−0.730199	−	1.59891i	0.0688352	−	0.997628i	$-0.478072\pi$
$410$	269.578	+	1874.95i	0.0324719	+	0.225847i
$411$	395.843	−	254.393i	0.0475072	−	0.0305310i
$412$	−429.214	+	495.339i	−0.0513248	+	0.0592320i
$413$	−22424.7			−2.67179
$414$	−2055.48	−	9074.83i	−0.244013	−	1.07730i
$415$	1457.57			0.172408
$416$	5470.71	−	6313.53i	0.644768	−	0.744102i
$417$	−977.290	+	628.066i	−0.114768	+	0.0737567i
$418$	−492.281	−	3423.89i	−0.0576034	−	0.400641i
$419$	3839.29	+	8406.88i	0.447641	+	0.980198i	0.990132	+	0.140136i	$0.0447540\pi$
$419$	3839.29	+	8406.88i	0.447641	+	0.980198i	−0.542491	+	0.840062i	$0.682519\pi$
$420$	−55.4268	+	385.502i	−0.00643941	+	0.0447871i
$421$	−114.307	+	33.5636i	−0.0132327	+	0.00388548i	−0.288342	−	0.957527i	$-0.593104\pi$
$421$	−114.307	+	33.5636i	−0.0132327	+	0.00388548i	0.275109	+	0.961413i	$0.411286\pi$
$422$	9244.75	+	5941.24i	1.06642	+	0.685344i
$423$	2768.37	−	6061.89i	0.318210	−	0.696783i
$424$	−2168.60	−	636.758i	−0.248388	−	0.0729332i
$425$	903.207	+	1042.36i	0.103087	+	0.118969i
$426$	849.620	+	980.513i	0.0966296	+	0.111516i
$427$	−7111.78	−	2088.21i	−0.806003	−	0.236664i
$428$	1517.86	−	3323.64i	0.171421	−	0.375360i
$429$	4172.17	+	2681.29i	0.469543	+	0.301757i
$430$	−3973.32	+	1166.67i	−0.445606	+	0.130842i
$431$	−408.984	+	2844.55i	−0.0457078	+	0.317905i	0.954121	+	0.299420i	$0.0967932\pi$
$431$	−408.984	+	2844.55i	−0.0457078	+	0.317905i	−0.999829	+	0.0184845i	$0.994116\pi$
$432$	−1642.49	−	3596.55i	−0.182927	−	0.400554i
$433$	−2427.59	−	16884.2i	−0.269428	−	1.87391i	−0.453868	−	0.891069i	$-0.649956\pi$
$433$	−2427.59	−	16884.2i	−0.269428	−	1.87391i	0.184440	−	0.982844i	$-0.440953\pi$
$434$	−7544.51	+	4848.56i	−0.834442	+	0.536264i
$435$	793.971	−	916.292i	0.0875127	−	0.100995i
$436$	−2092.82			−0.229881
$437$	111.068	−	1764.74i	0.0121581	−	0.193178i
$438$	355.625			0.0387955
$439$	5366.65	−	6193.44i	0.583454	−	0.673342i	−0.384890	−	0.922963i	$-0.625761\pi$
$439$	5366.65	−	6193.44i	0.583454	−	0.673342i	0.968344	+	0.249621i	$0.0803060\pi$
$440$	5026.24	−	3230.17i	0.544583	−	0.349982i
$441$	2761.58	+	19207.2i	0.298194	+	2.07399i
$442$	−5743.70	−	12576.9i	−0.618099	−	1.35345i
$443$	−1828.82	+	12719.7i	−0.196140	+	1.36418i	0.619215	+	0.785221i	$0.287451\pi$
$443$	−1828.82	+	12719.7i	−0.196140	+	1.36418i	−0.815355	+	0.578961i	$0.803458\pi$
$444$	226.098	−	66.3884i	0.0241670	−	0.00709606i
$445$	−2253.69	−	1448.36i	−0.240079	−	0.154289i
$446$	−6499.46	+	14231.8i	−0.690041	+	1.51098i
$447$	−167.399	−	49.1527i	−0.0177130	−	0.00520099i
$448$	5880.07	+	6785.97i	0.620106	+	0.715640i
$449$	−4669.04	−	5388.36i	−0.490747	−	0.566353i	0.455318	−	0.890329i	$-0.349526\pi$
$449$	−4669.04	−	5388.36i	−0.490747	−	0.566353i	−0.946065	+	0.323976i	$0.894980\pi$
$450$	−2023.45	−	594.139i	−0.211970	−	0.0622399i
$451$	3245.90	−	7107.52i	0.338899	−	0.742084i
$452$	−1988.32	−	1277.82i	−0.206909	−	0.132972i
$453$	−1327.31	+	389.732i	−0.137665	+	0.0404221i
$454$	1844.48	−	12828.7i	0.190674	−	1.32616i
$455$	5306.12	+	11618.8i	0.546714	+	1.19714i
$456$	−39.2082	−	272.699i	−0.00402651	−	0.0280050i
$457$	−7804.58	+	5015.70i	−0.798868	+	0.513401i	−0.875246	−	0.483678i	$-0.839301\pi$
$457$	−7804.58	+	5015.70i	−0.798868	+	0.513401i	0.0763783	+	0.997079i	$0.475664\pi$
