LMFDB - Embedded newform 168.4.p.a.139.12

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			139.12
Character	$\chi$	$=$	168.139
Dual form			168.4.p.a.139.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.20291 + 1.77404i) q^{2} +3.00000i q^{3} +(1.70558 - 7.81607i) q^{4} +4.80791 q^{5} +(-5.32211 - 6.60872i) q^{6} +(7.97009 - 16.7176i) q^{7} +(10.1088 + 20.2438i) q^{8} -9.00000 q^{9} +(-10.5914 + 8.52942i) q^{10} -46.9141 q^{11} +(23.4482 + 5.11675i) q^{12} -72.3890 q^{13} +(12.1003 + 50.9665i) q^{14} +14.4237i q^{15} +(-58.1820 - 26.6619i) q^{16} -51.4848i q^{17} +(19.8261 - 15.9663i) q^{18} -102.868i q^{19} +(8.20029 - 37.5790i) q^{20} +(50.1528 + 23.9103i) q^{21} +(103.347 - 83.2274i) q^{22} +120.251i q^{23} +(-60.7315 + 30.3263i) q^{24} -101.884 q^{25} +(159.466 - 128.421i) q^{26} -27.0000i q^{27} +(-117.072 - 90.8080i) q^{28} -66.4930i q^{29} +(-25.5883 - 31.7741i) q^{30} +166.816 q^{31} +(175.469 - 44.4833i) q^{32} -140.742i q^{33} +(91.3360 + 113.416i) q^{34} +(38.3195 - 80.3767i) q^{35} +(-15.3502 + 70.3447i) q^{36} -156.568i q^{37} +(182.492 + 226.609i) q^{38} -217.167i q^{39} +(48.6021 + 97.3306i) q^{40} -509.410i q^{41} +(-152.899 + 36.3008i) q^{42} -367.069 q^{43} +(-80.0159 + 366.684i) q^{44} -43.2712 q^{45} +(-213.330 - 264.902i) q^{46} +262.751 q^{47} +(79.9857 - 174.546i) q^{48} +(-215.955 - 266.481i) q^{49} +(224.441 - 180.746i) q^{50} +154.455 q^{51} +(-123.465 + 565.798i) q^{52} +373.897i q^{53} +(47.8990 + 59.4784i) q^{54} -225.559 q^{55} +(418.996 - 7.64901i) q^{56} +308.604 q^{57} +(117.961 + 146.478i) q^{58} +429.575i q^{59} +(112.737 + 24.6009i) q^{60} -748.653 q^{61} +(-367.480 + 295.938i) q^{62} +(-71.7308 + 150.458i) q^{63} +(-307.626 + 409.280i) q^{64} -348.040 q^{65} +(249.682 + 310.042i) q^{66} +583.540 q^{67} +(-402.409 - 87.8116i) q^{68} -360.754 q^{69} +(58.1770 + 245.043i) q^{70} -168.649i q^{71} +(-90.9789 - 182.195i) q^{72} +185.820i q^{73} +(277.758 + 344.905i) q^{74} -305.652i q^{75} +(-804.024 - 175.450i) q^{76} +(-373.910 + 784.291i) q^{77} +(385.263 + 478.399i) q^{78} -151.500i q^{79} +(-279.734 - 128.188i) q^{80} +81.0000 q^{81} +(903.713 + 1122.18i) q^{82} -139.413i q^{83} +(272.424 - 351.217i) q^{84} -247.535i q^{85} +(808.619 - 651.195i) q^{86} +199.479 q^{87} +(-474.244 - 949.722i) q^{88} +684.248i q^{89} +(95.3224 - 76.7648i) q^{90} +(-576.947 + 1210.17i) q^{91} +(939.893 + 205.098i) q^{92} +500.448i q^{93} +(-578.815 + 466.130i) q^{94} -494.581i q^{95} +(133.450 + 526.406i) q^{96} -1053.68i q^{97} +(948.477 + 203.920i) q^{98} +422.227 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 $

$2$	−2.20291	+	1.77404i	−0.778845	+	0.627217i
$2$	−2.20291	+	1.77404i	−0.778845	+	0.627217i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	1.70558	−	7.81607i	0.213198	−	0.977009i
$5$	4.80791			0.430033			0.215016	−	0.976610i	$-0.431019\pi$
$5$	4.80791			0.430033			0.215016	+	0.976610i	$0.431019\pi$
$6$	−5.32211	−	6.60872i	−0.362124	−	0.449666i
$7$	7.97009	−	16.7176i	0.430344	−	0.902665i
$7$	7.97009	−	16.7176i	0.430344	−	0.902665i
$8$	10.1088	+	20.2438i	0.446749	+	0.894659i
$9$	−9.00000			−0.333333
$10$	−10.5914	+	8.52942i	−0.334929	+	0.269724i
$11$	−46.9141			−1.28592			−0.642961	−	0.765899i	$-0.722294\pi$
$11$	−46.9141			−1.28592			−0.642961	+	0.765899i	$0.722294\pi$
$12$	23.4482	+	5.11675i	0.564076	+	0.123090i
$13$	−72.3890			−1.54439			−0.772196	−	0.635384i	$-0.780842\pi$
$13$	−72.3890			−1.54439			−0.772196	+	0.635384i	$0.780842\pi$
$14$	12.1003	+	50.9665i	0.230995	+	0.972955i
$15$			14.4237i			0.248280i
$16$	−58.1820	−	26.6619i	−0.909093	−	0.416592i
$17$		−	51.4848i		−	0.734524i	−0.930118	−	0.367262i	$-0.880295\pi$
$17$		−	51.4848i		−	0.734524i	0.930118	−	0.367262i	$-0.119705\pi$
$18$	19.8261	−	15.9663i	0.259615	−	0.209072i
$19$		−	102.868i		−	1.24208i	−0.783778	−	0.621041i	$-0.786710\pi$
$19$		−	102.868i		−	1.24208i	0.783778	−	0.621041i	$-0.213290\pi$
$20$	8.20029	−	37.5790i	0.0916821	−	0.420146i
$21$	50.1528	+	23.9103i	0.521154	+	0.248459i
$22$	103.347	−	83.2274i	1.00153	−	0.806552i
$23$			120.251i			1.09018i	0.838378	+	0.545090i	$0.183504\pi$
$23$			120.251i			1.09018i	−0.838378	+	0.545090i	$0.816496\pi$
$24$	−60.7315	+	30.3263i	−0.516532	+	0.257930i
$25$	−101.884			−0.815072
$26$	159.466	−	128.421i	1.20284	−	0.968669i
$27$		−	27.0000i		−	0.192450i
$28$	−117.072	−	90.8080i	−0.790163	−	0.612897i
$29$		−	66.4930i		−	0.425774i	−0.977077	−	0.212887i	$-0.931713\pi$
$29$		−	66.4930i		−	0.425774i	0.977077	−	0.212887i	$-0.0682866\pi$
$30$	−25.5883	−	31.7741i	−0.155725	−	0.193371i
$31$	166.816			0.966484			0.483242	−	0.875487i	$-0.339459\pi$
$31$	166.816			0.966484			0.483242	+	0.875487i	$0.339459\pi$
$32$	175.469	−	44.4833i	0.969336	−	0.245738i
$33$		−	140.742i		−	0.742427i
$34$	91.3360	+	113.416i	0.460706	+	0.572080i
$35$	38.3195	−	80.3767i	0.185062	−	0.388176i
$36$	−15.3502	+	70.3447i	−0.0710659	+	0.325670i
