LMFDB - Embedded newform 168.4.p.a.139.46

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(139,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.139"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.p (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.46
Character	$\chi$	$=$	168.139
Dual form			168.4.p.a.139.47

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.81393 - 0.285994i) q^{2} +3.00000i q^{3} +(7.83641 - 1.60954i) q^{4} +17.9897 q^{5} +(0.857983 + 8.44179i) q^{6} +(4.95393 - 17.8454i) q^{7} +(21.5908 - 6.77030i) q^{8} -9.00000 q^{9} +(50.6217 - 5.14495i) q^{10} -49.0130 q^{11} +(4.82861 + 23.5092i) q^{12} -3.98265 q^{13} +(8.83633 - 51.6325i) q^{14} +53.9691i q^{15} +(58.8188 - 25.2260i) q^{16} -25.2793i q^{17} +(-25.3254 + 2.57395i) q^{18} +134.046i q^{19} +(140.975 - 28.9551i) q^{20} +(53.5362 + 14.8618i) q^{21} +(-137.919 + 14.0175i) q^{22} -79.8326i q^{23} +(20.3109 + 64.7724i) q^{24} +198.629 q^{25} +(-11.2069 + 1.13901i) q^{26} -27.0000i q^{27} +(10.0982 - 147.818i) q^{28} +210.026i q^{29} +(15.4349 + 151.865i) q^{30} -107.371 q^{31} +(158.297 - 87.8061i) q^{32} -147.039i q^{33} +(-7.22973 - 71.1341i) q^{34} +(89.1197 - 321.033i) q^{35} +(-70.5277 + 14.4858i) q^{36} -51.8170i q^{37} +(38.3365 + 377.197i) q^{38} -11.9479i q^{39} +(388.412 - 121.796i) q^{40} +414.210i q^{41} +(154.898 + 26.5090i) q^{42} -186.321 q^{43} +(-384.086 + 78.8883i) q^{44} -161.907 q^{45} +(-22.8317 - 224.643i) q^{46} -517.341 q^{47} +(75.6780 + 176.456i) q^{48} +(-293.917 - 176.810i) q^{49} +(558.928 - 56.8068i) q^{50} +75.8378 q^{51} +(-31.2097 + 6.41022i) q^{52} -442.451i q^{53} +(-7.72185 - 75.9761i) q^{54} -881.729 q^{55} +(-13.8593 - 418.836i) q^{56} -402.139 q^{57} +(60.0661 + 590.997i) q^{58} -225.075i q^{59} +(86.8652 + 422.924i) q^{60} +111.256 q^{61} +(-302.136 + 30.7076i) q^{62} +(-44.5854 + 160.609i) q^{63} +(420.326 - 292.352i) q^{64} -71.6466 q^{65} +(-42.0524 - 413.758i) q^{66} +544.441 q^{67} +(-40.6879 - 198.099i) q^{68} +239.498 q^{69} +(158.963 - 928.853i) q^{70} +942.439i q^{71} +(-194.317 + 60.9327i) q^{72} -96.0065i q^{73} +(-14.8194 - 145.809i) q^{74} +595.887i q^{75} +(215.752 + 1050.44i) q^{76} +(-242.807 + 874.658i) q^{77} +(-3.41704 - 33.6207i) q^{78} -1229.26i q^{79} +(1058.13 - 453.808i) q^{80} +81.0000 q^{81} +(118.462 + 1165.56i) q^{82} -365.940i q^{83} +(443.453 + 30.2946i) q^{84} -454.766i q^{85} +(-524.295 + 53.2868i) q^{86} -630.077 q^{87} +(-1058.23 + 331.833i) q^{88} +395.170i q^{89} +(-455.596 + 46.3046i) q^{90} +(-19.7298 + 71.0720i) q^{91} +(-128.494 - 625.602i) q^{92} -322.114i q^{93} +(-1455.76 + 147.957i) q^{94} +2411.45i q^{95} +(263.418 + 474.892i) q^{96} -1071.98i q^{97} +(-877.629 - 413.472i) q^{98} +441.117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{2} + 10 q^{4} + 118 q^{8} - 432 q^{9} - 40 q^{11} + 38 q^{14} - 142 q^{16} + 18 q^{18} - 376 q^{22} + 1200 q^{25} - 274 q^{28} + 336 q^{30} + 318 q^{32} - 456 q^{35} - 90 q^{36} + 564 q^{42}+ \cdots + 360 q^{99}+O(q^{100}) $ 48 * q - 2 * q^2 + 10 * q^4 + 118 * q^8 - 432 * q^9 - 40 * q^11 + 38 * q^14 - 142 * q^16 + 18 * q^18 - 376 * q^22 + 1200 * q^25 - 274 * q^28 + 336 * q^30 + 318 * q^32 - 456 * q^35 - 90 * q^36 + 564 * q^42 - 808 * q^43 + 1584 * q^44 - 388 * q^46 + 360 * q^49 - 14 * q^50 + 226 * q^56 + 336 * q^57 - 3176 * q^58 - 192 * q^60 + 1954 * q^64 - 4104 * q^67 - 648 * q^70 - 1062 * q^72 + 2384 * q^74 - 1800 * q^78 + 3888 * q^81 + 264 * q^84 - 880 * q^86 + 4184 * q^88 + 104 * q^91 + 2044 * q^92 - 6018 * q^98 + 360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.81393	−	0.285994i	0.994875	−	0.101114i
$2$	2.81393	−	0.285994i	0.994875	−	0.101114i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	7.83641	−	1.60954i	0.979552	−	0.201192i
$5$	17.9897			1.60905			0.804523	−	0.593921i	$-0.202421\pi$
$5$	17.9897			1.60905			0.804523	+	0.593921i	$0.202421\pi$
$6$	0.857983	+	8.44179i	0.0583784	+	0.574391i
$7$	4.95393	−	17.8454i	0.267487	−	0.963561i
$7$	4.95393	−	17.8454i	0.267487	−	0.963561i
$8$	21.5908	−	6.77030i	0.954188	−	0.299208i
$9$	−9.00000			−0.333333
$10$	50.6217	−	5.14495i	1.60080	−	0.162698i
$11$	−49.0130			−1.34345			−0.671727	−	0.740799i	$-0.734447\pi$
$11$	−49.0130			−1.34345			−0.671727	+	0.740799i	$0.734447\pi$
$12$	4.82861	+	23.5092i	0.116158	+	0.565544i
$13$	−3.98265			−0.0849683			−0.0424841	−	0.999097i	$-0.513527\pi$
$13$	−3.98265			−0.0849683			−0.0424841	+	0.999097i	$0.513527\pi$
$14$	8.83633	−	51.6325i	0.168686	−	0.985670i
$15$			53.9691i			0.928984i
$16$	58.8188	−	25.2260i	0.919043	−	0.394156i
$17$		−	25.2793i		−	0.360654i	−0.983607	−	0.180327i	$-0.942284\pi$
$17$		−	25.2793i		−	0.360654i	0.983607	−	0.180327i	$-0.0577156\pi$
$18$	−25.3254	+	2.57395i	−0.331625	+	0.0337048i
$19$			134.046i			1.61854i	0.587435	+	0.809271i	$0.300138\pi$
$19$			134.046i			1.61854i	−0.587435	+	0.809271i	$0.699862\pi$
$20$	140.975	−	28.9551i	1.57614	−	0.323728i
$21$	53.5362	+	14.8618i	0.556312	+	0.154434i
$22$	−137.919	+	14.0175i	−1.33657	+	0.135842i
$23$		−	79.8326i		−	0.723750i	−0.932227	−	0.361875i	$-0.882137\pi$
$23$		−	79.8326i		−	0.723750i	0.932227	−	0.361875i	$-0.117863\pi$
$24$	20.3109	+	64.7724i	0.172748	+	0.550901i
$25$	198.629			1.58903
$26$	−11.2069	+	1.13901i	−0.0845328	+	0.00859151i
$27$		−	27.0000i		−	0.192450i
$28$	10.0982	−	147.818i	0.0681565	−	0.997675i
$29$			210.026i			1.34485i	0.740163	+	0.672427i	$0.234748\pi$
$29$			210.026i			1.34485i	−0.740163	+	0.672427i	$0.765252\pi$
$30$	15.4349	+	151.865i	0.0939335	+	0.924222i
$31$	−107.371			−0.622080			−0.311040	−	0.950397i	$-0.600677\pi$
$31$	−107.371			−0.622080			−0.311040	+	0.950397i	$0.600677\pi$
$32$	158.297	−	87.8061i	0.874478	−	0.485065i
$33$		−	147.039i		−	0.775643i
$34$	−7.22973	−	71.1341i	−0.0364673	−	0.358806i
$35$	89.1197	−	321.033i	0.430399	−	1.55042i
$36$	−70.5277	+	14.4858i	−0.326517	+	0.0670641i
$37$		−	51.8170i		−	0.230234i	−0.993352	−	0.115117i	$-0.963276\pi$
$37$		−	51.8170i		−	0.230234i	0.993352	−	0.115117i	$-0.0367243\pi$
$38$	38.3365	+	377.197i	0.163658	+	1.61025i
$39$		−	11.9479i		−	0.0490565i
$40$	388.412	−	121.796i	1.53533	−	0.481439i
$41$			414.210i			1.57777i	0.614539	+	0.788887i	$0.289342\pi$
$41$			414.210i			1.57777i	−0.614539	+	0.788887i	$0.710658\pi$
$42$	154.898	+	26.5090i	0.569077	+	0.0973911i
$43$	−186.321			−0.660784			−0.330392	−	0.943844i	$-0.607181\pi$
$43$	−186.321			−0.660784			−0.330392	+	0.943844i	$0.607181\pi$
$44$	−384.086	+	78.8883i	−1.31598	+	0.270292i
$45$	−161.907			−0.536349
$46$	−22.8317	−	224.643i	−0.0731815	−	0.720041i
$47$	−517.341			−1.60557			−0.802787	−	0.596266i	$-0.796650\pi$
$47$	−517.341			−1.60557			−0.802787	+	0.596266i	$0.796650\pi$
$48$	75.6780	+	176.456i	0.227566	+	0.530610i
$49$	−293.917	−	176.810i	−0.856901	−	0.515481i
$50$	558.928	−	56.8068i	1.58089	−	0.160674i
$51$	75.8378			0.208224
$52$	−31.2097	+	6.41022i	−0.0832308	+	0.0170949i
$53$		−	442.451i		−	1.14671i	−0.819309	−	0.573353i	$-0.805643\pi$
$53$		−	442.451i		−	1.14671i	0.819309	−	0.573353i	$-0.194357\pi$
$54$	−7.72185	−	75.9761i	−0.0194595	−	0.191464i
$55$	−881.729			−2.16168
$56$	−13.8593	−	418.836i	−0.0330720	−	0.999453i
$57$	−402.139			−0.934466
$58$	60.0661	+	590.997i	0.135984	+	1.33796i
$59$		−	225.075i		−	0.496649i	−0.968677	−	0.248325i	$-0.920120\pi$
$59$		−	225.075i		−	0.496649i	0.968677	−	0.248325i	$-0.0798800\pi$
$60$	86.8652	+	422.924i	0.186904	+	0.909988i
$61$	111.256			0.233523			0.116762	−	0.993160i	$-0.462749\pi$
$61$	111.256			0.233523			0.116762	+	0.993160i	$0.462749\pi$
$62$	−302.136	+	30.7076i	−0.618892	+	0.0629012i
$63$	−44.5854	+	160.609i	−0.0891624	+	0.321187i
$64$	420.326	−	292.352i	0.820950	−	0.571001i
$65$	−71.6466			−0.136718
$66$	−42.0524	−	413.758i	−0.0784286	−	0.771668i
$67$	544.441			0.992747			0.496374	−	0.868109i	$-0.334665\pi$
$67$	544.441			0.992747			0.496374	+	0.868109i	$0.334665\pi$
$68$	−40.6879	−	198.099i	−0.0725608	−	0.353280i
$69$	239.498			0.417857
$70$	158.963	−	928.853i	0.271424	−	1.58599i