$458$	9779.03	−	11285.6i	0.997694	−	1.15140i
$459$	−2809.69			−0.285720
$460$	−1268.28	+	485.428i	−0.128551	+	0.0492026i
$461$	−14700.0			−1.48513			−0.742565	−	0.669774i	$-0.766391\pi$
$461$	−14700.0			−1.48513			−0.742565	+	0.669774i	$0.766391\pi$
$462$	4470.19	−	5158.87i	0.450156	−	0.519508i
$463$	−1770.24	+	1137.66i	−0.177689	+	0.114194i	−0.626462	−	0.779452i	$-0.715498\pi$
$463$	−1770.24	+	1137.66i	−0.177689	+	0.114194i	0.448773	+	0.893646i	$0.351861\pi$
$464$	2792.29	+	19420.8i	0.279373	+	1.94308i
$465$	167.591	+	366.973i	0.0167136	+	0.0365978i
$466$	1766.82	−	12288.5i	0.175636	−	1.22157i
$467$	9362.20	−	2748.99i	0.927690	−	0.272394i	0.217220	−	0.976123i	$-0.430301\pi$
$467$	9362.20	−	2748.99i	0.927690	−	0.272394i	0.710469	+	0.703728i	$0.248483\pi$
$468$	4185.63	+	2689.94i	0.413420	+	0.265689i
$469$	2792.34	−	6114.38i	0.274922	−	0.601995i
$470$	−3965.24	−	1164.30i	−0.389155	−	0.114266i
$471$	−972.971	−	1122.87i	−0.0951850	−	0.109849i
$472$	−7977.98	−	9207.08i	−0.778001	−	0.897861i
$473$	16389.7	+	4812.46i	1.59324	+	0.467817i
$474$	1403.34	−	3072.89i	0.135986	−	0.297769i
$475$	−337.143	−	216.669i	−0.0325667	−	0.0209294i
$476$	−4297.39	+	1261.83i	−0.413804	+	0.121504i
$477$	468.318	−	3257.22i	0.0449535	−	0.312658i
$478$	−4940.84	−	10818.9i	−0.472780	−	1.03524i
$479$	1726.60	+	12008.8i	0.164698	+	1.14550i	0.889631	+	0.456681i	$0.150962\pi$
$479$	1726.60	+	12008.8i	0.164698	+	1.14550i	−0.724933	+	0.688820i	$0.758129\pi$
$480$	−435.139	+	279.647i	−0.0413777	+	0.0265918i
$481$	5060.92	−	5840.61i	0.479746	−	0.553657i
$482$	−7002.36			−0.661719
$483$	2775.46	−	2114.93i	0.261465	−	0.199239i
$484$	7680.97			0.721353
$485$	−968.004	+	1117.14i	−0.0906285	+	0.104591i
$486$	5452.47	−	3504.09i	0.508908	−	0.327055i
$487$	1989.96	+	13840.5i	0.185161	+	1.28782i	0.844327	+	0.535828i	$0.180000\pi$
$487$	1989.96	+	13840.5i	0.185161	+	1.28782i	−0.659166	+	0.751997i	$0.729091\pi$
$488$	−1672.77	−	3662.85i	−0.155169	−	0.339773i
$489$	−252.106	+	1753.43i	−0.0233141	+	0.162153i
$490$	11546.1	−	3390.23i	1.06449	−	0.312561i
$491$	6266.15	+	4027.01i	0.575942	+	0.370135i	0.795950	−	0.605363i	$-0.206972\pi$
$491$	6266.15	+	4027.01i	0.575942	+	0.370135i	−0.220008	+	0.975498i	$0.570608\pi$
$492$	−114.949	+	251.703i	−0.0105331	+	0.0230643i
$493$	13378.0	+	3928.13i	1.22214	+	0.358852i
$494$	2630.92	+	3036.24i	0.239617	+	0.276532i
$495$	5696.64	+	6574.27i	0.517262	+	0.596952i
$496$	−6264.20	−	1839.33i	−0.567078	−	0.166509i
$497$	5725.81	−	12537.8i	0.516776	−	1.13158i
$498$	761.085	+	489.120i	0.0684840	+	0.0440120i
$499$	9330.43	−	2739.66i	0.837049	−	0.245780i	0.165006	−	0.986292i	$-0.447236\pi$
$499$	9330.43	−	2739.66i	0.837049	−	0.245780i	0.672042	+	0.740513i	$0.265417\pi$
$500$	−43.8024	+	304.652i	−0.00391781	+	0.0272489i
$501$	−1607.80	−	3520.58i	−0.143375	−	0.313948i
$502$	−1200.68	−	8350.95i	−0.106751	−	0.742472i
$503$	−464.191	+	298.318i	−0.0411476	+	0.0264440i	−0.561053	−	0.827780i	$-0.689604\pi$
$503$	−464.191	+	298.318i	−0.0411476	+	0.0264440i	0.519905	+	0.854224i	$0.325967\pi$
$504$	−10086.0	+	11639.8i	−0.891399	+	1.02873i
$505$	−1068.28			−0.0941346
$506$	23300.1	+	4860.47i	2.04707	+	0.427024i
$507$	−3652.14			−0.319915
$508$	−2928.32	+	3379.46i	−0.255754	+	0.295156i
$509$	−7582.88	+	4873.22i	−0.660324	+	0.424365i	−0.827426	−	0.561575i	$-0.810196\pi$