$37$		−	156.568i		−	0.695667i	−0.937556	−	0.347834i	$-0.886917\pi$
$37$		−	156.568i		−	0.695667i	0.937556	−	0.347834i	$-0.113083\pi$
$38$	182.492	+	226.609i	0.779055	+	0.967389i
$39$		−	217.167i		−	0.891656i
$40$	48.6021	+	97.3306i	0.192117	+	0.384733i
$41$		−	509.410i		−	1.94040i	−0.242301	−	0.970201i	$-0.577902\pi$
$41$		−	509.410i		−	1.94040i	0.242301	−	0.970201i	$-0.422098\pi$
$42$	−152.899	+	36.3008i	−0.561736	+	0.133365i
$43$	−367.069			−1.30180			−0.650902	−	0.759162i	$-0.725609\pi$
$43$	−367.069			−1.30180			−0.650902	+	0.759162i	$0.725609\pi$
$44$	−80.0159	+	366.684i	−0.274156	+	1.25636i
$45$	−43.2712			−0.143344
$46$	−213.330	−	264.902i	−0.683779	−	0.849080i
$47$	262.751			0.815450			0.407725	−	0.913105i	$-0.366322\pi$
$47$	262.751			0.815450			0.407725	+	0.913105i	$0.366322\pi$
$48$	79.9857	−	174.546i	0.240520	−	0.524865i
$49$	−215.955	−	266.481i	−0.629607	−	0.776914i
$50$	224.441	−	180.746i	0.634814	−	0.511227i
$51$	154.455			0.424078
$52$	−123.465	+	565.798i	−0.329261	+	1.50889i
$53$			373.897i			0.969032i	0.874783	+	0.484516i	$0.161004\pi$
$53$			373.897i			0.969032i	−0.874783	+	0.484516i	$0.838996\pi$
$54$	47.8990	+	59.4784i	0.120708	+	0.149889i
$55$	−225.559			−0.552989
$56$	418.996	−	7.64901i	0.999833	−	0.0182525i
$57$	308.604			0.717116
$58$	117.961	+	146.478i	0.267053	+	0.331612i
$59$			429.575i			0.947897i	0.880553	+	0.473948i	$0.157172\pi$
$59$			429.575i			0.947897i	−0.880553	+	0.473948i	$0.842828\pi$
$60$	112.737	+	24.6009i	0.242571	+	0.0529327i
$61$	−748.653			−1.57140			−0.785699	−	0.618609i	$-0.787696\pi$
$61$	−748.653			−1.57140			−0.785699	+	0.618609i	$0.787696\pi$
$62$	−367.480	+	295.938i	−0.752741	+	0.606195i
$63$	−71.7308	+	150.458i	−0.143448	+	0.300888i
$64$	−307.626	+	409.280i	−0.600831	+	0.799376i
$65$	−348.040			−0.664140
$66$	249.682	+	310.042i	0.465663	+	0.578236i
$67$	583.540			1.06404			0.532020	−	0.846732i	$-0.321433\pi$
$67$	583.540			1.06404			0.532020	+	0.846732i	$0.321433\pi$
$68$	−402.409	−	87.8116i	−0.717637	−	0.156599i
$69$	−360.754			−0.629415
$70$	58.1770	+	245.043i	0.0993355	+	0.418403i
$71$		−	168.649i		−	0.281901i	−0.990017	−	0.140951i	$-0.954984\pi$
$71$		−	168.649i		−	0.281901i	0.990017	−	0.140951i	$-0.0450159\pi$
$72$	−90.9789	−	182.195i	−0.148916	−	0.298220i
$73$			185.820i			0.297927i	0.988843	+	0.148963i	$0.0475936\pi$
$73$			185.820i			0.297927i	−0.988843	+	0.148963i	$0.952406\pi$
$74$	277.758	+	344.905i	0.436334	+	0.541817i
$75$		−	305.652i		−	0.470582i
$76$	−804.024	−	175.450i	−1.21353	−	0.264809i
$77$	−373.910	+	784.291i	−0.553389	+	1.16076i
$78$	385.263	+	478.399i	0.559261	+	0.694461i
$79$		−	151.500i		−	0.215761i	−0.994164	−	0.107881i	$-0.965594\pi$
$79$		−	151.500i		−	0.215761i	0.994164	−	0.107881i	$-0.0344064\pi$
$80$	−279.734	−	128.188i	−0.390940	−	0.179148i
$81$	81.0000			0.111111
$82$	903.713	+	1122.18i	1.21705	+	1.51127i
$83$		−	139.413i		−	0.184369i	−0.995742	−	0.0921843i	$-0.970615\pi$
$83$		−	139.413i		−	0.184369i	0.995742	−	0.0921843i	$-0.0293849\pi$
$84$	272.424	−	351.217i	0.353856	−	0.456201i
$85$		−	247.535i		−	0.315870i
$86$	808.619	−	651.195i	1.01390	−	0.816513i
$87$	199.479			0.245821
$88$	−474.244	−	949.722i	−0.574484	−	1.15046i
$89$			684.248i			0.814945i	0.913217	+	0.407473i	$0.133590\pi$
$89$			684.248i			0.814945i	−0.913217	+	0.407473i	$0.866410\pi$
$90$	95.3224	−	76.7648i	0.111643	−	0.0899080i
$91$	−576.947	+	1210.17i	−0.664621	+	1.39407i
$92$	939.893	+	205.098i	1.06512	+	0.232424i
$93$			500.448i			0.558000i
$94$	−578.815	+	466.130i	−0.635109	+	0.511464i
$95$		−	494.581i		−	0.534136i
$96$	133.450	+	526.406i	0.141877	+	0.559647i
$97$		−	1053.68i		−	1.10294i	−0.834194	−	0.551471i	$-0.814067\pi$
$97$		−	1053.68i		−	1.10294i	0.834194	−	0.551471i	$-0.185933\pi$
$98$	948.477	+	203.920i	0.977660	+	0.210195i
$99$	422.227			0.428641
$100$	−173.771	+	796.332i	−0.173771	+	0.796332i
$101$	187.496			0.184718			0.0923592	−	0.995726i	$-0.470559\pi$
$101$	187.496			0.184718			0.0923592	+	0.995726i	$0.470559\pi$
$102$	−340.249	+	274.008i	−0.330291	+	0.265989i
$103$	1791.24			1.71356			0.856778	−	0.515685i	$-0.172463\pi$
$103$	1791.24			1.71356			0.856778	+	0.515685i	$0.172463\pi$
$104$	−731.764	−	1465.43i	−0.689955	−	1.38171i
$105$	241.130	+	114.959i	0.224113	+	0.106846i
$106$	−663.307	−	823.659i	−0.607793	−	0.754725i
$107$	−2.14700			−0.00193979			−0.000969897	−	1.00000i	$-0.500309\pi$
$107$	−2.14700			−0.00193979			−0.000969897		1.00000i	$0.500309\pi$
$108$	−211.034	−	46.0507i	−0.188025	−	0.0410299i
$109$			522.814i			0.459417i	0.973259	+	0.229709i	$0.0737774\pi$
$109$			522.814i			0.459417i	−0.973259	+	0.229709i	$0.926223\pi$
$110$	496.885	−	400.150i	0.430692	−	0.346844i
$111$	469.705			0.401644
$112$	−909.438	+	760.164i	−0.767267	+	0.641328i
$113$	−2134.09			−1.77662			−0.888310	−	0.459245i	$-0.848120\pi$
$113$	−2134.09			−1.77662			−0.888310	+	0.459245i	$0.848120\pi$