$71$			942.439i			1.57531i	0.616118	+	0.787654i	$0.288705\pi$
$71$			942.439i			1.57531i	−0.616118	+	0.787654i	$0.711295\pi$
$72$	−194.317	+	60.9327i	−0.318063	+	0.0997359i
$73$		−	96.0065i		−	0.153927i	−0.997034	−	0.0769637i	$-0.975477\pi$
$73$		−	96.0065i		−	0.153927i	0.997034	−	0.0769637i	$-0.0245226\pi$
$74$	−14.8194	−	145.809i	−0.0232800	−	0.229054i
$75$			595.887i			0.917428i
$76$	215.752	+	1050.44i	0.325638	+	1.58545i
$77$	−242.807	+	874.658i	−0.359356	+	1.29450i
$78$	−3.41704	−	33.6207i	−0.00496031	−	0.0488050i
$79$		−	1229.26i		−	1.75067i	−0.483521	−	0.875333i	$-0.660642\pi$
$79$		−	1229.26i		−	1.75067i	0.483521	−	0.875333i	$-0.339358\pi$
$80$	1058.13	−	453.808i	1.47878	−	0.634216i
$81$	81.0000			0.111111
$82$	118.462	+	1165.56i	0.159535	+	1.56969i
$83$		−	365.940i		−	0.483941i	−0.970284	−	0.241970i	$-0.922206\pi$
$83$		−	365.940i		−	0.483941i	0.970284	−	0.241970i	$-0.0777937\pi$
$84$	443.453	+	30.2946i	0.576008	+	0.0393502i
$85$		−	454.766i		−	0.580310i
$86$	−524.295	+	53.2868i	−0.657397	+	0.0668147i
$87$	−630.077			−0.776452
$88$	−1058.23	+	331.833i	−1.28191	+	0.401972i
$89$			395.170i			0.470651i	0.971917	+	0.235325i	$0.0756156\pi$
$89$			395.170i			0.470651i	−0.971917	+	0.235325i	$0.924384\pi$
$90$	−455.596	+	46.3046i	−0.533600	+	0.0542325i
$91$	−19.7298	+	71.0720i	−0.0227279	+	0.0818721i
$92$	−128.494	−	625.602i	−0.145613	−	0.708951i
$93$		−	322.114i		−	0.359158i
$94$	−1455.76	+	147.957i	−1.59734	+	0.162346i
$95$			2411.45i			2.60431i
$96$	263.418	+	474.892i	0.280052	+	0.504880i
$97$		−	1071.98i		−	1.12209i	−0.827784	−	0.561047i	$-0.810399\pi$
$97$		−	1071.98i		−	1.12209i	0.827784	−	0.561047i	$-0.189601\pi$
$98$	−877.629	−	413.472i	−0.904632	−	0.426194i
$99$	441.117			0.447818
$100$	1556.54	−	319.701i	1.55654	−	0.319701i
$101$	1529.51			1.50685			0.753427	−	0.657532i	$-0.228399\pi$
$101$	1529.51			1.50685			0.753427	+	0.657532i	$0.228399\pi$
$102$	213.402	−	21.6892i	0.207157	−	0.0210544i
$103$	−944.040			−0.903097			−0.451549	−	0.892246i	$-0.649128\pi$
$103$	−944.040			−0.903097			−0.451549	+	0.892246i	$0.649128\pi$
$104$	−85.9886	+	26.9637i	−0.0810757	+	0.0254232i
$105$	963.100	+	267.359i	0.895133	+	0.248491i
$106$	−126.539	−	1245.03i	−0.115948	−	1.14083i
$107$	−1406.01			−1.27032			−0.635161	−	0.772380i	$-0.719066\pi$
$107$	−1406.01			−1.27032			−0.635161	+	0.772380i	$0.719066\pi$
$108$	−43.4575	−	211.583i	−0.0387194	−	0.188515i
$109$		−	1319.50i		−	1.15950i	−0.814795	−	0.579749i	$-0.803150\pi$
$109$		−	1319.50i		−	1.15950i	0.814795	−	0.579749i	$-0.196850\pi$
$110$	−2481.13	+	252.170i	−2.15060	+	0.218577i
$111$	155.451			0.132926
$112$	−158.784	−	1174.61i	−0.133961	−	0.990987i
$113$	141.191			0.117541			0.0587704	−	0.998272i	$-0.481282\pi$
$113$	141.191			0.117541			0.0587704	+	0.998272i	$0.481282\pi$
$114$	−1131.59	+	115.009i	−0.929677	+	0.0944879i
$115$		−	1436.16i		−	1.16455i
$116$	338.044	+	1645.85i	0.270574	+	1.31735i
$117$	35.8438			0.0283228
$118$	−64.3703	−	633.346i	−0.0502183	−	0.494104i
$119$	−451.119	−	125.232i	−0.347513	−	0.0964704i
$120$	365.387	+	1165.24i	0.277959	+	0.886425i
$121$	1071.28			0.804866
$122$	313.068	−	31.8187i	0.232326	−	0.0236125i
$123$	−1242.63			−0.910928
$124$	−841.407	+	172.818i	−0.609360	+	0.125158i
$125$	1324.56			0.947779
$126$	−79.5270	+	464.693i	−0.0562288	+	0.328557i
$127$		−	928.424i		−	0.648695i	−0.945938	−	0.324348i	$-0.894855\pi$
$127$		−	928.424i		−	0.648695i	0.945938	−	0.324348i	$-0.105145\pi$
$128$	1099.16	−	942.870i	0.759006	−	0.651084i
$129$		−	558.964i		−	0.381504i
$130$	−201.609	+	20.4905i	−0.136017	+	0.0138241i
$131$			2560.59i			1.70778i	0.520450	+	0.853892i	$0.325764\pi$
$131$			2560.59i			1.70778i	−0.520450	+	0.853892i	$0.674236\pi$
$132$	−236.665	−	1152.26i	−0.156053	−	0.759783i
$133$	2392.11	+	664.056i	1.55957	+	0.432939i
$134$	1532.02	−	155.707i	0.987659	−	0.100381i
$135$		−	485.722i		−	0.309661i
$136$	−171.148	−	545.800i	−0.107911	−	0.344132i
$137$	364.333			0.227205			0.113602	−	0.993526i	$-0.463761\pi$
$137$	364.333			0.227205			0.113602	+	0.993526i	$0.463761\pi$
$138$	673.930	−	68.4951i	0.415716	−	0.0422514i
$139$			363.877i			0.222041i	0.993818	+	0.111020i	$0.0354119\pi$
$139$			363.877i			0.222041i	−0.993818	+	0.111020i	$0.964588\pi$
$140$	181.664	−	2659.19i	0.109667	−	1.60531i
$141$		−	1552.02i		−	0.926978i
$142$	269.532	+	2651.96i	0.159286	+	1.56723i
$143$	195.202			0.114151
$144$	−529.369	+	227.034i	−0.306348	+	0.131385i
$145$			3778.29i			2.16393i
$146$	−27.4573	−	270.156i	−0.0155643	−	0.153139i
$147$	530.430	−	881.751i	0.297613	−	0.494732i
$148$	−83.4014	−	406.059i	−0.0463213	−	0.225526i
$149$			1203.32i			0.661607i	0.943700	+	0.330803i	$0.107320\pi$
$149$			1203.32i			0.661607i	−0.943700	+	0.330803i	$0.892680\pi$
$150$	170.420	+	1676.78i	0.0927651	+	0.912726i
$151$			59.0521i			0.0318251i	0.999873	+	0.0159126i	$0.00506534\pi$
$151$			59.0521i			0.0318251i	−0.999873	+	0.0159126i	$0.994935\pi$
$152$	907.533	+	2894.17i	0.484281	+	1.54439i
$153$			227.513i			0.120218i
$154$	−433.095	+	2530.67i	−0.226622	+	1.32420i
$155$	−1931.58			−1.00096
$156$	−19.2307	−	93.6290i	−0.00986977	−	0.0480533i
$157$	2240.11			1.13873			0.569365	−	0.822085i	$-0.307189\pi$
$157$	2240.11			1.13873			0.569365	+	0.822085i	$0.307189\pi$
$158$	−351.562	−	3459.05i	−0.177017	−	1.74169i
$159$	1327.35			0.662051
$160$	2847.72	−	1579.60i	1.40708	−	0.780492i
$161$	−1424.65	−	395.485i	−0.697378	−	0.193594i
$162$	227.928	−	23.1655i	0.110542	−	0.0112349i
$163$	1108.33			0.532581			0.266291	−	0.963893i	$-0.414202\pi$
$163$	1108.33			0.532581			0.266291	+	0.963893i	$0.414202\pi$
$164$	666.686	+	3245.92i	0.317436	+	1.54551i
$165$		−	2645.19i		−	1.24805i
$166$	−104.657	−	1029.73i	−0.0489333	−	0.481461i
$167$	3481.99			1.61344			0.806721	−	0.590933i	$-0.201240\pi$
$167$	3481.99			1.61344			0.806721	+	0.590933i	$0.201240\pi$
$168$	1256.51	−	41.5780i	0.577034	−	0.0190941i
$169$	−2181.14			−0.992780
$170$	−130.061	−	1279.68i	−0.0586776	−	0.577335i
$171$		−	1206.42i		−	0.539514i
$172$	−1460.09	+	299.891i	−0.647272	+	0.132945i
$173$	2149.38			0.944593			0.472297	−	0.881440i	$-0.343425\pi$
$173$	2149.38			0.944593			0.472297	+	0.881440i	$0.343425\pi$
$174$	−1772.99	+	180.198i	−0.772472	+	0.0785104i
$175$	983.994	−	3544.61i	0.425046	−	1.53113i
$176$	−2882.89	+	1236.40i	−1.23469	+	0.529530i
$177$	675.226			0.286741
$178$	113.016	+	1111.98i	0.0475895	+	0.468239i
$179$	3291.14			1.37425			0.687126	−	0.726538i	$-0.258872\pi$
$179$	3291.14			1.37425			0.687126	+	0.726538i	$0.258872\pi$
$180$	−1268.77	+	260.596i	−0.525382	+	0.107909i
$181$	−692.415			−0.284347			−0.142173	−	0.989842i	$-0.545409\pi$
$181$	−692.415			−0.284347			−0.142173	+	0.989842i	$0.545409\pi$
$182$	−35.1920	+	205.634i	−0.0143330	+	0.0837506i
$183$			333.769i			0.134825i
$184$	−540.491	−	1723.65i	−0.216552	−	0.690594i
$185$		−	932.172i		−	0.370457i
$186$	−92.1229	−	906.407i	−0.0363160	−	0.357317i
$187$			1239.01i			0.484522i
$188$	−4054.10	+	832.680i	−1.57274	+	0.323029i
$189$	−481.826	−	133.756i	−0.185437	−	0.0514779i
$190$	689.661	+	6785.65i	0.263333	+	2.59096i
$191$			838.537i			0.317667i	0.987305	+	0.158834i	$0.0507733\pi$
$191$			838.537i			0.317667i	−0.987305	+	0.158834i	$0.949227\pi$
$192$	877.057	+	1260.98i	0.329667	+	0.473975i
$193$	469.002			0.174920			0.0874599	−	0.996168i	$-0.472125\pi$
$193$	469.002			0.174920			0.0874599	+	0.996168i	$0.472125\pi$
$194$	−306.580	−	3016.48i	−0.113460	−	1.11634i
$195$		−	214.940i		−	0.0789341i
$196$	−2587.84	−	912.485i	−0.943090	−	0.332538i
$197$		−	1210.67i		−	0.437850i	−0.975742	−	0.218925i	$-0.929745\pi$
$197$		−	1210.67i		−	0.437850i	0.975742	−	0.218925i	$-0.0702550\pi$
$198$	1241.27	−	126.157i	0.445523	−	0.0452808i
$199$	2002.69			0.713403			0.356702	−	0.934218i	$-0.383901\pi$
$199$	2002.69			0.713403			0.356702	+	0.934218i	$0.383901\pi$
$200$	4288.56	−	1344.78i	1.51623	−	0.475450i
$201$			1633.32i			0.573163i
$202$	4303.94	−	437.432i	1.49913	−	0.152364i
$203$	3747.99	+	1040.45i	1.29585	+	0.359731i