$509$	−7582.88	+	4873.22i	−0.660324	+	0.424365i	0.167102	+	0.985940i	$0.446559\pi$
$510$	121.833	+	847.370i	0.0105782	+	0.0735729i
$511$	−1569.47	−	3436.67i	−0.135870	−	0.297513i
$512$	−391.970	+	2726.21i	−0.0338336	+	0.235318i
$513$	783.339	−	230.009i	0.0674177	−	0.0197956i
$514$	−4569.35	−	2936.54i	−0.392112	−	0.251995i
$515$	552.890	−	1210.66i	0.0473073	−	0.103588i
$516$	−580.420	−	170.427i	−0.0495186	−	0.0145400i
$517$	11163.4	+	12883.2i	0.949642	+	1.09595i
$518$	−6965.81	−	8038.97i	−0.590850	−	0.681877i
$519$	−640.335	−	188.019i	−0.0541572	−	0.0159020i
$520$	−2882.67	+	6312.16i	−0.243102	+	0.532320i
$521$	2617.53	+	1682.19i	0.220108	+	0.141455i	0.646048	−	0.763296i	$-0.276420\pi$
$521$	2617.53	+	1682.19i	0.220108	+	0.141455i	−0.425941	+	0.904751i	$0.640057\pi$
$522$	−20455.2	+	6006.19i	−1.71513	+	0.503609i
$523$	−1804.61	+	12551.3i	−0.150880	+	1.04939i	0.763870	+	0.645370i	$0.223297\pi$
$523$	−1804.61	+	12551.3i	−0.150880	+	1.04939i	−0.914750	+	0.404021i	$0.867612\pi$
$524$	−952.754	−	2086.24i	−0.0794299	−	0.173927i
$525$	−112.552	−	782.814i	−0.00935649	−	0.0650758i
$526$	622.806	−	400.253i	0.0516267	−	0.0331784i
$527$	−3038.16	+	3506.23i	−0.251128	+	0.289817i
$528$	4969.32			0.409587
$529$	11152.3	+	4864.47i	0.916599	+	0.399808i
$530$	−2040.69			−0.167249
$531$	11615.7	−	13405.3i	0.949303	−	1.09555i
$532$	1094.81	−	703.593i	0.0892220	−	0.0573395i
$533$	1291.51	+	8982.67i	0.104956	+	0.729986i
$534$	−690.759	−	1512.55i	−0.0559777	−	0.122574i
$535$	−1055.92	+	7344.08i	−0.0853296	+	0.593480i
$536$	3503.85	−	1028.82i	0.282357	−	0.0829074i
$537$	203.406	+	130.721i	0.0163456	+	0.0105047i
$538$	−10927.3	+	23927.5i	−0.875669	+	1.91745i
$539$	−47627.0	−	13984.5i	−3.80601	−	1.11754i
$540$	−410.599	−	473.856i	−0.0327210	−	0.0377621i
$541$	5614.82	+	6479.85i	0.446211	+	0.514955i	0.933642	−	0.358207i	$-0.116612\pi$
$541$	5614.82	+	6479.85i	0.446211	+	0.514955i	−0.487432	+	0.873161i	$0.662066\pi$
$542$	−3093.28	−	908.268i	−0.245143	−	0.0719805i
$543$	450.243	−	985.894i	0.0355834	−	0.0779167i
$544$	−5004.05	−	3215.91i	−0.394388	−	0.253458i
$545$	4077.61	−	1197.30i	0.320488	−	0.0941037i
$546$	−1128.30	+	7847.48i	−0.0884371	+	0.615093i
$547$	−5086.00	−	11136.8i	−0.397554	−	0.870521i	−0.997512	−	0.0704900i	$-0.977544\pi$
$547$	−5086.00	−	11136.8i	−0.397554	−	0.870521i	0.599959	−	0.800031i	$-0.295184\pi$
$548$	171.850	+	1195.24i	0.0133961	+	0.0931719i
$549$	4932.12	−	3169.68i	0.383420	−	0.246409i
$550$	3532.68	−	4076.93i	0.273880	−	0.316074i
$551$	−4051.34			−0.313236
$552$	1855.76	+	387.116i	0.143091	+	0.0298492i
$553$	−35888.9			−2.75977
$554$	13308.3	−	15358.6i	1.02060	−	1.17784i
$555$	−402.545	+	258.700i	−0.0307875	+	0.0197859i
$556$	−424.277	−	2950.91i	−0.0323622	−	0.225084i
$557$	−1112.71	−	2436.50i	−0.0846447	−	0.185346i	0.862577	−	0.505926i	$-0.168849\pi$
$557$	−1112.71	−	2436.50i	−0.0846447	−	0.185346i	−0.947221	+	0.320581i	$0.896122\pi$
$558$	1009.54	−	7021.52i	0.0765902	−	0.532697i
$559$	−19035.7	+	5589.38i	−1.44029	+	0.422908i
$560$	10766.7	+	6919.36i	0.812460	+	0.522136i
$561$	1466.96	−	3212.19i	0.110401	−	0.241744i
$562$	−16676.6	−	4896.69i	−1.25171	−	0.367535i
$563$	16647.2	+	19211.8i	1.24617	+	1.43816i	0.855643	+	0.517566i	$0.173162\pi$