$114$	−679.826	+	547.476i	−0.558522	+	0.449788i
$115$			578.158i			0.468813i
$116$	−519.714	−	113.409i	−0.415985	−	0.0907740i
$117$	651.501			0.514798
$118$	−762.082	−	946.313i	−0.594537	−	0.738264i
$119$	−860.702	−	410.339i	−0.663029	−	0.316098i
$120$	−291.992	+	145.806i	−0.222126	+	0.110919i
$121$	869.935			0.653595
$122$	1649.21	−	1328.14i	1.22387	−	0.985607i
$123$	1528.23			1.12029
$124$	284.518	−	1303.84i	0.206052	−	0.944264i
$125$	−1090.84			−0.780541
$126$	−108.902	−	458.698i	−0.0769984	−	0.324318i
$127$		−	1767.79i		−	1.23517i	−0.786505	−	0.617584i	$-0.788112\pi$
$127$		−	1767.79i		−	1.23517i	0.786505	−	0.617584i	$-0.211888\pi$
$128$	−48.4089	−	1447.35i	−0.0334280	−	0.999441i
$129$		−	1101.21i		−	0.751597i
$130$	766.700	−	617.436i	0.517262	−	0.416560i
$131$			2438.63i			1.62644i	0.581955	+	0.813221i	$0.302288\pi$
$131$			2438.63i			1.62644i	−0.581955	+	0.813221i	$0.697712\pi$
$132$	−1100.05	−	240.048i	−0.725358	−	0.158284i
$133$	−1719.71	−	819.868i	−1.12118	−	0.534523i
$134$	−1285.48	+	1035.22i	−0.828722	+	0.667384i
$135$		−	129.814i		−	0.0827599i
$136$	1042.25	−	520.448i	0.657149	−	0.328148i
$137$	−1865.04			−1.16307			−0.581537	−	0.813520i	$-0.697549\pi$
$137$	−1865.04			−1.16307			−0.581537	+	0.813520i	$0.697549\pi$
$138$	794.707	−	639.991i	0.490217	−	0.394780i
$139$		−	898.779i		−	0.548442i	−0.961667	−	0.274221i	$-0.911580\pi$
$139$		−	898.779i		−	0.548442i	0.961667	−	0.274221i	$-0.0884200\pi$
$140$	−562.873	−	436.597i	−0.339796	−	0.263566i
$141$			788.252i			0.470800i
$142$	299.190	+	371.518i	0.176813	+	0.219557i
$143$	3396.07			1.98597
$144$	523.638	+	239.957i	0.303031	+	0.138864i
$145$		−	319.693i		−	0.183097i
$146$	−329.652	−	409.345i	−0.186865	−	0.232038i
$147$	799.444	−	647.866i	0.448551	−	0.363504i
$148$	−1223.75	−	267.040i	−0.679673	−	0.148315i
$149$		−	1332.55i		−	0.732665i	−0.930484	−	0.366332i	$-0.880613\pi$
$149$		−	1332.55i		−	0.732665i	0.930484	−	0.366332i	$-0.119387\pi$
$150$	542.238	+	673.322i	0.295157	+	0.366510i
$151$			2382.62i			1.28407i	0.766674	+	0.642037i	$0.221910\pi$
$151$			2382.62i			1.28407i	−0.766674	+	0.642037i	$0.778090\pi$
$152$	2082.44	−	1039.87i	1.11124	−	0.554899i
$153$			463.364i			0.244841i
$154$	−567.673	−	2391.05i	−0.297042	−	1.25114i
$155$	802.036			0.415620
$156$	−1697.39	−	370.396i	−0.871156	−	0.190099i
$157$	3040.39			1.54554			0.772769	−	0.634687i	$-0.218871\pi$
$157$	3040.39			1.54554			0.772769	+	0.634687i	$0.218871\pi$
$158$	268.767	+	333.741i	0.135329	+	0.168044i
$159$	−1121.69			−0.559471
$160$	843.638	−	213.872i	0.416846	−	0.105675i
$161$	2010.31	+	958.414i	0.984067	+	0.469153i
$162$	−178.435	+	143.697i	−0.0865383	+	0.0696908i
$163$	1419.40			0.682061			0.341030	−	0.940052i	$-0.389224\pi$
$163$	1419.40			0.682061			0.341030	+	0.940052i	$0.389224\pi$
$164$	−3981.59	−	868.841i	−1.89579	−	0.413689i
$165$		−	676.677i		−	0.319268i
$166$	247.324	+	307.114i	0.115639	+	0.143594i
$167$	−330.413			−0.153103			−0.0765514	−	0.997066i	$-0.524391\pi$
$167$	−330.413			−0.153103			−0.0765514	+	0.997066i	$0.524391\pi$
$168$	22.9470	+	1256.99i	0.0105381	+	0.577254i
$169$	3043.17			1.38515
$170$	439.136	+	545.295i	0.198119	+	0.246013i
$171$			925.813i			0.414027i
$172$	−626.067	+	2869.04i	−0.277542	+	1.27187i
$173$	1198.11			0.526537			0.263268	−	0.964723i	$-0.415200\pi$
$173$	1198.11			0.526537			0.263268	+	0.964723i	$0.415200\pi$
$174$	−439.433	+	353.883i	−0.191456	+	0.154183i
$175$	−812.024	+	1703.25i	−0.350762	+	0.735737i
$176$	2729.56	+	1250.82i	1.16902	+	0.535705i
$177$	−1288.73			−0.547268
$178$	−1213.88	−	1507.33i	−0.511148	−	0.634716i
$179$	−3734.89			−1.55955			−0.779773	−	0.626063i	$-0.784665\pi$
$179$	−3734.89			−1.55955			−0.779773	+	0.626063i	$0.784665\pi$
$180$	−73.8026	+	338.211i	−0.0305607	+	0.140049i
$181$	−2846.85			−1.16909			−0.584544	−	0.811362i	$-0.698727\pi$
$181$	−2846.85			−1.16909			−0.584544	+	0.811362i	$0.698727\pi$
$182$	−875.927	−	3689.42i	−0.356747	−	1.50262i
$183$		−	2245.96i		−	0.907247i
$184$	−2434.35	+	1215.59i	−0.975339	+	0.487036i
$185$		−	752.767i		−	0.299160i
$186$	−887.813	−	1102.44i	−0.349987	−	0.434595i
$187$			2415.37i			0.944541i
$188$	448.143	−	2053.68i	0.173852	−	0.796702i
$189$	−451.375	−	215.192i	−0.173718	−	0.0828198i
$190$	877.405	+	1089.51i	0.335019	+	0.416009i
$191$		−	509.914i		−	0.193173i	−0.995325	−	0.0965865i	$-0.969208\pi$
$191$		−	509.914i		−	0.193173i	0.995325	−	0.0965865i	$-0.0307924\pi$
$192$	−1227.84	−	922.877i	−0.461520	−	0.346890i
$193$	2507.82			0.935320			0.467660	−	0.883908i	$-0.345097\pi$
$193$	2507.82			0.935320			0.467660	+	0.883908i	$0.345097\pi$
$194$	1869.27	+	2321.16i	0.691784	+	0.859020i
$195$		−	1044.12i		−	0.383441i
$196$	−2451.17	+	1233.42i	−0.893282	+	0.449496i
$197$			2902.21i			1.04961i	0.851222	+	0.524806i	$0.175862\pi$
$197$			2902.21i			1.04961i	−0.851222	+	0.524806i	$0.824138\pi$
$198$	−930.126	+	749.047i	−0.333844	+	0.268851i