$204$	594.296	−	122.064i	0.203966	−	0.0418930i
$205$			7451.51i			2.53871i
$206$	−2656.46	+	269.990i	−0.898469	+	0.0913161i
$207$			718.494i			0.241250i
$208$	−234.254	+	100.466i	−0.0780895	+	0.0334908i
$209$		−	6570.01i		−	2.17444i
$210$	2786.56	+	476.889i	0.915671	+	0.156707i
$211$	4390.91			1.43262			0.716310	−	0.697782i	$-0.245830\pi$
$211$	4390.91			1.43262			0.716310	+	0.697782i	$0.245830\pi$
$212$	−712.142	−	3467.23i	−0.230708	−	1.12326i
$213$	−2827.32			−0.909505
$214$	−3956.42	+	402.112i	−1.26381	+	0.128448i
$215$	−3351.86			−1.06323
$216$	−182.798	−	582.952i	−0.0575825	−	0.183634i
$217$	−531.911	+	1916.09i	−0.166398	+	0.599412i
$218$	−377.370	−	3712.99i	−0.117242	−	1.15356i
$219$	288.019			0.0888701
$220$	−6909.60	+	1419.18i	−2.11748	+	0.434913i
$221$			100.678i			0.0306442i
$222$	437.428	−	44.4581i	0.132244	−	0.0134407i
$223$	−4483.21			−1.34627			−0.673134	−	0.739521i	$-0.735052\pi$
$223$	−4483.21			−1.34627			−0.673134	+	0.739521i	$0.735052\pi$
$224$	−782.740	−	3259.87i	−0.233478	−	0.972362i
$225$	−1787.66			−0.529677
$226$	397.301	−	40.3797i	0.116938	−	0.0118850i
$227$		−	2457.30i		−	0.718487i	−0.933244	−	0.359243i	$-0.883035\pi$
$227$		−	2457.30i		−	0.718487i	0.933244	−	0.359243i	$-0.116965\pi$
$228$	−3151.33	+	647.257i	−0.915358	+	0.188007i
$229$	−5046.86			−1.45636			−0.728179	−	0.685387i	$-0.759633\pi$
$229$	−5046.86			−1.45636			−0.728179	+	0.685387i	$0.759633\pi$
$230$	−410.735	−	4041.27i	−0.117752	−	1.15858i
$231$	−2623.97	−	728.422i	−0.747380	−	0.207475i
$232$	1421.94	+	4534.62i	0.402391	+	1.28324i
$233$	−1771.32			−0.498038			−0.249019	−	0.968499i	$-0.580108\pi$
$233$	−1771.32			−0.498038			−0.249019	+	0.968499i	$0.580108\pi$
$234$	100.862	−	10.2511i	0.0281776	−	0.00286384i
$235$	−9306.81			−2.58344
$236$	−362.267	−	1763.78i	−0.0999219	−	0.486494i
$237$	3687.78			1.01075
$238$	−1305.23	−	223.376i	−0.355486	−	0.0608375i
$239$			760.957i			0.205951i	0.994684	+	0.102975i	$0.0328363\pi$
$239$			760.957i			0.205951i	−0.994684	+	0.102975i	$0.967164\pi$
$240$	1361.42	+	3174.39i	0.366165	+	0.853776i
$241$			694.787i			0.185706i	0.995680	+	0.0928530i	$0.0295987\pi$
$241$			694.787i			0.185706i	−0.995680	+	0.0928530i	$0.970401\pi$
$242$	3014.50	−	306.379i	0.800741	−	0.0813835i
$243$			243.000i			0.0641500i
$244$	871.851	−	179.071i	0.228748	−	0.0469830i
$245$	−5287.48	−	3180.75i	−1.37879	−	0.829432i
$246$	−3496.67	+	355.385i	−0.906259	+	0.0921078i
$247$		−	533.859i		−	0.137525i
$248$	−2318.24	+	726.936i	−0.593581	+	0.186131i
$249$	1097.82			0.279403
$250$	3727.22	−	378.817i	0.942922	−	0.0958340i
$251$			1607.06i			0.404131i	0.979372	+	0.202066i	$0.0647654\pi$
$251$			1607.06i			0.404131i	−0.979372	+	0.202066i	$0.935235\pi$
$252$	−90.8839	+	1330.36i	−0.0227188	+	0.332558i
$253$			3912.84i			0.972324i
$254$	−265.524	−	2612.52i	−0.0655924	−	0.645371i
$255$	1364.30			0.335042
$256$	2823.30	−	2967.53i	0.689282	−	0.724493i
$257$			6933.24i			1.68282i	0.540400	+	0.841408i	$0.318273\pi$
$257$			6933.24i			1.68282i	−0.540400	+	0.841408i	$0.681727\pi$
$258$	−159.860	−	1572.88i	−0.0385755	−	0.379549i
$259$	−924.695	−	256.698i	−0.221845	−	0.0615847i
$260$	−561.452	+	115.318i	−0.133922	+	0.0275066i
$261$		−	1890.23i		−	0.448285i
$262$	732.314	+	7205.32i	0.172681	+	1.69903i
$263$			2831.36i			0.663838i	0.943308	+	0.331919i	$0.107696\pi$
$263$			2831.36i			0.663838i	−0.943308	+	0.331919i	$0.892304\pi$
$264$	−995.498	−	3174.69i	−0.232078	−	0.740109i
$265$		−	7959.56i		−	1.84510i
$266$	6921.15	+	1184.48i	1.59535	+	0.273026i
$267$	−1185.51			−0.271730
$268$	4266.47	−	876.298i	0.972448	−	0.199733i
$269$	−7470.97			−1.69336			−0.846679	−	0.532105i	$-0.821401\pi$
$269$	−7470.97			−1.69336			−0.846679	+	0.532105i	$0.821401\pi$
$270$	−138.914	−	1366.79i	−0.0313112	−	0.308074i
$271$	2680.89			0.600931			0.300466	−	0.953793i	$-0.402858\pi$
$271$	2680.89			0.600931			0.300466	+	0.953793i	$0.402858\pi$
$272$	−637.695	−	1486.90i	−0.142154	−	0.331457i
$273$	−213.216	−	59.1893i	−0.0472689	−	0.0131220i
$274$	1025.21	−	104.197i	0.226040	−	0.0229737i
$275$	−9735.41			−2.13479
$276$	1876.80	−	385.481i	0.409313	−	0.0840696i
$277$			5749.50i			1.24713i	0.781773	+	0.623563i	$0.214316\pi$
$277$			5749.50i			1.24713i	−0.781773	+	0.623563i	$0.785684\pi$
$278$	104.067	+	1023.93i	0.0224515	+	0.220903i
$279$	966.343			0.207360
$280$	−249.325	−	7534.74i	−0.0532143	−	1.60817i
$281$	4802.46			1.01954			0.509770	−	0.860311i	$-0.329731\pi$
$281$	4802.46			1.01954			0.509770	+	0.860311i	$0.329731\pi$
$282$	−443.870	−	4367.29i	−0.0937308	−	0.922227i
$283$		−	1743.48i		−	0.366216i	−0.983093	−	0.183108i	$-0.941384\pi$
$283$		−	1743.48i		−	0.366216i	0.983093	−	0.183108i	$-0.0586157\pi$
$284$	1516.89	+	7385.34i	0.316940	+	1.54310i
$285$	−7234.35			−1.50360
$286$	549.284	−	55.8266i	0.113566	−	0.0115423i
$287$	7391.74	+	2051.97i	1.52028	+	0.422034i
$288$	−1424.68	+	790.255i	−0.291493	+	0.161688i
$289$	4273.96			0.869928
$290$	1080.57	+	10631.9i	0.218805	+	2.15284i
$291$	3215.94			0.647841
$292$	−154.526	−	752.346i	−0.0309690	−	0.150780i
$293$	−6865.86			−1.36897			−0.684485	−	0.729027i	$-0.739973\pi$
$293$	−6865.86			−1.36897			−0.684485	+	0.729027i	$0.739973\pi$
$294$	1240.42	−	2632.89i	0.246063	−	0.522289i
$295$		−	4049.03i		−	0.799132i
$296$	−350.816	−	1118.77i	−0.0688878	−	0.219687i
$297$			1323.35i			0.258548i
$298$	344.141	+	3386.05i	0.0668979	+	0.658216i
$299$			317.945i			0.0614958i
$300$	959.102	+	4669.62i	0.184579	+	0.898668i
$301$	−923.022	+	3324.98i	−0.176751	+	0.636706i
$302$	16.8886	+	166.169i	0.00321797	+	0.0316620i
$303$			4588.54i			0.869983i
$304$	3381.45	+	7884.44i	0.637959	+	1.48751i
$305$	2001.47			0.375750
$306$	65.0676	+	640.207i	0.0121558	+	0.119602i
$307$		−	6083.49i		−	1.13096i	−0.824764	−	0.565478i	$-0.808692\pi$
$307$		−	6083.49i		−	1.13096i	0.824764	−	0.565478i	$-0.191308\pi$
$308$	−494.944	+	7244.99i	−0.0915651	+	1.34033i
$309$		−	2832.12i		−	0.521404i
$310$	−5435.33	+	552.421i	−0.995826	+	0.101211i
$311$	−5268.97			−0.960694			−0.480347	−	0.877079i	$-0.659489\pi$
$311$	−5268.97			−0.960694			−0.480347	+	0.877079i	$0.659489\pi$
$312$	−80.8911	−	257.966i	−0.0146781	−	0.0468091i
$313$		−	6377.14i		−	1.15162i	−0.817583	−	0.575811i	$-0.804686\pi$
$313$		−	6377.14i		−	1.15162i	0.817583	−	0.575811i	$-0.195314\pi$
$314$	6303.52	−	640.660i	1.13289	−	0.115142i
$315$	−802.077	+	2889.30i	−0.143466	+	0.516805i
$316$	−1978.54	−	9632.99i	−0.352220	−	1.71487i
$317$		−	5401.16i		−	0.956970i	−0.878096	−	0.478485i	$-0.841186\pi$
$317$		−	5401.16i		−	0.956970i	0.878096	−	0.478485i	$-0.158814\pi$
$318$	3735.08	−	379.616i	0.658657	−	0.0669428i
$319$		−	10294.0i		−	1.80675i
$320$	7561.54	−	5259.33i	1.32095	−	0.918767i
$321$		−	4218.04i		−	0.733421i
$322$	−4121.96	−	705.428i	−0.713379	−	0.122087i
$323$	3388.59			0.583734
$324$	634.750	−	130.373i	0.108839	−	0.0223547i
$325$	−791.069			−0.135017
$326$	3118.75	−	316.975i	0.529852	−	0.0538516i
$327$	3958.51			0.669437
$328$	2804.32	+	8943.13i	0.472082	+	1.50549i
$329$	−2562.87	+	9232.16i	−0.429470	+	1.54707i
$330$	−756.509	−	7443.38i	−0.126195	−	1.24165i
$331$	4418.61			0.733743			0.366872	−	0.930272i	$-0.380429\pi$
$331$	4418.61			0.733743			0.366872	+	0.930272i	$0.380429\pi$
$332$	−588.993	−	2867.65i	−0.0973651	−	0.474045i
$333$			466.353i			0.0767447i
$334$	9798.09	−	995.831i	1.60517	−	0.163142i
$335$	9794.33			1.59738
$336$	3523.84	−	476.352i	0.572146	−	0.0773427i
$337$	2111.13			0.341249			0.170624	−	0.985336i	$-0.445422\pi$
$337$	2111.13			0.341249			0.170624	+	0.985336i	$0.445422\pi$
$338$	−6137.57	+	623.793i	−0.987692	+	0.100384i
$339$			423.572i			0.0678622i
$340$	−731.963	−	3563.74i	−0.116754	−	0.568443i
$341$	5262.60			0.835735
$342$	−345.028	−	3394.77i	−0.0545526	−	0.536749i
$343$	−4611.29	+	4369.17i	−0.725907	+	0.687793i
$344$	−4022.82	+	1261.45i	−0.630512	+	0.197712i
$345$	4308.49			0.672352
$346$	6048.22	−	614.712i	0.939752	−	0.0955119i
$347$	7314.45			1.13159			0.565793	−	0.824547i	$-0.308570\pi$