$563$	16647.2	+	19211.8i	1.24617	+	1.43816i	0.390528	+	0.920591i	$0.372293\pi$
$564$	−395.336	−	456.242i	−0.0295153	−	0.0340625i
$565$	4605.04	+	1352.16i	0.342895	+	0.100683i
$566$	−1743.57	+	3817.89i	−0.129484	+	0.283530i
$567$	−18175.3	−	11680.5i	−1.34619	−	0.865143i
$568$	7184.78	−	2109.64i	0.530751	−	0.155843i
$569$	1167.68	−	8121.38i	0.0860309	−	0.598358i	−0.900509	−	0.434837i	$-0.856806\pi$
$569$	1167.68	−	8121.38i	0.0860309	−	0.598358i	0.986540	−	0.163521i	$-0.0522851\pi$
$570$	−103.335	−	226.272i	−0.00759338	−	0.0166272i
$571$	2178.10	+	15149.0i	0.159633	+	1.11028i	0.899310	+	0.437312i	$0.144070\pi$
$571$	2178.10	+	15149.0i	0.159633	+	1.11028i	−0.739676	+	0.672963i	$0.765021\pi$
$572$	−10706.9	+	6880.92i	−0.782656	+	0.502982i
$573$	81.9487	−	94.5738i	0.00597462	−	0.00689508i
$574$	12490.8			0.908287
$575$	2193.37	−	1671.37i	0.159078	−	0.121219i
$576$	−7102.39			−0.513772
$577$	−3995.38	+	4610.92i	−0.288267	+	0.332678i	−0.881350	−	0.472463i	$-0.843365\pi$
$577$	−3995.38	+	4610.92i	−0.288267	+	0.332678i	0.593084	+	0.805141i	$0.297910\pi$
$578$	5086.60	−	3268.96i	0.366046	−	0.235244i
$579$	−360.687	−	2508.63i	−0.0258889	−	0.180061i
$580$	1292.53	+	2830.25i	0.0925335	+	0.202620i
$581$	1367.84	−	9513.55i	0.0976724	−	0.679326i
$582$	−880.335	+	258.490i	−0.0626994	+	0.0184102i
$583$	7081.45	+	4550.97i	0.503059	+	0.323297i
$584$	852.650	−	1867.04i	0.0604159	−	0.132292i
$585$	−9694.10	−	2846.44i	−0.685131	−	0.201173i
$586$	14796.3	+	17075.8i	1.04305	+	1.20374i
$587$	12916.5	+	14906.4i	0.908211	+	1.04813i	0.998635	+	0.0522278i	$0.0166322\pi$
$587$	12916.5	+	14906.4i	0.908211	+	1.04813i	−0.0904244	+	0.995903i	$0.528822\pi$
$588$	1686.64	+	495.243i	0.118293	+	0.0347338i
$589$	560.007	−	1226.24i	0.0391760	−	0.0857835i
$590$	−9253.59	−	5946.92i	−0.645702	−	0.414967i
$591$	−846.796	+	248.642i	−0.0589383	+	0.0173058i
$592$	1102.03	−	7664.77i	0.0765085	−	0.532129i
$593$	−4071.00	−	8914.25i	−0.281916	−	0.617309i	0.714707	−	0.699424i	$-0.246560\pi$
$593$	−4071.00	−	8914.25i	−0.281916	−	0.617309i	−0.996623	+	0.0821144i	$0.973833\pi$
$594$	1563.96	+	10877.6i	0.108031	+	0.751369i
$595$	7651.07	−	4917.05i	0.527165	−	0.338789i
$596$	293.199	−	338.370i	0.0201508	−	0.0232553i
$597$	−3010.55			−0.206388
$598$	−25817.7	+	9881.62i	−1.76549	+	0.675735i
$599$	11643.9			0.794251			0.397126	−	0.917764i	$-0.370008\pi$
$599$	11643.9			0.794251			0.397126	+	0.917764i	$0.370008\pi$
$600$	281.363	−	324.711i	0.0191444	−	0.0220938i
$601$	−5161.32	+	3316.98i	−0.350307	+	0.225129i	−0.703946	−	0.710253i	$-0.748581\pi$
$601$	−5161.32	+	3316.98i	−0.350307	+	0.225129i	0.353639	+	0.935382i	$0.384944\pi$
$602$	3886.14	+	27028.7i	0.263102	+	1.82991i
$603$	2208.71	+	4836.40i	0.149164	+	0.326623i
$604$	505.222	−	3513.90i	0.0340351	−	0.236719i
$605$	−14965.4	+	4394.25i	−1.00567	+	0.295292i
$606$	−557.816	−	358.487i	−0.0373923	−	0.0240306i
$607$	1353.16	−	2963.00i	0.0904826	−	0.198129i	−0.858980	−	0.512009i	$-0.828902\pi$
$607$	1353.16	−	2963.00i	0.0904826	−	0.198129i	0.949463	+	0.313880i	$0.101629\pi$
$608$	1658.39	+	486.946i	0.110619	+	0.0324807i
$609$	−5235.55	−	6042.14i	−0.348366	−	0.402036i
$610$	−2380.90	−	2747.71i	−0.158033	−	0.182379i
$611$	−18997.0	−	5578.02i	−1.25783	−	0.369333i
$612$	1471.69	−	3222.55i	0.0972050	−	0.212849i