$199$	40.6909			0.0144950			0.00724749	−	0.999974i	$-0.497693\pi$
$199$	40.6909			0.0144950			0.00724749	+	0.999974i	$0.497693\pi$
$200$	−1029.92	−	2062.52i	−0.364132	−	0.729212i
$201$			1750.62i			0.614324i
$202$	−413.036	+	332.625i	−0.143867	+	0.115859i
$203$	−1111.60	−	529.955i	−0.384331	−	0.183229i
$204$	263.435	−	1207.23i	0.0904124	−	0.414328i
$205$		−	2449.20i		−	0.834437i
$206$	−3945.94	+	3177.73i	−1.33459	+	1.07477i
$207$		−	1082.26i		−	0.363393i
$208$	4211.74	+	1930.03i	1.40400	+	0.643382i
$209$			4825.97i			1.59722i
$210$	−735.128	+	174.531i	−0.241565	+	0.0573514i
$211$	−1097.26			−0.358001			−0.179001	−	0.983849i	$-0.557286\pi$
$211$	−1097.26			−0.358001			−0.179001	+	0.983849i	$0.557286\pi$
$212$	2922.40	+	637.712i	0.946753	+	0.206595i
$213$	505.948			0.162756
$214$	4.72963	−	3.80885i	0.00151080	−	0.00121667i
$215$	−1764.84			−0.559818
$216$	546.584	−	272.937i	0.172177	−	0.0859768i
$217$	1329.54	−	2788.76i	0.415921	−	0.872411i
$218$	−927.492	−	1151.71i	−0.288154	−	0.357815i
$219$	−557.461			−0.172008
$220$	−384.710	+	1762.99i	−0.117896	+	0.540275i
$221$			3726.94i			1.13439i
$222$	−1034.72	+	833.274i	−0.312818	+	0.251918i
$223$	2630.89			0.790032			0.395016	−	0.918674i	$-0.370739\pi$
$223$	2630.89			0.790032			0.395016	+	0.918674i	$0.370739\pi$
$224$	654.847	−	3287.95i	0.195329	−	0.980738i
$225$	916.956			0.271691
$226$	4701.19	−	3785.95i	1.38371	−	1.11433i
$227$		−	2.95880i		−	0.000865120i	−1.00000		0.000432560i	$-0.999862\pi$
$227$		−	2.95880i		−	0.000865120i	1.00000		0.000432560i	$-0.000137688\pi$
$228$	526.350	−	2412.07i	0.152888	−	0.700629i
$229$	−453.634			−0.130904			−0.0654520	−	0.997856i	$-0.520849\pi$
$229$	−453.634			−0.130904			−0.0654520	+	0.997856i	$0.520849\pi$
$230$	−1025.67	−	1273.63i	−0.294047	−	0.365132i
$231$	−2352.87	−	1121.73i	−0.670163	−	0.319500i
$232$	1346.07	−	672.162i	0.380923	−	0.190214i
$233$	−4514.35			−1.26929			−0.634646	−	0.772803i	$-0.718854\pi$
$233$	−4514.35			−1.26929			−0.634646	+	0.772803i	$0.718854\pi$
$234$	−1435.20	+	1155.79i	−0.400947	+	0.322890i
$235$	1263.28			0.350670
$236$	3357.59	+	732.676i	0.926104	+	0.202090i
$237$	454.501			0.124570
$238$	2624.00	−	622.980i	0.714659	−	0.169672i
$239$			3206.73i			0.867892i	0.900939	+	0.433946i	$0.142879\pi$
$239$			3206.73i			0.867892i	−0.900939	+	0.433946i	$0.857121\pi$
$240$	384.565	−	839.202i	0.103431	−	0.225709i
$241$		−	657.422i		−	0.175719i	−0.996133	−	0.0878595i	$-0.971997\pi$
$241$		−	657.422i		−	0.175719i	0.996133	−	0.0878595i	$-0.0280027\pi$
$242$	−1916.39	+	1543.30i	−0.509049	+	0.409946i
$243$			243.000i			0.0641500i
$244$	−1276.89	+	5851.53i	−0.335018	+	1.53527i
$245$	−1038.29	−	1281.22i	−0.270752	−	0.334098i
$246$	−3366.55	+	2711.14i	−0.872533	+	0.702666i
$247$			7446.52i			1.91826i
$248$	1686.30	+	3376.99i	0.431776	+	0.864674i
$249$	418.240			0.106445
$250$	2403.01	−	1935.19i	0.607920	−	0.489568i
$251$		−	1192.65i		−	0.299918i	−0.988692	−	0.149959i	$-0.952086\pi$
$251$		−	1192.65i		−	0.299918i	0.988692	−	0.149959i	$-0.0479141\pi$
$252$	1053.65	+	817.272i	0.263388	+	0.204299i
$253$		−	5641.48i		−	1.40189i
$254$	3136.13	+	3894.28i	0.774718	+	0.962003i
$255$	742.604			0.182367
$256$	2674.29	+	3102.49i	0.652902	+	0.757443i
$257$			970.309i			0.235511i	0.993043	+	0.117755i	$0.0375698\pi$
$257$			970.309i			0.235511i	−0.993043	+	0.117755i	$0.962430\pi$
$258$	1953.58	+	2425.86i	0.471414	+	0.585377i
$259$	−2617.45	−	1247.86i	−0.627954	−	0.299376i
$260$	−593.611	+	2720.31i	−0.141593	+	0.648870i
$261$			598.437i			0.141925i
$262$	−4326.22	−	5372.07i	−1.02013	−	1.26675i
$263$		−	2045.21i		−	0.479516i	−0.970833	−	0.239758i	$-0.922932\pi$
$263$		−	2045.21i		−	0.479516i	0.970833	−	0.239758i	$-0.0770681\pi$
$264$	2849.17	−	1422.73i	0.664220	−	0.331678i
$265$			1797.66i			0.416715i
$266$	5242.83	−	1244.73i	1.20849	−	0.286915i
$267$	−2052.74			−0.470509
$268$	995.275	−	4560.99i	0.226851	−	1.03958i
$269$	6862.26			1.55539			0.777694	−	0.628643i	$-0.216389\pi$
$269$	6862.26			1.55539			0.777694	+	0.628643i	$0.216389\pi$
$270$	230.294	+	285.967i	0.0519084	+	0.0644571i
$271$	−2117.65			−0.474678			−0.237339	−	0.971427i	$-0.576275\pi$
$271$	−2117.65			−0.474678			−0.237339	+	0.971427i	$0.576275\pi$
$272$	−1372.68	+	2995.49i	−0.305997	+	0.667751i
$273$	−3630.51	−	1730.84i	−0.804866	−	0.383719i
$274$	4108.51	−	3308.65i	0.905855	−	0.729500i
$275$	4779.80			1.04812
$276$	−615.295	+	2819.68i	−0.134190	+	0.614945i
$277$		−	7334.96i		−	1.59103i	−0.605935	−	0.795514i	$-0.707201\pi$
$277$		−	7334.96i		−	1.59103i	0.605935	−	0.795514i	$-0.292799\pi$
$278$	1594.47	+	1979.93i	0.343992	+	0.427151i
$279$	−1501.34			−0.322161
$280$	2014.50	−	36.7758i	0.429961	−	0.00784919i
$281$	38.6602			0.00820738			0.00410369	−	0.999992i	$-0.498694\pi$
$281$	38.6602			0.00820738			0.00410369	+	0.999992i	$0.498694\pi$
$282$	−1398.39	−	1736.44i	−0.295294	−	0.366680i