$347$	7314.45			1.13159			0.565793	+	0.824547i	$0.308570\pi$
$348$	−4937.54	+	1014.13i	−0.760575	+	0.156216i
$349$	−332.075			−0.0509328			−0.0254664	−	0.999676i	$-0.508107\pi$
$349$	−332.075			−0.0509328			−0.0254664	+	0.999676i	$0.508107\pi$
$350$	1755.15	−	10255.7i	0.268048	−	1.56626i
$351$			107.531i			0.0163522i
$352$	−7758.64	+	4303.64i	−1.17482	+	0.651662i
$353$		−	3201.11i		−	0.482656i	−0.970444	−	0.241328i	$-0.922417\pi$
$353$		−	3201.11i		−	0.482656i	0.970444	−	0.241328i	$-0.0775830\pi$
$354$	1900.04	−	193.111i	0.285271	−	0.0289936i
$355$			16954.2i			2.53474i
$356$	636.040	+	3096.71i	0.0946912	+	0.461027i
$357$	375.695	−	1353.36i	0.0556972	−	0.200636i
$358$	9261.04	−	941.247i	1.36721	−	0.138957i
$359$		−	2489.55i		−	0.365999i	−0.983113	−	0.183000i	$-0.941419\pi$
$359$		−	2489.55i		−	0.365999i	0.983113	−	0.183000i	$-0.0585807\pi$
$360$	−3495.71	+	1096.16i	−0.511778	+	0.160480i
$361$	−11109.4			−1.61968
$362$	−1948.41	+	198.027i	−0.282890	+	0.0287515i
$363$			3213.83i			0.464690i
$364$	−40.2176	+	588.705i	−0.00579114	+	0.0847707i
$365$		−	1727.13i		−	0.247676i
$366$	95.4561	+	939.203i	0.0136327	+	0.134134i
$367$	10747.1			1.52859			0.764297	−	0.644864i	$-0.223086\pi$
$367$	10747.1			1.52859			0.764297	+	0.644864i	$0.223086\pi$
$368$	−2013.86	−	4695.66i	−0.285271	−	0.665158i
$369$		−	3727.89i		−	0.525924i
$370$	−266.596	−	2623.07i	−0.0374585	−	0.368559i
$371$	−7895.73	−	2191.87i	−1.10492	−	0.306729i
$372$	−518.455	−	2524.22i	−0.0722598	−	0.351814i
$373$		−	8517.68i		−	1.18238i	−0.806531	−	0.591191i	$-0.798658\pi$
$373$		−	8517.68i		−	1.18238i	0.806531	−	0.591191i	$-0.201342\pi$
$374$	354.351	+	3486.50i	0.0489921	+	0.482039i
$375$			3973.68i			0.547201i
$376$	−11169.8	+	3502.55i	−1.53202	+	0.480400i
$377$		−	836.458i		−	0.114270i
$378$	−1394.08	−	238.581i	−0.189692	−	0.0324637i
$379$	9286.94			1.25868			0.629338	−	0.777132i	$-0.283326\pi$
$379$	9286.94			1.25868			0.629338	+	0.777132i	$0.283326\pi$
$380$	3881.32	+	18897.1i	0.523967	+	2.55106i
$381$	2785.27			0.374524
$382$	239.817	+	2359.58i	0.0321207	+	0.316039i
$383$	−3123.30			−0.416692			−0.208346	−	0.978055i	$-0.566808\pi$
$383$	−3123.30			−0.416692			−0.208346	+	0.978055i	$0.566808\pi$
$384$	2828.61	+	3297.47i	0.375904	+	0.438212i
$385$	−4368.03	+	15734.8i	−0.578221	+	2.08291i
$386$	1319.74	−	134.132i	0.174023	−	0.0176869i
$387$	1676.89			0.220261
$388$	−1725.39	−	8400.48i	−0.225756	−	1.09915i
$389$			5041.45i			0.657099i	0.944487	+	0.328549i	$0.106560\pi$
$389$			5041.45i			0.657099i	−0.944487	+	0.328549i	$0.893440\pi$
$390$	−61.4716	−	604.826i	−0.00798137	−	0.0785296i
$391$	−2018.11			−0.261024
$392$	−7542.96	−	1827.56i	−0.971881	−	0.235474i
$393$	−7681.77			−0.985990
$394$	−346.244	−	3406.73i	−0.0442729	−	0.435606i
$395$		−	22114.0i		−	2.81690i
$396$	3456.78	−	709.995i	0.438661	−	0.0900974i
$397$	−2500.99			−0.316174			−0.158087	−	0.987425i	$-0.550533\pi$
$397$	−2500.99			−0.316174			−0.158087	+	0.987425i	$0.550533\pi$
$398$	5635.44	−	572.759i	0.709747	−	0.0721353i
$399$	−1992.17	+	7176.33i	−0.249958	+	0.900416i
$400$	11683.1	−	5010.61i	1.46039	−	0.626327i
$401$	−1012.94			−0.126144			−0.0630720	−	0.998009i	$-0.520090\pi$
$401$	−1012.94			−0.126144			−0.0630720	+	0.998009i	$0.520090\pi$
$402$	467.121	+	4596.06i	0.0579550	+	0.570225i
$403$	427.622			0.0528571
$404$	11985.9	−	2461.81i	1.47604	−	0.303167i
$405$	1457.16			0.178783
$406$	10844.2	+	1855.86i	1.32558	+	0.226859i
$407$			2539.71i			0.309309i
$408$	1637.40	−	513.444i	0.198685	−	0.0623022i
$409$		−	8986.88i		−	1.08649i	−0.839576	−	0.543243i	$-0.817196\pi$
$409$		−	8986.88i		−	1.08649i	0.839576	−	0.543243i	$-0.182804\pi$
$410$	2131.09	+	20968.0i	0.256700	+	2.52570i
$411$			1093.00i			0.131177i
$412$	−7397.89	+	1519.47i	−0.884631	+	0.181696i
$413$	−4016.56	−	1115.01i	−0.478552	−	0.132847i
$414$	205.485	+	2021.79i	0.0243938	+	0.240014i
$415$		−	6583.14i		−	0.778684i
$416$	−630.443	+	349.701i	−0.0743029	+	0.0412151i
$417$	−1091.63			−0.128195
$418$	−1878.99	−	18487.6i	−0.219867	−	2.16329i
$419$			10182.4i			1.18721i	0.804756	+	0.593605i	$0.202296\pi$
$419$			10182.4i			1.18721i	−0.804756	+	0.593605i	$0.797704\pi$
$420$	7977.58	+	544.991i	0.926823	+	0.0633163i
$421$			16474.2i			1.90714i	0.301175	+	0.953569i	$0.402621\pi$
$421$			16474.2i			1.90714i	−0.301175	+	0.953569i	$0.597379\pi$
$422$	12355.7	−	1255.78i	1.42528	−	0.144858i
$423$	4656.07			0.535191
$424$	−2995.53	−	9552.88i	−0.343103	−	1.09417i
$425$		−	5021.19i		−	0.573091i
$426$	−7955.87	+	808.597i	−0.904843	+	0.0919639i
$427$	551.156	−	1985.41i	0.0624644	−	0.225014i
$428$	−11018.1	+	2263.03i	−1.24435	+	0.255579i
$429$			585.605i			0.0659050i
$430$	−9431.90	+	958.613i	−1.05778	+	0.107508i
$431$		−	12206.2i		−	1.36416i	−0.731279	−	0.682079i	$-0.761076\pi$
$431$		−	12206.2i		−	1.36416i	0.731279	−	0.682079i	$-0.238924\pi$
$432$	−681.102	−	1588.11i	−0.0758554	−	0.176870i
$433$			8186.21i			0.908555i	0.890860	+	0.454277i	$0.150102\pi$
$433$			8186.21i			0.908555i	−0.890860	+	0.454277i	$0.849898\pi$
$434$	−948.770	+	5543.86i	−0.104936	+	0.613165i
$435$	−11334.9			−1.24935
$436$	−2123.79	−	10340.2i	−0.233282	−	1.13579i
$437$	10701.3			1.17142
$438$	810.467	−	82.3719i	0.0884146	−	0.00898603i
$439$	−770.764			−0.0837963			−0.0418981	−	0.999122i	$-0.513340\pi$
$439$	−770.764			−0.0837963			−0.0418981	+	0.999122i	$0.513340\pi$
$440$	−19037.2	+	5969.57i	−2.06265	+	0.646791i
$441$	2645.25	+	1591.29i	0.285634	+	0.171827i
$442$	28.7935	+	283.302i	0.00309856	+	0.0304871i
$443$	1199.43			0.128638			0.0643191	−	0.997929i	$-0.479512\pi$
$443$	1199.43			0.128638			0.0643191	+	0.997929i	$0.479512\pi$
$444$	1218.18	−	250.204i	0.130208	−	0.0267436i
$445$			7108.98i			0.757299i
$446$	−12615.4	+	1282.17i	−1.33937	+	0.136127i
$447$	−3609.95			−0.381979
$448$	−3134.88	−	8949.19i	−0.330601	−	0.943771i
$449$	−7474.09			−0.785577			−0.392789	−	0.919629i	$-0.628490\pi$
$449$	−7474.09			−0.785577			−0.392789	+	0.919629i	$0.628490\pi$
$450$	−5030.35	+	511.261i	−0.526962	+	0.0535579i
$451$		−	20301.7i		−	2.11966i
$452$	1106.43	−	227.252i	0.115137	−	0.0236483i
$453$	−177.156			−0.0183742
$454$	−702.773	−	6914.66i	−0.0726493	−	0.714804i
$455$	−354.932	+	1278.56i	−0.0365703	+	0.131736i
$456$	−8682.50	+	2722.60i	−0.891656	+	0.279599i
$457$	−2601.21			−0.266257			−0.133129	−	0.991099i	$-0.542502\pi$
$457$	−2601.21			−0.266257			−0.133129	+	0.991099i	$0.542502\pi$
$458$	−14201.5	+	1443.37i	−1.44889	+	0.147259i
$459$	−682.540			−0.0694079
$460$	−2311.56	−	11254.4i	−0.234298	−	1.14073i
$461$	−10407.9			−1.05150			−0.525752	−	0.850638i	$-0.676216\pi$
$461$	−10407.9			−1.05150			−0.525752	+	0.850638i	$0.676216\pi$
$462$	−7592.00	−	1299.29i	−0.764528	−	0.130840i
$463$			3988.70i			0.400368i	0.979758	+	0.200184i	$0.0641540\pi$
$463$			3988.70i			0.400368i	−0.979758	+	0.200184i	$0.935846\pi$
$464$	5298.10	+	12353.4i	0.530083	+	1.23598i
$465$		−	5794.74i		−	0.577902i
$466$	−4984.36	+	506.587i	−0.495485	+	0.0503587i
$467$			9030.77i			0.894848i	0.894322	+	0.447424i	$0.147659\pi$
$467$			9030.77i			0.894848i	−0.894322	+	0.447424i	$0.852341\pi$
$468$	280.887	−	57.6920i	0.0277436	−	0.00569832i
$469$	2697.12	−	9715.77i	0.265547	−	0.956573i
$470$	−26188.7	+	2661.69i	−2.57020	+	0.261223i
$471$			6720.34i			0.657446i
$472$	−1523.83	−	4859.56i	−0.148601	−	0.473897i
$473$	9132.17			0.887732
$474$	10377.2	−	1054.68i	1.00557	−	0.102201i
$475$			26625.5i			2.57192i
$476$	−3736.72	−	255.275i	−0.359816	−	0.0245809i
$477$			3982.06i			0.382235i
$478$	217.629	+	2141.28i	0.0208246	+	0.204895i
$479$	11039.0			1.05300			0.526498	−	0.850176i	$-0.323505\pi$
$479$	11039.0			1.05300			0.526498	+	0.850176i	$0.323505\pi$
$480$	4738.81	+	8543.17i	0.450617	+	0.812376i
$481$			206.369i			0.0195626i
$482$	198.705	+	1955.08i	0.0187775	+	0.184754i
$483$	1186.46	−	4273.94i	0.111771	−	0.402631i
$484$	8394.97	−	1724.26i	0.788408	−	0.161933i
$485$		−	19284.6i		−	1.80550i
$486$	69.4966	+	683.785i	0.00648649	+	0.0638212i
$487$		−	17874.5i		−	1.66318i	−0.555387	−	0.831592i	$-0.687430\pi$