$613$	3966.61	+	2549.18i	0.261354	+	0.167962i	0.664755	−	0.747061i	$-0.268536\pi$
$613$	3966.61	+	2549.18i	0.261354	+	0.167962i	−0.403402	+	0.915023i	$0.632172\pi$
$614$	−15941.1	+	4680.72i	−1.04777	+	0.307653i
$615$	79.9660	−	556.176i	0.00524316	−	0.0364669i
$616$	−16366.5	−	35837.6i	−1.07049	−	2.34405i
$617$	−2434.46	−	16932.1i	−0.158846	−	1.10480i	−0.900765	−	0.434307i	$-0.856993\pi$
$617$	−2434.46	−	16932.1i	−0.158846	−	1.10480i	0.741919	−	0.670489i	$-0.233916\pi$
$618$	694.963	−	446.625i	0.0452354	−	0.0290710i
$619$	2498.03	−	2882.89i	0.162204	−	0.187194i	−0.668829	−	0.743416i	$-0.733204\pi$
$619$	2498.03	−	2882.89i	0.162204	−	0.187194i	0.831034	+	0.556222i	$0.187750\pi$
$620$	−1035.31			−0.0670632
$621$	−352.858	+	5606.53i	−0.0228015	+	0.362290i
$622$	−7746.28			−0.499353
$623$	−11568.4	+	13350.6i	−0.743945	+	0.858558i
$624$	−4855.34	+	3120.34i	−0.311489	+	0.200182i
$625$	−88.9468	−	618.638i	−0.00569259	−	0.0395929i
$626$	1905.05	+	4171.48i	0.121631	+	0.266335i
$627$	−146.027	+	1015.64i	−0.00930107	+	0.0646904i
$628$	3658.44	−	1074.21i	0.232464	−	0.0682577i
$629$	−4629.22	−	2975.02i	−0.293448	−	0.188588i
$630$	−5776.84	+	12649.5i	−0.365325	+	0.799950i
$631$	−1559.95	−	458.043i	−0.0984164	−	0.0288977i	0.232154	−	0.972679i	$-0.425423\pi$
$631$	−1559.95	−	458.043i	−0.0984164	−	0.0288977i	−0.330570	+	0.943781i	$0.607241\pi$
$632$	−12768.1	−	14735.2i	−0.803619	−	0.927426i
$633$	−2134.71	−	2463.59i	−0.134040	−	0.154690i
$634$	−4379.19	−	1285.85i	−0.274322	−	0.0805481i
$635$	3772.11	−	8259.76i	0.235735	−	0.516187i
$636$	−250.780	−	161.166i	−0.0156353	−	0.0100482i
$637$	55315.8	−	16242.2i	3.44064	−	1.01026i
$638$	7760.98	−	53978.8i	0.481599	−	3.34959i
$639$	4529.05	+	9917.24i	0.280386	+	0.613959i
$640$	1240.59	+	8628.48i	0.0766227	+	0.532923i
$641$	−584.336	+	375.530i	−0.0360061	+	0.0231397i	−0.558520	−	0.829491i	$-0.688631\pi$
$641$	−584.336	+	375.530i	−0.0360061	+	0.0231397i	0.522514	+	0.852631i	$0.324994\pi$
$642$	−3015.83	+	3480.46i	−0.185398	+	0.213960i
$643$	−6693.73			−0.410536			−0.205268	−	0.978706i	$-0.565807\pi$
$643$	−6693.73			−0.410536			−0.205268	+	0.978706i	$0.565807\pi$
$644$	1978.19	+	8733.59i	0.121043	+	0.534397i
$645$	1228.38			0.0749883
$646$	1873.30	−	2161.91i	0.114093	−	0.131670i
$647$	6670.53	−	4286.89i	0.405326	−	0.260487i	−0.322055	−	0.946721i	$-0.604374\pi$
$647$	6670.53	−	4286.89i	0.405326	−	0.260487i	0.727381	+	0.686234i	$0.240737\pi$
$648$	−1670.40	−	11617.9i	−0.101265	−	0.704311i
$649$	18848.8	+	41273.2i	1.14003	+	2.49632i
$650$	−891.664	+	6201.66i	−0.0538061	+	0.374230i
$651$	2552.51	−	749.484i	0.153672	−	0.0451223i
$652$	−3824.39	−	2457.79i	−0.229716	−	0.147629i
$653$	−4259.41	+	9326.81i	−0.255258	+	0.558938i	−0.993266	−	0.115854i	$-0.963039\pi$
$653$	−4259.41	+	9326.81i	−0.255258	+	0.558938i	0.738008	+	0.674792i	$0.235767\pi$
$654$	2530.95	+	743.155i	0.151327	+	0.0444337i
$655$	3049.86	+	3519.73i	0.181936	+	0.209965i
$656$	5954.69	+	6872.08i	0.354408	+	0.409009i
$657$	2867.37	+	841.936i	0.170269	+	0.0499955i
$658$	−11320.5	+	24788.5i	−0.670700	+	1.46863i
$659$	3477.02	+	2234.55i	0.205532	+	0.132087i	0.639358	−	0.768909i	$-0.279200\pi$
$659$	3477.02	+	2234.55i	0.205532	+	0.132087i	−0.433826	+	0.900997i	$0.642837\pi$
$660$	756.112	−	222.015i	0.0445934	−	0.0130938i