$283$		−	3982.79i		−	0.836581i	−0.908313	−	0.418291i	$-0.862629\pi$
$283$		−	3982.79i		−	0.836581i	0.908313	−	0.418291i	$-0.137371\pi$
$284$	−1318.17	−	287.645i	−0.275420	−	0.0601007i
$285$	1483.74			0.308384
$286$	−7481.22	+	6024.75i	−1.54676	+	1.24563i
$287$	−8516.11	−	4060.04i	−1.75153	−	0.835041i
$288$	−1579.22	+	400.350i	−0.323112	+	0.0819127i
$289$	2262.31			0.460474
$290$	567.147	+	704.252i	0.114841	+	0.142604i
$291$	3161.05			0.636784
$292$	1452.39	+	316.932i	0.291077	+	0.0635173i
$293$	4674.36			0.932011			0.466005	−	0.884782i	$-0.345693\pi$
$293$	4674.36			0.932011			0.466005	+	0.884782i	$0.345693\pi$
$294$	−611.761	+	2845.43i	−0.121356	+	0.564452i
$295$			2065.36i			0.407627i
$296$	3169.54	−	1582.71i	0.622385	−	0.310788i
$297$			1266.68i			0.247476i
$298$	2364.00	+	2935.49i	0.459540	+	0.570632i
$299$		−	8704.87i		−	1.68367i
$300$	−2389.00	−	521.314i	−0.459763	−	0.100327i
$301$	−2925.58	+	6136.51i	−0.560224	+	1.17509i
$302$	−4226.86	−	5248.69i	−0.805393	−	1.00009i
$303$			562.488i			0.106647i
$304$	−2742.66	+	5985.07i	−0.517442	+	1.12917i
$305$	−3599.46			−0.675753
$306$	−822.024	−	1020.75i	−0.153569	−	0.190693i
$307$		−	6915.51i		−	1.28563i	−0.766020	−	0.642816i	$-0.777766\pi$
$307$		−	6915.51i		−	1.28563i	0.766020	−	0.642816i	$-0.222234\pi$
$308$	5492.34	+	4260.18i	1.01609	+	0.788137i
$309$			5373.73i			0.989322i
$310$	−1766.81	+	1422.84i	−0.323703	+	0.260684i
$311$	−6458.69			−1.17762			−0.588808	−	0.808273i	$-0.700403\pi$
$311$	−6458.69			−1.17762			−0.588808	+	0.808273i	$0.700403\pi$
$312$	4396.29	−	2195.29i	0.797728	−	0.398346i
$313$			821.073i			0.148274i	0.997248	+	0.0741371i	$0.0236202\pi$
$313$			821.073i			0.148274i	−0.997248	+	0.0741371i	$0.976380\pi$
$314$	−6697.69	+	5393.77i	−1.20373	+	0.969388i
$315$	−344.876	+	723.390i	−0.0616874	+	0.129392i
$316$	−1184.14	−	258.396i	−0.210801	−	0.0459998i
$317$		−	1884.71i		−	0.333929i	−0.985963	−	0.166965i	$-0.946603\pi$
$317$		−	1884.71i		−	0.333929i	0.985963	−	0.166965i	$-0.0533966\pi$
$318$	2470.98	−	1989.92i	0.435741	−	0.350909i
$319$			3119.46i			0.547512i
$320$	−1479.04	+	1967.79i	−0.258377	+	0.343758i
$321$		−	6.44099i		−	0.00111994i
$322$	−6128.79	+	1455.07i	−1.06070	+	0.251826i
$323$	−5296.15			−0.912339
$324$	138.152	−	633.102i	0.0236886	−	0.108557i
$325$	7375.28			1.25879
$326$	−3126.80	+	2518.07i	−0.531219	+	0.427800i
$327$	−1568.44			−0.265245
$328$	10312.4	−	5149.51i	1.73600	−	0.866872i
$329$	2094.15	−	4392.56i	0.350924	−	0.736078i
$330$	1200.45	+	1490.66i	0.200250	+	0.248660i
$331$	−10027.1			−1.66507			−0.832535	−	0.553973i	$-0.813111\pi$
$331$	−10027.1			−1.66507			−0.832535	+	0.553973i	$0.813111\pi$
$332$	−1089.66	−	237.781i	−0.180130	−	0.0393070i
$333$			1409.12i			0.231889i
$334$	727.870	−	586.166i	0.119243	−	0.0960286i
$335$	2805.61			0.457573
$336$	−2280.49	−	2728.32i	−0.370271	−	0.442982i
$337$	6709.98			1.08462			0.542308	−	0.840179i	$-0.317550\pi$
$337$	6709.98			1.08462			0.542308	+	0.840179i	$0.317550\pi$
$338$	−6703.82	+	5398.70i	−1.07882	+	0.868789i
$339$		−	6402.26i		−	1.02573i
$340$	−1934.75	−	422.191i	−0.308607	−	0.0673427i
$341$	−7826.02			−1.24282
$342$	−1642.43	−	2039.48i	−0.259685	−	0.322463i
$343$	−6176.11	+	1486.37i	−0.972240	+	0.233984i
$344$	−3710.62	−	7430.89i	−0.581579	−	1.16467i
$345$	−1734.47			−0.270669
$346$	−2639.33	+	2125.50i	−0.410090	+	0.330253i
$347$	3019.93			0.467199			0.233600	−	0.972333i	$-0.424949\pi$
$347$	3019.93			0.467199			0.233600	+	0.972333i	$0.424949\pi$
$348$	340.228	−	1559.14i	0.0524084	−	0.240169i
$349$	984.692			0.151030			0.0755149	−	0.997145i	$-0.475940\pi$
$349$	984.692			0.151030			0.0755149	+	0.997145i	$0.475940\pi$
$350$	−1232.82	−	5192.67i	−0.188278	−	0.793028i
$351$			1954.50i			0.297219i
$352$	−8231.96	+	2086.90i	−1.24649	+	0.316000i
$353$		−	6593.78i		−	0.994198i	−0.867694	−	0.497099i	$-0.834399\pi$
$353$		−	6593.78i		−	0.994198i	0.867694	−	0.497099i	$-0.165601\pi$
$354$	2838.94	−	2286.25i	0.426237	−	0.343256i
$355$		−	810.851i		−	0.121227i
$356$	5348.13	+	1167.04i	0.796209	+	0.173745i
$357$	1231.02	−	2582.11i	0.182499	−	0.382800i
$358$	8227.60	−	6625.83i	1.21464	−	0.978173i
$359$		−	6343.59i		−	0.932596i	−0.884628	−	0.466298i	$-0.845588\pi$
$359$		−	6343.59i		−	0.932596i	0.884628	−	0.466298i	$-0.154412\pi$
$360$	−437.419	−	875.975i	−0.0640389	−	0.128244i
$361$	−3722.84			−0.542768
$362$	6271.35	−	5050.43i	0.910538	−	0.733272i
$363$			2609.81i			0.377353i
$364$	8474.74	+	6573.50i	1.22032	+	0.946553i
$365$			893.409i			0.128118i
$366$	3984.42	+	4947.64i	0.569041	+	0.706604i
$367$	9993.35			1.42139			0.710693	−	0.703502i	$-0.248382\pi$
$367$	9993.35			1.42139			0.710693	+	0.703502i	$0.248382\pi$
$368$	3206.13	−	6996.46i	0.454160	−	0.991075i
$369$			4584.69i			0.646801i
$370$	1335.44	+	1658.27i	0.187638	+	0.232999i
$371$	6250.65	+	2979.99i	0.874711	+	0.417017i
$372$	3911.53	+	853.555i	0.545171	+	0.118964i