$487$		−	17874.5i		−	1.66318i	0.555387	−	0.831592i	$-0.312570\pi$
$488$	2402.11	−	753.238i	0.222825	−	0.0698719i
$489$			3324.98i			0.307486i
$490$	−15788.3	−	7438.23i	−1.45560	−	0.685766i
$491$	6063.89			0.557351			0.278676	−	0.960385i	$-0.410105\pi$
$491$	6063.89			0.557351			0.278676	+	0.960385i	$0.410105\pi$
$492$	−9737.76	+	2000.06i	−0.892301	+	0.183272i
$493$	5309.29			0.485027
$494$	−152.681	−	1502.24i	−0.0139057	−	0.136820i
$495$	7935.56			0.720560
$496$	−6315.46	+	2708.55i	−0.571718	+	0.245197i
$497$	16818.2	+	4668.78i	1.51791	+	0.421375i
$498$	3089.19	−	313.970i	0.277971	−	0.0282517i
$499$	1084.55			0.0972968			0.0486484	−	0.998816i	$-0.484509\pi$
$499$	1084.55			0.0972968			0.0486484	+	0.998816i	$0.484509\pi$
$500$	10379.8	−	2131.93i	0.928399	−	0.190686i
$501$			10446.0i			0.931521i
$502$	459.611	+	4522.16i	0.0408634	+	0.402060i
$503$	−8014.53			−0.710438			−0.355219	−	0.934783i	$-0.615594\pi$
$503$	−8014.53			−0.710438			−0.355219	+	0.934783i	$0.615594\pi$
$504$	124.734	+	3769.53i	0.0110240	+	0.333151i
$505$	27515.5			2.42460
$506$	1119.05	+	11010.5i	0.0983159	+	0.967341i
$507$		−	6543.42i		−	0.573182i
$508$	−1494.33	−	7275.52i	−0.130512	−	0.635431i
$509$	16820.5			1.46474			0.732372	−	0.680905i	$-0.238413\pi$
$509$	16820.5			1.46474			0.732372	+	0.680905i	$0.238413\pi$
$510$	3839.04	−	390.182i	0.333325	−	0.0338775i
$511$	−1713.27	−	475.609i	−0.148319	−	0.0411736i
$512$	7095.87	−	9157.86i	0.612492	−	0.790477i
$513$	3619.25			0.311489
$514$	1982.87	+	19509.7i	0.170157	+	1.67419i
$515$	−16983.0			−1.45313
$516$	−899.673	−	4380.27i	−0.0767556	−	0.373703i
$517$	25356.5			2.15701
$518$	−2675.44	−	457.872i	−0.226935	−	0.0388374i
$519$			6448.15i			0.545361i
$520$	−1546.91	+	485.069i	−0.130455	+	0.0409071i
$521$			10049.0i			0.845022i	0.906358	+	0.422511i	$0.138851\pi$
$521$			10049.0i			0.845022i	−0.906358	+	0.422511i	$0.861149\pi$
$522$	−540.595	−	5318.98i	−0.0453280	−	0.445987i
$523$		−	20900.8i		−	1.74747i	−0.486399	−	0.873737i	$-0.661690\pi$
$523$		−	20900.8i		−	1.74747i	0.486399	−	0.873737i	$-0.338310\pi$
$524$	4121.36	+	20065.8i	0.343593	+	1.67286i
$525$	10633.8	+	2951.98i	0.883998	+	0.245400i
$526$	809.754	+	7967.26i	0.0671235	+	0.660436i
$527$			2714.27i			0.224356i
$528$	−3709.21	−	8648.66i	−0.305725	−	0.712850i
$529$	5793.75			0.476186
$530$	−2276.39	−	22397.7i	−0.186566	−	1.83565i
$531$			2025.68i			0.165550i
$532$	19814.4	+	1353.63i	1.61478	+	0.110314i
$533$		−	1649.65i		−	0.134061i
$534$	−3335.94	+	339.049i	−0.270338	+	0.0274758i
$535$	−25293.7			−2.04401
$536$	11754.9	−	3686.03i	0.947268	−	0.297038i
$537$			9873.42i			0.793425i
$538$	−21022.8	+	2136.66i	−1.68468	+	0.171223i
$539$	14405.8	+	8665.99i	1.15121	+	0.692524i
$540$	−781.787	−	3806.32i	−0.0623014	−	0.303329i
$541$			6378.46i			0.506897i	0.967349	+	0.253449i	$0.0815649\pi$
$541$			6378.46i			0.506897i	−0.967349	+	0.253449i	$0.918435\pi$
$542$	7543.84	−	766.719i	0.597852	−	0.0607628i
$543$		−	2077.24i		−	0.164168i
$544$	−2219.67	−	4001.64i	−0.174941	−	0.315384i
$545$		−	23737.4i		−	1.86569i
$546$	−616.902	−	105.576i	−0.0483535	−	0.00827516i
$547$	−17810.4			−1.39217			−0.696086	−	0.717958i	$-0.745077\pi$
$547$	−17810.4			−1.39217			−0.696086	+	0.717958i	$0.745077\pi$
$548$	2855.06	−	586.407i	0.222559	−	0.0457118i
$549$	−1001.31			−0.0778410
$550$	−27394.8	+	2784.27i	−2.12385	+	0.215858i
$551$	−28153.1			−2.17670
$552$	5170.95	−	1621.47i	0.398714	−	0.125026i
$553$	−21936.7	−	6089.67i	−1.68687	−	0.468281i
$554$	1644.33	+	16178.7i	0.126102	+	1.24074i
$555$	2796.52			0.213884
$556$	585.674	+	2851.49i	0.0446728	+	0.217500i
$557$		−	20174.1i		−	1.53466i	−0.641254	−	0.767328i	$-0.721586\pi$
$557$		−	20174.1i		−	1.53466i	0.641254	−	0.767328i	$-0.278414\pi$
$558$	2719.22	−	276.369i	0.206297	−	0.0209671i
$559$	742.051			0.0561457
$560$	−2856.48	−	21130.9i	−0.215550	−	1.59454i
$561$	−3717.04			−0.279739
$562$	13513.8	−	1373.48i	1.01431	−	0.103090i
$563$			445.596i			0.0333564i	0.999861	+	0.0166782i	$0.00530908\pi$
$563$			445.596i			0.0333564i	−0.999861	+	0.0166782i	$0.994691\pi$
$564$	−2498.04	−	12162.3i	−0.186501	−	0.908023i
$565$	2539.98			0.189129
$566$	−498.625	−	4906.03i	−0.0370296	−	0.364339i
$567$	401.268	−	1445.48i	0.0297208	−	0.107062i
$568$	6380.59	+	20348.0i	0.471344	+	1.50314i
$569$	−14296.1			−1.05329			−0.526646	−	0.850085i	$-0.676551\pi$
$569$	−14296.1			−1.05329			−0.526646	+	0.850085i	$0.676551\pi$
$570$	−20357.0	+	2068.98i	−1.49589	+	0.152035i
$571$	−997.878			−0.0731347			−0.0365673	−	0.999331i	$-0.511642\pi$
$571$	−997.878			−0.0731347			−0.0365673	+	0.999331i	$0.511642\pi$
$572$	1529.68	−	314.184i	0.111817	−	0.0229663i
$573$	−2515.61			−0.183405
$574$	21386.7	+	3660.10i	1.55516	+	0.266149i
$575$		−	15857.1i		−	1.15006i
$576$	−3782.94	+	2631.17i	−0.273650	+	0.190334i
$577$			14158.8i			1.02156i	0.859712	+	0.510780i	$0.170643\pi$
$577$			14158.8i			1.02156i	−0.859712	+	0.510780i	$0.829357\pi$
$578$	12026.6	−	1222.33i	0.865470	−	0.0879622i
$579$			1407.01i			0.100990i
$580$	6081.31	+	29608.3i	0.435366	+	2.11968i
$581$	−6530.34	−	1812.84i	−0.466307	−	0.129448i
$582$	9049.43	−	919.741i	0.644521	−	0.0655060i
$583$			21685.9i			1.54054i
$584$	−649.992	−	2072.86i	−0.0460563	−	0.146876i
$585$	644.819			0.0455726
$586$	−19320.1	+	1963.60i	−1.36195	+	0.138422i
$587$			25354.3i			1.78277i	0.453250	+	0.891383i	$0.350264\pi$
$587$			25354.3i			1.78277i	−0.453250	+	0.891383i	$0.649736\pi$
$588$	2737.45	−	7763.52i	0.191991	−	0.544493i
$589$		−	14392.7i		−	1.00686i
$590$	−1158.00	−	11393.7i	−0.0808037	−	0.795036i
$591$	3632.00			0.252793
$592$	−1307.14	−	3047.81i	−0.0907482	−	0.211595i
$593$		−	10449.0i		−	0.723592i	−0.932257	−	0.361796i	$-0.882164\pi$
$593$		−	10449.0i		−	0.723592i	0.932257	−	0.361796i	$-0.117836\pi$
$594$	378.471	+	3723.82i	0.0261429	+	0.257223i
$595$	−8115.49	−	2252.88i	−0.559164	−	0.155225i
$596$	1936.78	+	9429.68i	0.133110	+	0.648078i
$597$			6008.08i			0.411883i
$598$	90.9305	+	894.676i	0.00621810	+	0.0611806i
$599$			5231.47i			0.356848i	0.983954	+	0.178424i	$0.0570999\pi$
$599$			5231.47i			0.356848i	−0.983954	+	0.178424i	$0.942900\pi$
$600$	4034.33	+	12865.7i	0.274501	+	0.875399i
$601$		−	25487.4i		−	1.72987i	−0.501885	−	0.864935i	$-0.667360\pi$
$601$		−	25487.4i		−	1.72987i	0.501885	−	0.864935i	$-0.332640\pi$
$602$	−1646.40	+	9620.24i	−0.111465	+	0.651315i
$603$	−4899.97			−0.330916
$604$	95.0465	+	462.757i	0.00640296	+	0.0311743i
$605$	19271.9			1.29507
$606$	1312.30	+	12911.8i	0.0879677	+	0.865524i
$607$	23913.0			1.59901			0.799505	−	0.600659i	$-0.205095\pi$
$607$	23913.0			1.59901			0.799505	+	0.600659i	$0.205095\pi$
$608$	11770.1	+	21219.2i	0.785098	+	1.41538i
$609$	−3121.36	+	11244.0i	−0.207691	+	0.748159i
$610$	5631.99	−	572.408i	0.373824	−	0.0379937i
$611$	2060.39			0.136423
$612$	366.191	+	1782.89i	0.0241869	+	0.117760i
$613$			603.562i			0.0397678i	0.999802	+	0.0198839i	$0.00632966\pi$
$613$			603.562i			0.0397678i	−0.999802	+	0.0198839i	$0.993670\pi$
$614$	−1739.84	−	17118.5i	−0.114356	−	1.12516i
$615$	−22354.5			−1.46573
$616$	679.287	+	20528.4i	0.0444306	+	1.34272i
$617$	−18810.0			−1.22733			−0.613665	−	0.789566i	$-0.710306\pi$
$617$	−18810.0			−1.22733			−0.613665	+	0.789566i	$0.710306\pi$
$618$	−809.971	−	7969.39i	−0.0527214	−	0.518731i
$619$		−	19294.0i		−	1.25282i	−0.779495	−	0.626408i	$-0.784524\pi$
$619$		−	19294.0i		−	1.25282i	0.779495	−	0.626408i	$-0.215476\pi$
$620$	−15136.7	+	3108.95i	−0.980488	+	0.201384i
$621$	−2155.48			−0.139286
$622$	−14826.5	+	1506.90i	−0.955770	+	0.0971399i
$623$	7051.97	+	1957.64i	0.453501	+	0.125893i
$624$	−301.399	−	702.763i	−0.0193359	−	0.0450850i
$625$	−1000.16			−0.0640105
$626$	−1823.83	−	17944.8i	−0.116445	−	1.14572i
$627$	19710.0			1.25541
$628$	17554.5	−	3605.54i	1.11544	−	0.229103i
$629$	−1309.90			−0.0830349
$630$	−1430.67	+	8359.68i	−0.0904748	+	0.528663i
$631$			2707.27i			0.170800i	0.996347	+	0.0853999i	$0.0272168\pi$
$631$			2707.27i			0.170800i	−0.996347	+	0.0853999i	$0.972783\pi$