$661$	1911.05	−	13291.6i	0.112453	−	0.782125i	−0.853068	−	0.521799i	$-0.825261\pi$
$661$	1911.05	−	13291.6i	0.112453	−	0.782125i	0.965521	−	0.260326i	$-0.0838299\pi$
$662$	7914.03	+	17329.3i	0.464634	+	1.01741i
$663$	583.688	+	4059.64i	0.0341909	+	0.237803i
$664$	4392.68	−	2823.00i	0.256730	−	0.164991i
$665$	−1730.59	+	1997.20i	−0.100916	+	0.116464i
$666$	8413.82			0.489533
$667$	9518.38	−	26201.5i	0.552554	−	1.52103i
$668$	9932.35			0.575291
$669$	3039.24	−	3507.47i	0.175641	−	0.202701i
$670$	2773.76	−	1782.59i	0.159940	−	0.102787i
$671$	2134.33	+	14844.6i	0.122794	+	0.854052i
$672$	1416.90	+	3102.59i	0.0813367	+	0.178103i
$673$	−779.192	+	5419.40i	−0.0446295	+	0.310405i	0.955263	+	0.295757i	$0.0955719\pi$
$673$	−779.192	+	5419.40i	−0.0446295	+	0.310405i	−0.999893	+	0.0146480i	$0.995337\pi$
$674$	1776.67	−	521.677i	0.101535	−	0.0298134i
$675$	1071.09	+	688.350i	0.0610762	+	0.0392513i
$676$	3893.43	−	8525.42i	0.221520	−	0.485061i
$677$	10362.3	+	3042.64i	0.588264	+	0.172730i	0.562301	−	0.826933i	$-0.309916\pi$
$677$	10362.3	+	3042.64i	0.588264	+	0.172730i	0.0259638	+	0.999663i	$0.491735\pi$
$678$	1950.83	+	2251.37i	0.110503	+	0.127527i
$679$	6383.14	+	7366.54i	0.360770	+	0.416350i
$680$	4740.83	+	1392.03i	0.267356	+	0.0785029i
$681$	−1597.08	+	3497.13i	−0.0898684	+	0.196784i
$682$	15265.3	+	9810.42i	0.857095	+	0.550822i
$683$	13215.5	−	3880.42i	0.740376	−	0.217394i	0.110269	−	0.993902i	$-0.464829\pi$
$683$	13215.5	−	3880.42i	0.740376	−	0.217394i	0.630108	+	0.776508i	$0.283011\pi$
$684$	−146.498	+	1018.92i	−0.00818934	+	0.0569581i
$685$	−1018.62	−	2230.47i	−0.0568169	−	0.124412i
$686$	−6086.98	−	42335.9i	−0.338779	−	2.35626i
$687$	−3726.45	+	2394.84i	−0.206947	+	0.132997i
$688$	−13017.8	+	15023.3i	−0.721364	+	0.832499i
$689$	−9776.68			−0.540583
$690$	1706.16	−	136.691i	0.0941341	−	0.00754167i
$691$	15843.5			0.872235			0.436118	−	0.899890i	$-0.356353\pi$
$691$	15843.5			0.872235			0.436118	+	0.899890i	$0.356353\pi$
$692$	1121.55	−	1294.33i	0.0616110	−	0.0711029i
$693$	48256.3	−	31012.4i	2.64517	−	1.69995i
$694$	−5585.42	−	38847.5i	−0.305504	−	2.12483i
$695$	2514.86	+	5506.78i	0.137258	+	0.300553i
$696$	618.130	−	4299.19i	0.0336640	−	0.234138i
$697$	6199.98	−	1820.48i	0.336931	−	0.0989319i
$698$	14244.2	+	9154.22i	0.772425	+	0.496407i
$699$	−1529.84	+	3349.87i	−0.0827807	+	0.181264i
$700$	1947.36	+	571.797i	0.105148	+	0.0308742i
$701$	−3553.92	−	4101.44i	−0.191483	−	0.220983i	0.651887	−	0.758316i	$-0.273977\pi$
$701$	−3553.92	−	4101.44i	−0.191483	−	0.220983i	−0.843370	+	0.537333i	$0.819432\pi$
$702$	−8358.36	−	9646.06i	−0.449382	−	0.518614i
$703$	1534.16	+	450.471i	0.0823073	+	0.0241676i
$704$	7547.28	−	16526.2i	0.404047	−	0.884739i
$705$	1031.28	+	662.763i	0.0550925	+	0.0354058i
$706$	−30835.2	+	9054.02i	−1.64376	+	0.482652i
$707$	−1002.52	+	6972.69i	−0.0533291	+	0.370912i
$708$	−667.505	−	1461.63i	−0.0354328	−	0.0775869i
$709$	−3460.38	−	24067.5i	−0.183297	−	1.27486i	−0.848901	−	0.528552i	$-0.822735\pi$
$709$	−3460.38	−	24067.5i	−0.183297	−	1.27486i	0.665604	−	0.746305i	$-0.268174\pi$
$710$	5687.71	−	3655.27i	0.300642	−	0.193211i
$711$	18590.0	−	21454.0i	0.980562	−	1.13163i
$712$	−9597.11			−0.505150
$713$	6614.85	+	6502.75i	0.347445	+	0.341557i