$373$			125.208i			0.0173808i	0.999962	+	0.00869040i	$0.00276628\pi$
$373$			125.208i			0.0173808i	−0.999962	+	0.00869040i	$0.997234\pi$
$374$	−4284.95	−	5320.82i	−0.592432	−	0.735650i
$375$		−	3272.52i		−	0.450645i
$376$	2656.09	+	5319.08i	0.364301	+	0.729550i
$377$			4813.36i			0.657562i
$378$	1376.10	−	326.707i	0.187245	−	0.0444550i
$379$	−276.555			−0.0374820			−0.0187410	−	0.999824i	$-0.505966\pi$
$379$	−276.555			−0.0374820			−0.0187410	+	0.999824i	$0.505966\pi$
$380$	−3865.68	−	843.549i	−0.521856	−	0.113877i
$381$	5303.38			0.713124
$382$	904.606	+	1123.29i	0.121161	+	0.150452i
$383$	1526.11			0.203604			0.101802	−	0.994805i	$-0.467539\pi$
$383$	1526.11			0.203604			0.101802	+	0.994805i	$0.467539\pi$
$384$	4342.04	−	145.227i	0.577028	−	0.0192997i
$385$	−1797.73	+	3770.80i	−0.237976	+	0.499163i
$386$	−5524.49	+	4448.96i	−0.728469	+	0.586648i
$387$	3303.62			0.433935
$388$	−8235.67	−	1797.14i	−1.07758	−	0.235145i
$389$		−	7087.88i		−	0.923830i	−0.886924	−	0.461915i	$-0.847163\pi$
$389$		−	7087.88i		−	0.923830i	0.886924	−	0.461915i	$-0.152837\pi$
$390$	1852.31	+	2300.10i	0.240501	+	0.298641i
$391$	6191.12			0.800763
$392$	3211.56	−	7065.56i	0.413797	−	0.910369i
$393$	−7315.88			−0.939027
$394$	−5148.62	−	6393.29i	−0.658335	−	0.817485i
$395$		−	728.401i		−	0.0927844i
$396$	720.143	−	3300.16i	0.0913852	−	0.418786i
$397$	−5758.40			−0.727974			−0.363987	−	0.931404i	$-0.618585\pi$
$397$	−5758.40			−0.727974			−0.363987	+	0.931404i	$0.618585\pi$
$398$	−89.6382	+	72.1872i	−0.0112893	+	0.00909150i
$399$	2459.60	−	5159.12i	0.308607	−	0.647316i
$400$	5927.81	+	2716.42i	0.740976	+	0.339553i
$401$	9286.85			1.15652			0.578258	−	0.815854i	$-0.303733\pi$
$401$	9286.85			1.15652			0.578258	+	0.815854i	$0.303733\pi$
$402$	−3105.66	−	3856.45i	−0.385315	−	0.478463i
$403$	−12075.6			−1.49263
$404$	319.790	−	1465.48i	0.0393816	−	0.180472i
$405$	389.441			0.0477814
$406$	3388.91	−	804.583i	0.414259	−	0.0983517i
$407$			7345.27i			0.894574i
$408$	1561.35	+	3126.75i	0.189456	+	0.379405i
$409$		−	11838.7i		−	1.43126i	−0.698482	−	0.715628i	$-0.746141\pi$
$409$		−	11838.7i		−	1.43126i	0.698482	−	0.715628i	$-0.253859\pi$
$410$	4344.97	+	5395.35i	0.523373	+	0.649897i
$411$		−	5595.13i		−	0.671502i
$412$	3055.11	−	14000.5i	0.365326	−	1.67416i
$413$	7181.46	+	3423.75i	0.855633	+	0.407922i
$414$	1919.97	+	2384.12i	0.227926	+	0.283027i
$415$		−	670.287i		−	0.0792845i
$416$	−12702.0	+	3220.11i	−1.49704	+	0.379516i
$417$	2696.34			0.316643
$418$	−8561.45	−	10631.1i	−1.00180	−	1.24399i
$419$		−	15228.9i		−	1.77561i	−0.460224	−	0.887803i	$-0.652231\pi$
$419$		−	15228.9i		−	1.77561i	0.460224	−	0.887803i	$-0.347769\pi$
$420$	1309.79	−	1688.62i	0.152170	−	0.196181i
$421$		−	8508.48i		−	0.984983i	−0.870317	−	0.492491i	$-0.836086\pi$
$421$		−	8508.48i		−	0.984983i	0.870317	−	0.492491i	$-0.163914\pi$
$422$	2417.15	−	1946.57i	0.278827	−	0.224544i
$423$	−2364.76			−0.271817
$424$	−7569.10	+	3779.64i	−0.866953	+	0.432914i
$425$			5245.48i			0.598690i
$426$	−1114.55	+	897.570i	−0.126761	+	0.102083i
$427$	−5966.84	+	12515.7i	−0.676242	+	1.41845i
$428$	−3.66188	+	16.7811i	−0.000413560	+	0.00189520i
$429$			10188.2i			1.14660i
$430$	3887.77	−	3130.89i	0.436011	−	0.351128i
$431$		−	3202.57i		−	0.357917i	−0.983857	−	0.178958i	$-0.942727\pi$
$431$		−	3202.57i		−	0.357917i	0.983857	−	0.178958i	$-0.0572728\pi$
$432$	−719.872	+	1570.91i	−0.0801732	+	0.174955i
$433$			6785.78i			0.753126i	0.926391	+	0.376563i	$0.122894\pi$
$433$			6785.78i			0.753126i	−0.926391	+	0.376563i	$0.877106\pi$
$434$	2018.52	+	8502.02i	0.223253	+	0.940346i
$435$	959.078			0.105711
$436$	4086.35	+	891.702i	0.448855	+	0.0979468i
$437$	12370.0			1.35409
$438$	1228.03	−	988.957i	0.133967	−	0.107886i
$439$	−18232.6			−1.98222			−0.991108	−	0.133060i	$-0.957520\pi$
$439$	−18232.6			−1.98222			−0.991108	+	0.133060i	$0.957520\pi$
$440$	−2280.12	−	4566.18i	−0.247047	−	0.494737i
$441$	1943.60	+	2398.33i	0.209869	+	0.258971i
$442$	−6611.73	−	8210.09i	−0.711511	−	0.883516i
$443$	10489.2			1.12496			0.562479	−	0.826811i	$-0.309848\pi$
$443$	10489.2			1.12496			0.562479	+	0.826811i	$0.309848\pi$
$444$	801.121	−	3671.25i	0.0856295	−	0.392409i
$445$			3289.81i			0.350453i
$446$	−5795.59	+	4667.29i	−0.615312	+	0.495521i
$447$	3997.66			0.423004
$448$	4390.38	+	8404.76i	0.463004	+	0.886356i
$449$	1602.32			0.168414			0.0842071	−	0.996448i	$-0.473164\pi$
$449$	1602.32			0.168414			0.0842071	+	0.996448i	$0.473164\pi$
$450$	−2019.97	+	1626.71i	−0.211605	+	0.170409i
$451$			23898.5i			2.49521i
$452$	−3639.86	+	16680.2i	−0.378771	+	1.73577i
$453$	−7147.87			−0.741360
$454$	5.24902	+	6.51795i	0.000542618	+	0.000673794i
$455$	−2773.91	+	5818.39i	−0.285809	+	0.599495i
$456$	3119.61	+	6247.33i	0.320371	+	0.641575i
$457$	−5887.93			−0.602682			−0.301341	−	0.953516i	$-0.597434\pi$
$457$	−5887.93			−0.602682			−0.301341	+	0.953516i	$0.597434\pi$
$458$	999.313	−	804.764i	0.101954	−	0.0821052i