$632$	−8322.46	−	26540.7i	−0.523813	−	1.67046i
$633$			13172.7i			0.827124i
$634$	−1544.70	−	15198.5i	−0.0967633	−	0.952065i
$635$		−	16702.1i		−	1.04378i
$636$	10401.7	−	2136.43i	0.648513	−	0.133199i
$637$	1170.57	+	704.171i	0.0728094	+	0.0437995i
$638$	−2944.02	−	28966.6i	−0.182688	−	1.79749i
$639$		−	8481.95i		−	0.525103i
$640$	19773.5	−	16961.9i	1.22128	−	1.04762i
$641$	−23173.7			−1.42794			−0.713969	−	0.700177i	$-0.753104\pi$
$641$	−23173.7			−1.42794			−0.713969	+	0.700177i	$0.753104\pi$
$642$	−1206.34	−	11869.3i	−0.0741593	−	0.729662i
$643$			23999.2i			1.47191i	0.677033	+	0.735953i	$0.263265\pi$
$643$			23999.2i			1.47191i	−0.677033	+	0.735953i	$0.736735\pi$
$644$	−11800.7	−	806.167i	−0.722067	−	0.0493283i
$645$		−	10055.6i		−	0.613857i
$646$	9535.26	−	969.118i	0.580743	−	0.0590239i
$647$	−10137.5			−0.615988			−0.307994	−	0.951388i	$-0.599658\pi$
$647$	−10137.5			−0.615988			−0.307994	+	0.951388i	$0.599658\pi$
$648$	1748.86	−	548.394i	0.106021	−	0.0332453i
$649$			11031.6i			0.667225i
$650$	−2226.01	+	226.241i	−0.134325	+	0.0136522i
$651$	−5748.26	−	1595.73i	−0.346071	−	0.0960702i
$652$	8685.30	−	1783.89i	0.521691	−	0.107151i
$653$			16692.2i			1.00033i	0.865929	+	0.500166i	$0.166728\pi$
$653$			16692.2i			1.00033i	−0.865929	+	0.500166i	$0.833272\pi$
$654$	11139.0	−	1132.11i	0.666006	−	0.0676897i
$655$			46064.2i			2.74790i
$656$	10448.9	+	24363.3i	0.621889	+	1.45004i
$657$			864.058i			0.0513092i
$658$	−4571.40	+	26711.6i	−0.270838	+	1.58257i
$659$	13914.4			0.822500			0.411250	−	0.911523i	$-0.365092\pi$
$659$	13914.4			0.822500			0.411250	+	0.911523i	$0.365092\pi$
$660$	−4257.53	−	20728.8i	−0.251097	−	1.22253i
$661$	−22714.6			−1.33661			−0.668303	−	0.743889i	$-0.732979\pi$
$661$	−22714.6			−1.33661			−0.668303	+	0.743889i	$0.732979\pi$
$662$	12433.7	−	1263.70i	0.729983	−	0.0741919i
$663$	−302.035			−0.0176924
$664$	−2477.52	−	7900.93i	−0.144799	−	0.461771i
$665$	43033.3	+	11946.2i	2.50941	+	0.696620i
$666$	133.374	+	1312.29i	0.00775999	+	0.0763514i
$667$	16766.9			0.973338
$668$	27286.3	−	5604.40i	1.58045	−	0.324612i
$669$		−	13449.6i		−	0.777268i
$670$	27560.6	−	2801.12i	1.58919	−	0.161518i
$671$	−5453.01			−0.313727
$672$	9779.61	−	2348.22i	0.561394	−	0.134798i
$673$	−1887.15			−0.108090			−0.0540449	−	0.998539i	$-0.517211\pi$
$673$	−1887.15			−0.108090			−0.0540449	+	0.998539i	$0.517211\pi$
$674$	5940.58	−	603.773i	0.339500	−	0.0345051i
$675$		−	5362.98i		−	0.305809i
$676$	−17092.3	+	3510.62i	−0.972480	+	0.199740i
$677$	6620.71			0.375856			0.187928	−	0.982183i	$-0.439823\pi$
$677$	6620.71			0.375856			0.187928	+	0.982183i	$0.439823\pi$
$678$	121.139	+	1191.90i	0.00686184	+	0.0675144i
$679$	−19129.9	−	5310.51i	−1.08121	−	0.300146i
$680$	−3078.90	−	9818.77i	−0.173633	−	0.553724i
$681$	7371.89			0.414818
$682$	14808.6	−	1505.07i	0.831452	−	0.0845048i
$683$	11075.0			0.620457			0.310228	−	0.950662i	$-0.399595\pi$
$683$	11075.0			0.620457			0.310228	+	0.950662i	$0.399595\pi$
$684$	−1941.77	−	9453.98i	−0.108546	−	0.528482i
$685$	6554.24			0.365583
$686$	−11726.3	+	13613.3i	−0.652641	+	0.757667i
$687$		−	15140.6i		−	0.840829i
$688$	−10959.2	+	4700.14i	−0.607289	+	0.260452i
$689$			1762.13i			0.0974335i
$690$	12123.8	−	1232.20i	0.668906	−	0.0679844i
$691$		−	3087.15i		−	0.169958i	−0.996383	−	0.0849789i	$-0.972918\pi$
$691$		−	3087.15i		−	0.169958i	0.996383	−	0.0849789i	$-0.0270823\pi$
$692$	16843.5	−	3459.51i	0.925278	−	0.190045i
$693$	2185.26	−	7871.92i	0.119785	−	0.431500i
$694$	20582.4	−	2091.89i	1.12579	−	0.114420i
$695$			6546.04i			0.357274i
$696$	−13603.9	+	4265.81i	−0.740881	+	0.232320i
$697$	10470.9			0.569031
$698$	−934.436	+	94.9716i	−0.0506718	+	0.00515004i
$699$		−	5313.95i		−	0.287542i
$700$	2005.80	−	29360.8i	0.108303	−	1.58534i
$701$		−	17766.5i		−	0.957250i	−0.878019	−	0.478625i	$-0.841135\pi$
$701$		−	17766.5i		−	0.957250i	0.878019	−	0.478625i	$-0.158865\pi$
$702$	30.7534	+	302.586i	0.00165344	+	0.0162683i
$703$	6945.87			0.372644
$704$	−20601.5	+	14329.1i	−1.10291	+	0.767113i
$705$		−	27920.4i		−	1.49155i
$706$	−915.499	−	9007.69i	−0.0488035	−	0.480183i
$707$	7577.10	−	27294.8i	0.403064	−	1.45195i
$708$	5291.35	−	1086.80i	0.280877	−	0.0576900i
$709$			4977.18i			0.263642i	0.991274	+	0.131821i	$0.0420824\pi$
$709$			4977.18i			0.263642i	−0.991274	+	0.131821i	$0.957918\pi$
$710$	4848.80	+	47707.9i	0.256299	+	2.52175i
$711$			11063.3i			0.583555i
$712$	2675.42	+	8532.03i	0.140822	+	0.449089i
$713$			8571.74i			0.450230i
$714$	670.128	−	3915.70i	0.0351245	−	0.205240i
$715$	3511.62			0.183674
$716$	25790.7	−	5297.21i	1.34615	−	0.276489i
$717$	−2282.87			−0.118906
$718$	−711.999	−	7005.43i	−0.0370077	−	0.364123i
$719$	−12592.4			−0.653151			−0.326576	−	0.945171i	$-0.605895\pi$
$719$	−12592.4			−0.653151			−0.326576	+	0.945171i	$0.605895\pi$
$720$	−9523.18	+	4084.27i	−0.492928	+	0.211405i
$721$	−4676.71	+	16846.8i	−0.241567	+	0.870190i
$722$	−31261.1	+	3177.23i	−1.61138	+	0.163773i
$723$	−2084.36			−0.107217
$724$	−5426.05	+	1114.47i	−0.278533	+	0.0572084i
$725$			41717.1i			2.13702i
$726$	919.138	+	9043.50i	0.0469868	+	0.462308i
$727$	−7152.93			−0.364907			−0.182453	−	0.983214i	$-0.558404\pi$
$727$	−7152.93			−0.364907			−0.182453	+	0.983214i	$0.558404\pi$
$728$	55.1968	+	1668.08i	0.00281007	+	0.0849218i
$729$	−729.000			−0.0370370
$730$	−493.949	−	4860.01i	−0.0250436	−	0.246407i
$731$			4710.06i			0.238315i
$732$	537.214	+	2615.55i	0.0271257	+	0.132068i
$733$	10730.6			0.540714			0.270357	−	0.962760i	$-0.412858\pi$
$733$	10730.6			0.540714			0.270357	+	0.962760i	$0.412858\pi$
$734$	30241.6	−	3073.61i	1.52076	−	0.154563i
$735$	9542.26	−	15862.4i	0.478873	−	0.796047i
$736$	−7009.79	−	12637.3i	−0.351066	−	0.632904i
$737$	−26684.7			−1.33371
$738$	−1066.16	−	10490.0i	−0.0531785	−	0.523229i
$739$	−12369.8			−0.615739			−0.307869	−	0.951429i	$-0.599616\pi$
$739$	−12369.8			−0.615739			−0.307869	+	0.951429i	$0.599616\pi$
$740$	−1500.37	−	7304.88i	−0.0745331	−	0.362882i
$741$	1601.58			0.0794000
$742$	−22844.9	−	3909.65i	−1.13027	−	0.193434i
$743$			7335.02i			0.362175i	0.983467	+	0.181087i	$0.0579616\pi$
$743$			7335.02i			0.362175i	−0.983467	+	0.181087i	$0.942038\pi$
$744$	−2180.81	−	6954.71i	−0.107463	−	0.342704i
$745$			21647.3i			1.06456i
$746$	−2436.01	−	23968.2i	−0.119556	−	1.17632i
$747$			3293.46i			0.161314i
$748$	1994.24	+	9709.42i	0.0974821	+	0.474615i
$749$	−6965.29	+	25090.9i	−0.339795	+	1.22403i
$750$	1136.45	+	11181.7i	0.0553298	+	0.544396i
$751$			1804.43i			0.0876759i	0.999039	+	0.0438379i	$0.0139585\pi$
$751$			1804.43i			0.0876759i	−0.999039	+	0.0438379i	$0.986041\pi$
$752$	−30429.4	+	13050.4i	−1.47559	+	0.632847i
$753$	−4821.19			−0.233325
$754$	−239.222	−	2353.73i	−0.0115543	−	0.113684i
$755$			1062.33i			0.0512081i
$756$	−3991.07	−	272.652i	−0.192003	−	0.0131167i
$757$		−	14363.2i		−	0.689616i	−0.938673	−	0.344808i	$-0.887944\pi$
$757$		−	14363.2i		−	0.689616i	0.938673	−	0.344808i	$-0.112056\pi$
$758$	26132.8	−	2656.01i	1.25222	−	0.127270i
$759$	−11738.5			−0.561372
$760$	16326.2	+	52065.2i	0.779230	+	2.48500i
$761$		−	12360.1i		−	0.588768i	−0.955687	−	0.294384i	$-0.904886\pi$
$761$		−	12360.1i		−	0.588768i	0.955687	−	0.294384i	$-0.0951144\pi$
$762$	7837.56	−	796.572i	0.372605	−	0.0378698i
$763$	−23547.1	−	6536.72i	−1.11725	−	0.310151i
$764$	1349.66	+	6571.12i	0.0639121	+	0.311171i
$765$			4092.90i			0.193437i
$766$	−8788.74	+	893.246i	−0.414556	+	0.0421335i
$767$			896.395i			0.0421994i
$768$	8902.58	+	8469.89i	0.418286	+	0.397957i
$769$		−	22355.4i		−	1.04832i	−0.851621	−	0.524159i	$-0.824380\pi$
$769$		−	22355.4i		−	1.04832i	0.851621	−	0.524159i	$-0.175620\pi$
$770$	−7791.25	+	45525.9i	−0.364646	+	2.13070i
$771$	−20799.7			−0.971574
$772$	3675.30	−	754.877i	0.171343	−	0.0351925i
$773$	−8766.01			−0.407880			−0.203940	−	0.978983i	$-0.565375\pi$
$773$	−8766.01			−0.407880			−0.203940	+	0.978983i	$0.565375\pi$
$774$	4718.65	−	479.581i	0.219132	−	0.0222716i
$775$	−21327.1			−0.988505