$714$	5645.12			0.295887
$715$	16924.6	−	19532.1i	0.885238	−	1.02162i
$716$	−521.995	+	335.466i	−0.0272456	+	0.0175097i
$717$	502.100	+	3492.18i	0.0261524	+	0.181894i
$718$	7160.86	+	15680.1i	0.372202	+	0.815009i
$719$	4181.86	−	29085.5i	0.216908	−	1.50863i	−0.532447	−	0.846463i	$-0.678727\pi$
$719$	4181.86	−	29085.5i	0.216908	−	1.50863i	0.749355	−	0.662168i	$-0.230364\pi$
$720$	−9713.36	+	2852.10i	−0.502771	+	0.147627i
$721$	−7383.13	−	4744.85i	−0.381362	−	0.245087i
$722$	8871.00	−	19424.8i	0.457264	−	1.00127i
$723$	1993.00	+	585.198i	0.102518	+	0.0301020i
$724$	1821.45	+	2102.06i	0.0934994	+	0.107904i
$725$	−4137.52	−	4774.95i	−0.211950	−	0.244603i
$726$	−9288.97	−	2727.49i	−0.474857	−	0.139431i
$727$	−12656.4	+	27713.6i	−0.645665	+	1.41381i	0.249633	+	0.968340i	$0.419690\pi$
$727$	−12656.4	+	27713.6i	−0.645665	+	1.41381i	−0.895298	+	0.445468i	$0.853037\pi$
$728$	38494.3	+	24738.8i	1.95974	+	1.25945i
$729$	15131.1	−	4442.91i	0.768742	−	0.225723i
$730$	263.741	−	1834.36i	0.0133719	−	0.0930037i
$731$	5868.25	+	12849.7i	0.296915	+	0.650154i
$732$	−75.5844	−	525.701i	−0.00381650	−	0.0265444i
$733$	−18646.8	+	11983.6i	−0.939614	+	0.603853i	−0.918285	−	0.395920i	$-0.870426\pi$
$733$	−18646.8	+	11983.6i	−0.939614	+	0.603853i	−0.0213284	+	0.999773i	$0.506790\pi$
$734$	5688.02	−	6564.33i	0.286034	−	0.330100i
$735$	−3569.55			−0.179136
$736$	−7045.54	+	9581.33i	−0.352856	+	0.479854i
$737$	−13600.7			−0.679767
$738$	−6470.09	+	7466.88i	−0.322720	+	0.372439i
$739$	−31268.5	+	20095.1i	−1.55647	+	1.00028i	−0.572928	+	0.819605i	$0.694193\pi$
$739$	−31268.5	+	20095.1i	−1.55647	+	1.00028i	−0.983542	+	0.180678i	$0.942171\pi$
$740$	−174.759	−	1215.48i	−0.00868146	−	0.0603809i
$741$	−495.065	−	1084.04i	−0.0245434	−	0.0537426i
$742$	−1915.07	+	13319.6i	−0.0947497	+	0.658999i
$743$	−28073.6	+	8243.14i	−1.38616	+	0.407014i	−0.887910	−	0.460017i	$-0.847843\pi$
$743$	−28073.6	+	8243.14i	−1.38616	+	0.407014i	−0.498253	+	0.867031i	$0.666025\pi$
$744$	1215.82	+	781.360i	0.0599115	+	0.0385028i
$745$	−377.684	+	827.012i	−0.0185735	+	0.0406703i
$746$	24101.5	+	7076.83i	1.18286	+	0.347320i
$747$	4978.58	+	5745.58i	0.243851	+	0.281419i
$748$	5934.54	+	6848.82i	0.290091	+	0.334783i
$749$	46943.9	+	13784.0i	2.29011	+	0.672437i
$750$	161.154	−	352.877i	0.00784600	−	0.0171803i
$751$	−3846.55	−	2472.02i	−0.186901	−	0.120114i	0.443844	−	0.896104i	$-0.353614\pi$
$751$	−3846.55	−	2472.02i	−0.186901	−	0.120114i	−0.630745	+	0.775990i	$0.717251\pi$
$752$	−19034.7	+	5589.10i	−0.923038	+	0.271029i
$753$	−356.164	+	2477.18i	−0.0172369	+	0.119885i
$754$	26311.4	+	57614.0i	1.27083	+	2.78273i
$755$	1025.92	+	7135.45i	0.0494532	+	0.343954i
$756$	−3478.19	+	2235.29i	−0.167329	+	0.107536i
$757$	−1021.50	+	1178.87i	−0.0490450	+	0.0566009i	−0.779742	−	0.626101i	$-0.784650\pi$
$757$	−1021.50	+	1178.87i	−0.0490450	+	0.0566009i	0.730697	+	0.682702i	$0.239195\pi$
$758$	−15568.9			−0.746024
$759$	−6225.44	−	3330.60i	−0.297720	−	0.159280i
$760$	−1435.69			−0.0685237
$761$	−18373.1	+	21203.7i	−0.875195	+	1.01003i	0.124646	+	0.992201i	$0.460221\pi$
$761$	−18373.1	+	21203.7i	−0.875195	+	1.01003i	−0.999841	+	0.0178280i	$0.994325\pi$
$762$	4741.40	−	3047.11i	0.225411	−	0.144863i
$763$	−3988.15	−	27738.2i	−0.189228	−	1.31611i
$764$	133.407	+	292.120i	0.00631740	+	0.0138332i