$459$	−1390.09			−0.141359
$460$	4518.92	+	986.096i	0.458035	+	0.0999499i
$461$	−7506.55			−0.758384			−0.379192	−	0.925318i	$-0.623798\pi$
$461$	−7506.55			−0.758384			−0.379192	+	0.925318i	$0.623798\pi$
$462$	7173.15	−	1703.02i	0.722348	−	0.171497i
$463$		−	9799.46i		−	0.983628i	−0.870700	−	0.491814i	$-0.836334\pi$
$463$		−	9799.46i		−	0.983628i	0.870700	−	0.491814i	$-0.163666\pi$
$464$	−1772.83	+	3868.69i	−0.177374	+	0.387068i
$465$			2406.11i			0.239958i
$466$	9944.70	−	8008.63i	0.988582	−	0.796122i
$467$			13640.0i			1.35157i	0.737097	+	0.675787i	$0.236196\pi$
$467$			13640.0i			1.35157i	−0.737097	+	0.675787i	$0.763804\pi$
$468$	1111.19	−	5092.18i	0.109754	−	0.502962i
$469$	4650.86	−	9755.38i	0.457904	−	0.960472i
$470$	−2782.89	+	2241.11i	−0.273118	+	0.219946i
$471$			9121.17i			0.892317i
$472$	−8696.25	+	4342.48i	−0.848045	+	0.423472i
$473$	17220.7			1.67402
$474$	−1001.22	+	806.302i	−0.0970205	+	0.0781323i
$475$			10480.6i			1.01239i
$476$	−4675.24	+	6027.44i	−0.450187	+	0.580394i
$477$		−	3365.07i		−	0.323011i
$478$	−5688.86	−	7064.12i	−0.544356	−	0.675953i
$479$	12957.9			1.23604			0.618018	−	0.786164i	$-0.287936\pi$
$479$	12957.9			1.23604			0.618018	+	0.786164i	$0.287936\pi$
$480$	641.616	+	2530.91i	0.0610118	+	0.240666i
$481$			11333.8i			1.07438i
$482$	1166.29	+	1448.24i	0.110214	+	0.136858i
$483$	−2875.24	+	6030.93i	−0.270865	+	0.568151i
$484$	1483.75	−	6799.48i	0.139345	−	0.638569i
$485$		−	5066.02i		−	0.474301i
$486$	−431.091	−	535.306i	−0.0402360	−	0.0499629i
$487$			16132.4i			1.50108i	0.660824	+	0.750541i	$0.270207\pi$
$487$			16132.4i			1.50108i	−0.660824	+	0.750541i	$0.729793\pi$
$488$	−7567.96	−	15155.6i	−0.702020	−	1.40587i
$489$			4258.20i			0.393788i
$490$	4560.20	+	980.431i	0.420426	+	0.0903906i
$491$	12630.2			1.16088			0.580442	−	0.814301i	$-0.302880\pi$
$491$	12630.2			1.16088			0.580442	+	0.814301i	$0.302880\pi$
$492$	2606.52	−	11944.8i	0.238844	−	1.09454i
$493$	−3423.38			−0.312741
$494$	−13210.4	−	16404.0i	−1.20317	−	1.49403i
$495$	2030.03			0.184330
$496$	−9705.68	−	4447.63i	−0.878625	−	0.402630i
$497$	−2819.41	−	1344.15i	−0.254462	−	0.121315i
$498$	−921.342	+	741.973i	−0.0829043	+	0.0667642i
$499$	1838.40			0.164926			0.0824628	−	0.996594i	$-0.473721\pi$
$499$	1838.40			0.164926			0.0824628	+	0.996594i	$0.473721\pi$
$500$	−1860.52	+	8526.07i	−0.166410	+	0.762595i
$501$		−	991.240i		−	0.0883939i
$502$	2115.80	+	2627.29i	0.188114	+	0.233589i
$503$	5570.45			0.493785			0.246893	−	0.969043i	$-0.420590\pi$
$503$	5570.45			0.493785			0.246893	+	0.969043i	$0.420590\pi$
$504$	−3770.96	+	68.8411i	−0.333278	+	0.00608418i
$505$	901.465			0.0794350
$506$	10008.2	+	12427.7i	0.879286	+	1.09185i
$507$			9129.51i			0.799716i
$508$	−13817.2	−	3015.12i	−1.20677	−	0.263335i
$509$	−21067.8			−1.83460			−0.917302	−	0.398192i	$-0.869638\pi$
$509$	−21067.8			−1.83460			−0.917302	+	0.398192i	$0.869638\pi$
$510$	−1635.89	+	1317.41i	−0.142036	+	0.114384i
$511$	3106.47	+	1481.01i	0.268928	+	0.128211i
$512$	−11395.1	−	2090.20i	−0.983590	−	0.180419i
$513$	−2777.44			−0.239039
$514$	−1721.36	−	2137.50i	−0.147716	−	0.183426i
$515$	8612.14			0.736886
$516$	−8607.12	−	1878.20i	−0.734317	−	0.160239i
$517$	−12326.7			−1.04860
$518$	7979.74	−	1894.52i	0.676853	−	0.160696i
$519$			3594.34i			0.303996i
$520$	−3518.26	−	7045.67i	−0.296704	−	0.594179i
$521$			1657.29i			0.139362i	0.997569	+	0.0696808i	$0.0221981\pi$
$521$			1657.29i			0.139362i	−0.997569	+	0.0696808i	$0.977802\pi$
$522$	−1061.65	−	1318.30i	−0.0890175	−	0.110537i
$523$		−	12353.6i		−	1.03286i	−0.856330	−	0.516429i	$-0.827261\pi$
$523$		−	12353.6i		−	1.03286i	0.856330	−	0.516429i	$-0.172739\pi$
$524$	19060.5	+	4159.28i	1.58905	+	0.346754i
$525$	−5109.76	−	2436.07i	−0.424778	−	0.202512i
$526$	3628.27	+	4505.39i	0.300761	+	0.373469i
$527$		−	8588.49i		−	0.709906i
$528$	−3752.46	+	8188.67i	−0.309290	+	0.674936i
$529$	−2293.37			−0.188491
$530$	−3189.12	−	3960.08i	−0.261371	−	0.324557i
$531$		−	3866.18i		−	0.315966i
$532$	−9341.25	+	12043.0i	−0.761268	+	0.981447i
$533$			36875.7i			2.99674i
$534$	4522.00	−	3641.64i	0.366453	−	0.295111i
$535$	−10.3226			−0.000834175
$536$	5898.87	+	11813.1i	0.475359	+	0.951954i
$537$		−	11204.7i		−	0.900404i
$538$	−15116.9	+	12173.9i	−1.21141	+	0.975565i
$539$	10131.4	+	12501.7i	0.809626	+	0.999050i
$540$	−1014.63	−	221.408i	−0.0808571	−	0.0176442i
$541$			1186.11i			0.0942601i	0.998889	+	0.0471301i	$0.0150075\pi$
$541$			1186.11i			0.0942601i	−0.998889	+	0.0471301i	$0.984992\pi$
$542$	4664.97	−	3756.78i	0.369701	−	0.297726i
$543$		−	8540.56i		−	0.674974i
$544$	−2290.22	−	9033.97i	−0.180501	−	0.712001i
$545$			2513.64i			0.197565i
$546$	11068.2	−	2627.78i	0.867541	−	0.205968i
$547$	8057.45			0.629820			0.314910	−	0.949122i	$-0.398026\pi$
$547$	8057.45			0.629820			0.314910	+	0.949122i	$0.398026\pi$
$548$	−3180.98	+	14577.3i	−0.247965	+	1.13633i