$776$	−7257.62	−	23144.9i	−0.335739	−	1.07069i
$777$	770.094	−	2774.09i	0.0355559	−	0.128082i
$778$	1441.83	+	14186.3i	0.0664421	+	0.653731i
$779$	−55523.3			−2.55369
$780$	−345.953	−	1684.36i	−0.0158809	−	0.0773201i
$781$		−	46191.8i		−	2.11635i
$782$	−5678.82	+	577.168i	−0.259686	+	0.0263932i
$783$	5670.69			0.258817
$784$	−21748.1	−	2985.39i	−0.990709	−	0.135996i
$785$	40298.9			1.83227
$786$	−21616.0	+	2196.94i	−0.980936	+	0.0996976i
$787$			13959.2i			0.632266i	0.948715	+	0.316133i	$0.102385\pi$
$787$			13959.2i			0.632266i	−0.948715	+	0.316133i	$0.897615\pi$
$788$	−1948.61	−	9487.28i	−0.0880919	−	0.428896i
$789$	−8494.09			−0.383267
$790$	−6324.49	−	62227.3i	−0.284829	−	2.80247i
$791$	699.449	−	2519.61i	0.0314406	−	0.113258i
$792$	9524.08	−	2986.50i	0.427302	−	0.133991i
$793$	−443.095			−0.0198421
$794$	−7037.60	+	715.268i	−0.314553	+	0.0319697i
$795$	23878.7			1.06527
$796$	15693.9	−	3223.41i	0.698815	−	0.143531i
$797$	4883.76			0.217053			0.108527	−	0.994094i	$-0.465387\pi$
$797$	4883.76			0.217053			0.108527	+	0.994094i	$0.465387\pi$
$798$	−3553.43	+	20763.4i	−0.157632	+	0.921075i
$799$			13078.0i			0.579057i
$800$	31442.5	−	17440.8i	1.38957	−	0.770783i
$801$		−	3556.53i		−	0.156884i
$802$	−2850.34	+	289.695i	−0.125497	+	0.0127550i
$803$			4705.57i			0.206794i
$804$	2628.90	+	12799.4i	0.115316	+	0.561443i
$805$	−25628.9	−	7114.66i	−1.12211	−	0.311502i
$806$	1203.30	−	122.298i	0.0525861	−	0.00534460i
$807$		−	22412.9i		−	0.977660i
$808$	33023.4	−	10355.3i	1.43782	−	0.450862i
$809$	−5194.65			−0.225753			−0.112877	−	0.993609i	$-0.536006\pi$
$809$	−5194.65			−0.225753			−0.112877	+	0.993609i	$0.536006\pi$
$810$	4100.36	−	416.741i	0.177867	−	0.0180775i
$811$			12097.1i			0.523783i	0.965097	+	0.261892i	$0.0843463\pi$
$811$			12097.1i			0.523783i	−0.965097	+	0.261892i	$0.915654\pi$
$812$	31045.5	+	2120.88i	1.34173	+	0.0916606i
$813$			8042.67i			0.346948i
$814$	726.342	+	7146.56i	0.0312755	+	0.307723i
$815$	19938.4			0.856948
$816$	4460.69	−	1913.08i	0.191367	−	0.0820727i
$817$		−	24975.7i		−	1.06951i
$818$	−2570.20	−	25288.5i	−0.109859	−	1.08092i
$819$	177.568	−	639.648i	0.00757597	−	0.0272907i
$820$	11993.5	+	58393.1i	0.510769	+	2.48680i
$821$			28449.4i			1.20937i	0.796465	+	0.604685i	$0.206701\pi$
$821$			28449.4i			1.20937i	−0.796465	+	0.604685i	$0.793299\pi$
$822$	312.592	+	3075.62i	0.0132638	+	0.130504i
$823$			15491.6i			0.656142i	0.944653	+	0.328071i	$0.106399\pi$
$823$			15491.6i			0.656142i	−0.944653	+	0.328071i	$0.893601\pi$
$824$	−20382.6	+	6391.43i	−0.861725	+	0.270214i
$825$		−	29206.2i		−	1.23252i
$826$	−11621.2	−	1988.84i	−0.489532	−	0.0837780i
$827$	−24609.9			−1.03479			−0.517395	−	0.855747i	$-0.673098\pi$
$827$	−24609.9			−1.03479			−0.517395	+	0.855747i	$0.673098\pi$
$828$	1156.44	+	5630.41i	0.0485376	+	0.236317i
$829$	−24653.6			−1.03288			−0.516438	−	0.856325i	$-0.672742\pi$
$829$	−24653.6			−1.03288			−0.516438	+	0.856325i	$0.672742\pi$
$830$	−1882.74	−	18524.5i	−0.0787360	−	0.774693i
$831$	−17248.5			−0.720029
$832$	−1674.01	+	1164.34i	−0.0697547	+	0.0485169i
$833$	−4469.62	+	7430.01i	−0.185910	+	0.309045i
$834$	−3071.78	+	312.200i	−0.127538	+	0.0129624i
$835$	62640.0			2.59610
$836$	−10574.7	−	51485.3i	−0.437480	−	2.12997i
$837$			2899.03i			0.119719i
$838$	2912.10	+	28652.5i	0.120044	+	1.18113i
$839$	−13820.1			−0.568682			−0.284341	−	0.958723i	$-0.591775\pi$
$839$	−13820.1			−0.568682			−0.284341	+	0.958723i	$0.591775\pi$
$840$	22604.2	−	747.975i	0.928475	−	0.0307233i
$841$	−19721.7			−0.808632
$842$	4711.54	+	46357.3i	0.192839	+	1.89736i
$843$			14407.4i			0.588632i
$844$	34409.0	−	7067.34i	1.40333	−	0.288232i
$845$	−39238.0			−1.59743
$846$	13101.9	−	1331.61i	0.532448	−	0.0541155i
$847$	5307.03	−	19117.4i	0.215291	−	0.775538i
$848$	−11161.3	−	26024.5i	−0.451981	−	1.05387i
$849$	5230.43			0.211435
$850$	−1436.03	−	14129.3i	−0.0579477	−	0.570154i
$851$	−4136.69			−0.166632
$852$	−22156.0	+	4550.67i	−0.890907	+	0.182985i
$853$	−18893.4			−0.758381			−0.379190	−	0.925319i	$-0.623797\pi$
$853$	−18893.4			−0.758381			−0.379190	+	0.925319i	$0.623797\pi$
$854$	983.098	−	5744.45i	0.0393922	−	0.230177i
$855$		−	21703.1i		−	0.868104i
$856$	−30357.0	+	9519.13i	−1.21213	+	0.380090i
$857$			31550.3i			1.25757i	0.777579	+	0.628785i	$0.216447\pi$
$857$			31550.3i			1.25757i	−0.777579	+	0.628785i	$0.783553\pi$
$858$	167.480	+	1647.85i	0.00666394	+	0.0655673i
$859$			26012.5i			1.03322i	0.856221	+	0.516610i	$0.172806\pi$
$859$			26012.5i			1.03322i	−0.856221	+	0.516610i	$0.827194\pi$
$860$	−26266.6	+	5394.94i	−1.04149	+	0.213914i
$861$	−6155.90	+	22175.2i	−0.243662	+	0.877735i
$862$	−3490.91	−	34347.4i	−0.137936	−	1.35717i
$863$		−	37818.9i		−	1.49174i	−0.666092	−	0.745869i	$-0.732034\pi$
$863$		−	37818.9i		−	1.49174i	0.666092	−	0.745869i	$-0.267966\pi$
$864$	−2370.76	−	4274.03i	−0.0933507	−	0.168293i
$865$	38666.8			1.51989
$866$	2341.21	+	23035.4i	0.0918679	+	0.903898i
$867$			12821.9i			0.502253i
$868$	−1084.26	+	15871.4i	−0.0423988	+	0.620633i
$869$			60249.8i			2.35194i
$870$	−31895.6	+	3241.71i	−1.24294	+	0.126327i
$871$	−2168.32			−0.0843520
$872$	−8933.42	−	28489.1i	−0.346931	−	1.10638i
$873$			9647.82i			0.374031i
$874$	30112.6	−	3060.50i	1.16542	−	0.118447i
$875$	6561.79	−	23637.3i	0.253519	−	0.913243i
$876$	2257.04	−	463.578i	0.0870528	−	0.0178800i
$877$			12334.9i			0.474939i	0.971395	+	0.237470i	$0.0763180\pi$
$877$			12334.9i			0.474939i	−0.971395	+	0.237470i	$0.923682\pi$
$878$	−2168.88	+	220.434i	−0.0833668	+	0.00847300i
$879$		−	20597.6i		−	0.790375i
$880$	−51862.2	+	22242.5i	−1.98668	+	0.852039i
$881$		−	29928.2i		−	1.14450i	−0.820078	−	0.572252i	$-0.806070\pi$
$881$		−	29928.2i		−	1.14450i	0.820078	−	0.572252i	$-0.193930\pi$
$882$	7898.66	+	3721.25i	0.301544	+	0.142065i
$883$	−11412.1			−0.434934			−0.217467	−	0.976068i	$-0.569779\pi$
$883$	−11412.1			−0.434934			−0.217467	+	0.976068i	$0.569779\pi$
$884$	162.046	+	788.958i	0.00616537	+	0.0300175i
$885$	12147.1			0.461379
$886$	3375.12	−	343.031i	0.127979	−	0.0130072i
$887$	48774.0			1.84630			0.923151	−	0.384437i	$-0.125604\pi$
$887$	48774.0			1.84630			0.923151	+	0.384437i	$0.125604\pi$
$888$	3356.31	−	1052.45i	0.126836	−	0.0397724i
$889$	−16568.1	−	4599.35i	−0.625058	−	0.173518i
$890$	2033.13	+	20004.2i	0.0765738	+	0.753418i
$891$	−3970.06			−0.149273
$892$	−35132.3	+	7215.89i	−1.31874	+	0.270858i
$893$		−	69347.6i		−	2.59869i
$894$	−10158.1	+	1032.42i	−0.380021	+	0.0386235i
$895$	59206.6			2.21124
$896$	−11380.8	−	24285.8i	−0.424335	−	0.905505i
$897$	−953.835			−0.0355046
$898$	−21031.6	+	2137.55i	−0.781551	+	0.0794331i
$899$		−	22550.7i		−	0.836607i
$900$	−14008.8	+	2877.31i	−0.518846	+	0.106567i
$901$	−11184.8			−0.413564
$902$	−5806.17	−	57127.5i	−0.214328	−	2.10880i
$903$	−9974.93	−	2769.07i	−0.367602	−	0.102047i
$904$	3048.42	−	955.903i	0.112156	−	0.0351691i
$905$	−12456.3			−0.457528
$906$	−498.506	+	50.6657i	−0.0182801	+	0.00185790i
$907$	−25357.8			−0.928325			−0.464162	−	0.885750i	$-0.653645\pi$
$907$	−25357.8			−0.928325			−0.464162	+	0.885750i	$0.653645\pi$
$908$	−3955.11	−	19256.4i	−0.144554	−	0.703795i
$909$	−13765.6			−0.502285
$910$	−633.093	+	3699.29i	−0.0230625	+	0.134759i
$911$			27285.0i			0.992309i	0.868234	+	0.496154i	$0.165255\pi$
$911$			27285.0i			0.992309i	−0.868234	+	0.496154i	$0.834745\pi$
$912$	−23653.3	+	10144.4i	−0.858815	+	0.368326i
$913$			17935.8i			0.650152i
$914$	−7319.63	+	743.932i	−0.264893	+	0.0269224i
$915$			6004.40i			0.216939i
$916$	−39549.3	+	8123.11i	−1.42658	+	0.293008i
$917$	45694.8	+	12685.0i	1.64555	+	0.456810i
$918$	−1920.62	+	195.203i	−0.0690522	+	0.00701814i
$919$		−	4591.82i		−	0.164821i	−0.996598	−	0.0824103i	$-0.973738\pi$
$919$		−	4591.82i		−	0.164821i	0.996598	−	0.0824103i	$-0.0262618\pi$
$920$	−9723.26	−	31007.9i	−0.348442	−	1.11120i
$921$	18250.5			0.652957
$922$	−29287.0	+	2976.59i	−1.04611	+	0.106322i
$923$		−	3753.40i		−	0.133851i
$924$	−21735.0	−	1484.83i	−0.773839	−	0.0528651i
$925$		−	10292.4i		−	0.365849i