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)

\(f(q)\)	\(=\)	\(q+(2.11818 - 2.44451i) q^{2} +(-0.807164 + 0.518733i) q^{3} +(-0.350419 - 2.43722i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.441670 + 3.07188i) q^{6} +(31.6351 - 9.28890i) q^{7} +(15.0685 + 9.68396i) q^{8} +(-10.8338 + 23.7227i) q^{9} +O(q^{10})\)	\(q+(2.11818 - 2.44451i) q^{2} +(-0.807164 + 0.518733i) q^{3} +(-0.350419 - 2.43722i) q^{4} +(2.07708 + 4.54816i) q^{5} +(-0.441670 + 3.07188i) q^{6} +(31.6351 - 9.28890i) q^{7} +(15.0685 + 9.68396i) q^{8} +(-10.8338 + 23.7227i) q^{9} +(15.5176 + 4.55638i) q^{10} +(-43.6869 - 50.4173i) q^{11} +(1.54711 + 1.78546i) q^{12} +(74.3430 + 21.8291i) q^{13} +(44.3019 - 97.0077i) q^{14} +(-4.03582 - 2.59366i) q^{15} +(74.4906 - 21.8724i) q^{16} +(7.85142 - 54.6078i) q^{17} +(35.0423 + 76.7320i) q^{18} +(2.28138 + 15.8673i) q^{19} +(10.3570 - 6.65605i) q^{20} +(-20.7162 + 23.9078i) q^{21} -215.782 q^{22} +(-107.980 - 22.5249i) q^{23} -17.1862 q^{24} +(-16.3715 + 18.8937i) q^{25} +(210.833 - 135.494i) q^{26} +(-7.24788 - 50.4101i) q^{27} +(-33.7246 - 73.8466i) q^{28} +(-35.9668 + 250.154i) q^{29} +(-14.8888 + 4.37175i) q^{30} +(-70.7442 - 45.4645i) q^{31} +(44.7898 - 98.0759i) q^{32} +(61.4156 + 18.0332i) q^{33} +(-116.859 - 134.862i) q^{34} +(107.956 + 124.588i) q^{35} +(61.6137 + 18.0914i) q^{36} +(41.4347 - 90.7294i) q^{37} +(43.6202 + 28.0330i) q^{38} +(-71.3304 + 20.9445i) q^{39} +(-12.7457 + 88.6484i) q^{40} +(48.6556 + 106.541i) q^{41} +(14.5621 + 101.282i) q^{42} +(-215.405 + 138.432i) q^{43} +(-107.569 + 124.142i) q^{44} -130.397 q^{45} +(-283.782 + 216.245i) q^{46} -255.532 q^{47} +(-48.7802 + 56.2954i) q^{48} +(625.945 - 402.270i) q^{49} +(11.5081 + 80.0406i) q^{50} +(21.9895 + 48.1503i) q^{51} +(27.1510 - 188.839i) q^{52} +(-121.070 + 35.5492i) q^{53} +(-138.580 - 89.0600i) q^{54} +(138.565 - 303.415i) q^{55} +(566.648 + 166.383i) q^{56} +(-10.0724 - 11.6241i) q^{57} +(535.320 + 617.792i) q^{58} +(-652.592 - 191.618i) q^{59} +(-4.90710 + 10.7450i) q^{60} +(-189.119 - 121.540i) q^{61} +(-260.987 + 76.6327i) q^{62} +(-122.370 + 851.102i) q^{63} +(113.133 + 247.726i) q^{64} +(55.1338 + 383.464i) q^{65} +(174.171 - 111.933i) q^{66} +(133.508 - 154.077i) q^{67} -135.843 q^{68} +(98.8417 - 37.8313i) q^{69} +533.225 q^{70} +(273.764 - 315.941i) q^{71} +(-392.978 + 252.552i) q^{72} +(-16.3078 - 113.423i) q^{73} +(-134.023 - 293.468i) q^{74} +(3.41370 - 23.7428i) q^{75} +(37.8728 - 11.1204i) q^{76} +(-1850.36 - 1189.15i) q^{77} +(-99.8914 + 218.732i) q^{78} +(-1044.42 - 306.669i) q^{79} +(254.202 + 293.365i) q^{80} +(-429.117 - 495.227i) q^{81} +(363.501 + 106.733i) q^{82} +(121.099 - 265.170i) q^{83} +(65.5280 + 42.1123i) q^{84} +(264.673 - 77.7151i) q^{85} +(-117.867 + 819.782i) q^{86} +(-100.732 - 220.573i) q^{87} +(-170.058 - 1182.78i) q^{88} +(-450.737 + 289.671i) q^{89} +(-276.204 + 318.756i) q^{90} +2554.61 q^{91} +(-17.0599 + 271.064i) q^{92} +80.6860 q^{93} +(-541.261 + 624.649i) q^{94} +(-67.4286 + 43.3338i) q^{95} +(14.7225 + 102.397i) q^{96} +(122.812 + 268.921i) q^{97} +(342.509 - 2382.21i) q^{98} +(1669.33 - 490.159i) 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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