$926$	1140.75	+	11223.9i	0.0404830	+	0.398316i
$927$	8496.36			0.301032
$928$	18441.5	+	33246.5i	0.652341	+	1.17605i
$929$			27171.1i			0.959586i	0.877382	+	0.479793i	$0.159288\pi$
$929$			27171.1i			0.959586i	−0.877382	+	0.479793i	$0.840712\pi$
$930$	−1657.26	−	16306.0i	−0.0584342	−	0.574940i
$931$	23700.7	−	39398.5i	0.834328	−	1.38693i
$932$	−13880.8	+	2851.00i	−0.487854	+	0.100201i
$933$		−	15806.9i		−	0.554657i
$934$	2582.75	+	25412.0i	0.0904819	+	0.890262i
$935$			22289.5i			0.779619i
$936$	773.897	−	242.673i	0.0270252	−	0.00847439i
$937$		−	18475.1i		−	0.644137i	−0.946716	−	0.322068i	$-0.895622\pi$
$937$		−	18475.1i		−	0.644137i	0.946716	−	0.322068i	$-0.104378\pi$
$938$	4810.86	−	28110.9i	0.167463	−	0.978521i
$939$	19131.4			0.664889
$940$	−72932.0	+	14979.6i	−2.53062	+	0.519768i
$941$	−22764.8			−0.788641			−0.394321	−	0.918973i	$-0.629020\pi$
$941$	−22764.8			−0.788641			−0.394321	+	0.918973i	$0.629020\pi$
$942$	1921.98	+	18910.6i	0.0664771	+	0.654076i
$943$	33067.5			1.14191
$944$	−5677.75	−	13238.7i	−0.195757	−	0.456442i
$945$	−8667.90	−	2406.23i	−0.298378	−	0.0828304i
$946$	25697.3	−	2611.75i	0.883183	−	0.0897624i
$947$	32782.2			1.12490			0.562449	−	0.826832i	$-0.309859\pi$
$947$	32782.2			1.12490			0.562449	+	0.826832i	$0.309859\pi$
$948$	28899.0	−	5935.62i	0.990079	−	0.203354i
$949$			382.360i			0.0130789i
$950$	7614.73	+	74922.2i	0.260057	+	2.55873i
$951$	16203.5			0.552507
$952$	−10587.9	+	350.354i	−0.360457	+	0.0119275i
$953$	17560.9			0.596909			0.298455	−	0.954424i	$-0.403529\pi$
$953$	17560.9			0.596909			0.298455	+	0.954424i	$0.403529\pi$
$954$	1138.85	+	11205.2i	0.0386494	+	0.380276i
$955$			15085.0i			0.511141i
$956$	1224.79	+	5963.17i	0.0414357	+	0.201739i
$957$	30882.0			1.04313
$958$	31063.0	−	3157.10i	1.04760	−	0.106473i
$959$	1804.88	−	6501.67i	0.0607744	−	0.218926i
$960$	15778.0	+	22684.6i	0.530450	+	0.762649i
$961$	−18262.4			−0.613017
$962$	59.0203	+	580.708i	0.00197806	+	0.0194623i
$963$	12654.1			0.423441
$964$	1118.29	+	5444.64i	0.0373626	+	0.181909i
$965$	8437.21			0.281454
$966$	2116.28	−	12365.9i	0.0704868	−	0.411869i
$967$			21637.9i			0.719574i	0.933034	+	0.359787i	$0.117151\pi$
$967$			21637.9i			0.719574i	−0.933034	+	0.359787i	$0.882849\pi$
$968$	23129.7	−	7252.87i	0.767994	−	0.240822i
$969$			10165.8i			0.337019i
$970$	−5515.28	−	54265.5i	−0.182562	−	1.79625i
$971$			29037.6i			0.959691i	0.877353	+	0.479845i	$0.159307\pi$
$971$			29037.6i			0.959691i	−0.877353	+	0.479845i	$0.840693\pi$
$972$	391.118	+	1904.25i	0.0129065	+	0.0628383i
$973$	6493.54	+	1802.62i	0.213950	+	0.0593930i
$974$	−5112.01	−	50297.6i	−0.168172	−	1.65466i
$975$		−	2373.21i		−	0.0779522i
$976$	6543.96	−	2806.55i	0.214618	−	0.0920446i
$977$	−28193.5			−0.923225			−0.461613	−	0.887082i	$-0.652729\pi$
$977$	−28193.5			−0.923225			−0.461613	+	0.887082i	$0.652729\pi$
$978$	950.925	+	9356.26i	0.0310912	+	0.305910i
$979$		−	19368.5i		−	0.632297i
$980$	−46554.4	−	16415.3i	−1.51748	−	0.535069i
$981$			11875.5i			0.386500i
$982$	17063.4	−	1734.24i	0.554495	−	0.0563562i
$983$	−17518.9			−0.568429			−0.284215	−	0.958761i	$-0.591733\pi$
$983$	−17518.9			−0.568429			−0.284215	+	0.958761i	$0.591733\pi$
$984$	−26829.4	+	8412.97i	−0.869196	+	0.272557i
$985$		−	21779.5i		−	0.704521i
$986$	14940.0	−	1518.43i	0.482541	−	0.0490432i
$987$	−27696.5	−	7688.62i	−0.893200	−	0.247955i
$988$	−859.266	−	4183.54i	−0.0276689	−	0.134713i
$989$			14874.5i			0.478242i
$990$	22330.1	−	2269.53i	0.716867	−	0.0728589i
$991$		−	27590.6i		−	0.884403i	−0.896916	−	0.442202i	$-0.854198\pi$
$991$		−	27590.6i		−	0.884403i	0.896916	−	0.442202i	$-0.145802\pi$
$992$	−16996.6	+	9427.86i	−0.543995	+	0.301749i
$993$			13255.8i			0.423627i
$994$	48660.5	+	8327.70i	1.55273	+	0.265733i
$995$	36027.8			1.14790
$996$	8602.96	−	1766.98i	0.273690	−	0.0562138i
$997$	43182.7			1.37172			0.685862	−	0.727731i	$-0.259425\pi$
$997$	43182.7			1.37172			0.685862	+	0.727731i	$0.259425\pi$
$998$	3051.85	−	310.175i	0.0967981	−	0.00983810i
$999$	−1399.06			−0.0443086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.p.a.139.46	yes	48
4.3	odd	2		672.4.p.a.559.29		48
7.6	odd	2	inner	168.4.p.a.139.45	✓	48
8.3	odd	2	inner	168.4.p.a.139.48	yes	48
8.5	even	2		672.4.p.a.559.37		48
28.27	even	2		672.4.p.a.559.38		48
56.13	odd	2		672.4.p.a.559.30		48
56.27	even	2	inner	168.4.p.a.139.47	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.p.a.139.45	✓	48	7.6	odd	2	inner
168.4.p.a.139.46	yes	48	1.1	even	1	trivial
168.4.p.a.139.47	yes	48	56.27	even	2	inner
168.4.p.a.139.48	yes	48	8.3	odd	2	inner
672.4.p.a.559.29		48	4.3	odd	2
672.4.p.a.559.30		48	56.13	odd	2
672.4.p.a.559.37		48	8.5	even	2
672.4.p.a.559.38		48	28.27	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81393 - 0.285994i) q^{2} +3.00000i q^{3} +(7.83641 - 1.60954i) q^{4} +17.9897 q^{5} +(0.857983 + 8.44179i) q^{6} +(4.95393 - 17.8454i) q^{7} +(21.5908 - 6.77030i) q^{8} -9.00000 q^{9} +(50.6217 - 5.14495i) q^{10} -49.0130 q^{11} +(4.82861 + 23.5092i) q^{12} -3.98265 q^{13} +(8.83633 - 51.6325i) q^{14} +53.9691i q^{15} +(58.8188 - 25.2260i) q^{16} -25.2793i q^{17} +(-25.3254 + 2.57395i) q^{18} +134.046i q^{19} +(140.975 - 28.9551i) q^{20} +(53.5362 + 14.8618i) q^{21} +(-137.919 + 14.0175i) q^{22} -79.8326i q^{23} +(20.3109 + 64.7724i) q^{24} +198.629 q^{25} +(-11.2069 + 1.13901i) q^{26} -27.0000i q^{27} +(10.0982 - 147.818i) q^{28} +210.026i q^{29} +(15.4349 + 151.865i) q^{30} -107.371 q^{31} +(158.297 - 87.8061i) q^{32} -147.039i q^{33} +(-7.22973 - 71.1341i) q^{34} +(89.1197 - 321.033i) q^{35} +(-70.5277 + 14.4858i) q^{36} -51.8170i q^{37} +(38.3365 + 377.197i) q^{38} -11.9479i q^{39} +(388.412 - 121.796i) q^{40} +414.210i q^{41} +(154.898 + 26.5090i) q^{42} -186.321 q^{43} +(-384.086 + 78.8883i) q^{44} -161.907 q^{45} +(-22.8317 - 224.643i) q^{46} -517.341 q^{47} +(75.6780 + 176.456i) q^{48} +(-293.917 - 176.810i) q^{49} +(558.928 - 56.8068i) q^{50} +75.8378 q^{51} +(-31.2097 + 6.41022i) q^{52} -442.451i q^{53} +(-7.72185 - 75.9761i) q^{54} -881.729 q^{55} +(-13.8593 - 418.836i) q^{56} -402.139 q^{57} +(60.0661 + 590.997i) q^{58} -225.075i q^{59} +(86.8652 + 422.924i) q^{60} +111.256 q^{61} +(-302.136 + 30.7076i) q^{62} +(-44.5854 + 160.609i) q^{63} +(420.326 - 292.352i) q^{64} -71.6466 q^{65} +(-42.0524 - 413.758i) q^{66} +544.441 q^{67} +(-40.6879 - 198.099i) q^{68} +239.498 q^{69} +(158.963 - 928.853i) q^{70} +942.439i q^{71} +(-194.317 + 60.9327i) q^{72} -96.0065i q^{73} +(-14.8194 - 145.809i) q^{74} +595.887i q^{75} +(215.752 + 1050.44i) q^{76} +(-242.807 + 874.658i) q^{77} +(-3.41704 - 33.6207i) q^{78} -1229.26i q^{79} +(1058.13 - 453.808i) q^{80} +81.0000 q^{81} +(118.462 + 1165.56i) q^{82} -365.940i q^{83} +(443.453 + 30.2946i) q^{84} -454.766i q^{85} +(-524.295 + 53.2868i) q^{86} -630.077 q^{87} +(-1058.23 + 331.833i) q^{88} +395.170i q^{89} +(-455.596 + 46.3046i) q^{90} +(-19.7298 + 71.0720i) q^{91} +(-128.494 - 625.602i) q^{92} -322.114i q^{93} +(-1455.76 + 147.957i) q^{94} +2411.45i q^{95} +(263.418 + 474.892i) q^{96} -1071.98i q^{97} +(-877.629 - 413.472i) q^{98} +441.117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{2} + 10 q^{4} + 118 q^{8} - 432 q^{9} - 40 q^{11} + 38 q^{14} - 142 q^{16} + 18 q^{18} - 376 q^{22} + 1200 q^{25} - 274 q^{28} + 336 q^{30} + 318 q^{32} - 456 q^{35} - 90 q^{36} + 564 q^{42}+ \cdots + 360 q^{99}+O(q^{100}) \) 48 * q - 2 * q^2 + 10 * q^4 + 118 * q^8 - 432 * q^9 - 40 * q^11 + 38 * q^14 - 142 * q^16 + 18 * q^18 - 376 * q^22 + 1200 * q^25 - 274 * q^28 + 336 * q^30 + 318 * q^32 - 456 * q^35 - 90 * q^36 + 564 * q^42 - 808 * q^43 + 1584 * q^44 - 388 * q^46 + 360 * q^49 - 14 * q^50 + 226 * q^56 + 336 * q^57 - 3176 * q^58 - 192 * q^60 + 1954 * q^64 - 4104 * q^67 - 648 * q^70 - 1062 * q^72 + 2384 * q^74 - 1800 * q^78 + 3888 * q^81 + 264 * q^84 - 880 * q^86 + 4184 * q^88 + 104 * q^91 + 2044 * q^92 - 6018 * q^98 + 360 * q^99

Introduction

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