$549$	6737.88			0.523799
$550$	−10529.4	+	8479.54i	−0.816322	+	0.657398i
$551$	−6840.01			−0.528846
$552$	−3646.78	−	7303.04i	−0.281190	−	0.563112i
$553$	−2532.72	−	1207.47i	−0.194760	−	0.0928516i
$554$	13012.5	+	16158.2i	0.997920	+	1.23916i
$555$	2258.30			0.172720
$556$	−7024.92	−	1532.94i	−0.535833	−	0.116927i
$557$		−	10565.7i		−	0.803737i	−0.915697	−	0.401868i	$-0.868361\pi$
$557$		−	10565.7i		−	0.803737i	0.915697	−	0.401868i	$-0.131639\pi$
$558$	3307.32	−	2663.44i	0.250914	−	0.202065i
$559$	26571.8			2.01050
$560$	−4372.50	+	3654.80i	−0.329950	+	0.275792i
$561$	−7246.10			−0.545331
$562$	−85.1648	+	68.5846i	−0.00639228	+	0.00514781i
$563$			9688.27i			0.725243i	0.931936	+	0.362622i	$0.118118\pi$
$563$			9688.27i			0.725243i	−0.931936	+	0.362622i	$0.881882\pi$
$564$	6161.04	+	1344.43i	0.459976	+	0.100374i
$565$	−10260.5			−0.764005
$566$	7065.62	+	8773.72i	0.524718	+	0.651567i
$567$	645.577	−	1354.12i	0.0478161	−	0.100296i
$568$	3414.11	−	1704.84i	0.252206	−	0.125939i
$569$	−1318.86			−0.0971696			−0.0485848	−	0.998819i	$-0.515471\pi$
$569$	−1318.86			−0.0971696			−0.0485848	+	0.998819i	$0.515471\pi$
$570$	−3268.54	+	2632.22i	−0.240183	+	0.193423i
$571$	3264.82			0.239279			0.119640	−	0.992817i	$-0.461826\pi$
$571$	3264.82			0.239279			0.119640	+	0.992817i	$0.461826\pi$
$572$	5792.27	−	26543.9i	0.423404	−	1.94031i
$573$	1529.74			0.111529
$574$	25962.8	−	6164.00i	1.88792	−	0.448224i
$575$		−	12251.7i		−	0.888574i
$576$	2768.63	−	3683.52i	0.200277	−	0.266459i
$577$		−	10315.0i		−	0.744227i	−0.928187	−	0.372114i	$-0.878633\pi$
$577$		−	10315.0i		−	0.744227i	0.928187	−	0.372114i	$-0.121367\pi$
$578$	−4983.66	+	4013.42i	−0.358638	+	0.288817i
$579$			7523.46i			0.540007i
$580$	−2498.74	−	545.262i	−0.178887	−	0.0390358i
$581$	−2330.65	−	1111.14i	−0.166423	−	0.0793420i
$582$	−6963.49	+	5607.82i	−0.495955	+	0.399401i
$583$		−	17541.0i		−	1.24610i
$584$	−3761.72	+	1878.42i	−0.266543	+	0.133098i
$585$	3132.36			0.221380
$586$	−10297.2	+	8292.49i	−0.725891	+	0.584573i
$587$		−	17199.2i		−	1.20934i	−0.796474	−	0.604672i	$-0.793304\pi$
$587$		−	17199.2i		−	1.20934i	0.796474	−	0.604672i	$-0.206696\pi$
$588$	−3700.25	−	7353.50i	−0.259517	−	0.515737i
$589$		−	17160.0i		−	1.20045i
$590$	−3664.03	−	4549.79i	−0.255670	−	0.317478i
$591$	−8706.62			−0.605994
$592$	−4174.41	+	9109.46i	−0.289810	+	0.632426i
$593$		−	26004.5i		−	1.80081i	−0.435056	−	0.900403i	$-0.643271\pi$
$593$		−	26004.5i		−	1.80081i	0.435056	−	0.900403i	$-0.356729\pi$
$594$	−2247.14	−	2790.38i	−0.155221	−	0.192745i
$595$	−4138.18	−	1972.87i	−0.285124	−	0.135933i
$596$	−10415.3	−	2272.78i	−0.715820	−	0.156203i
$597$			122.073i			0.00836868i
$598$	15442.8	+	19176.0i	1.05602	+	1.31131i
$599$		−	4097.99i		−	0.279531i	−0.990185	−	0.139766i	$-0.955365\pi$
$599$		−	4097.99i		−	0.279531i	0.990185	−	0.139766i	$-0.0446349\pi$
$600$	6187.57	−	3089.76i	0.421011	−	0.210232i
$601$			12434.6i			0.843959i	0.906605	+	0.421979i	$0.138665\pi$
$601$			12434.6i			0.843959i	−0.906605	+	0.421979i	$0.861335\pi$
$602$	−4441.64	−	18708.2i	−0.300710	−	1.26660i
$603$	−5251.86			−0.354680
$604$	18622.7	+	4063.76i	1.25455	+	0.273762i
$605$	4182.57			0.281067
$606$	−997.875	−	1239.11i	−0.0668910	−	0.0830616i
$607$	20334.3			1.35971			0.679855	−	0.733347i	$-0.262043\pi$
$607$	20334.3			1.35971			0.679855	+	0.733347i	$0.262043\pi$
$608$	−4575.92	−	18050.1i	−0.305227	−	1.20400i
$609$	1589.87	−	3334.81i	0.105788	−	0.221894i
$610$	7929.27	−	6385.58i	0.526306	−	0.423843i
$611$	−19020.3			−1.25937
$612$	3621.68	+	790.305i	0.239212	+	0.0521996i
$613$			25493.7i			1.67974i	0.542785	+	0.839871i	$0.317370\pi$
$613$			25493.7i			1.67974i	−0.542785	+	0.839871i	$0.682630\pi$
$614$	12268.4	+	15234.2i	0.806371	+	1.00131i
$615$	7347.60			0.481762
$616$	−19656.8	+	358.847i	−1.28571	+	0.0234713i
$617$	6936.29			0.452584			0.226292	−	0.974059i	$-0.427340\pi$
$617$	6936.29			0.452584			0.226292	+	0.974059i	$0.427340\pi$
$618$	−9533.19	−	11837.8i	−0.620520	−	0.770528i
$619$		−	2598.37i		−	0.168719i	−0.996435	−	0.0843597i	$-0.973116\pi$
$619$		−	2598.37i		−	0.168719i	0.996435	−	0.0843597i	$-0.0268845\pi$
$620$	1367.94	−	6268.77i	0.0886093	−	0.406065i
$621$	3246.78			0.209805
$622$	14227.9	−	11458.0i	0.917180	−	0.738621i
$623$	11439.0	+	5453.52i	0.735623	+	0.350707i
$624$	−5790.09	+	12635.2i	−0.371457	+	0.810598i
$625$	7490.84			0.479414
$626$	−1456.62	−	1808.75i	−0.0930001	−	0.115483i
$627$	−14477.9			−0.922156
$628$	5185.64	−	23763.9i	0.329505	−	1.51001i
$629$	−8060.90			−0.510984
$630$	−523.593	−	2205.38i	−0.0331118	−	0.139468i
$631$		−	10697.0i		−	0.674867i	−0.941349	−	0.337433i	$-0.890441\pi$
$631$		−	10697.0i		−	0.674867i	0.941349	−	0.337433i	$-0.109559\pi$
$632$	3066.95	−	1531.48i	0.193033	−	0.0963910i
$633$		−	3291.77i		−	0.206692i
$634$	3343.54	+	4151.83i	0.209446	+	0.260079i
$635$		−	8499.40i		−	0.531163i
$636$	−1913.14	+	8767.21i	−0.119278	+	0.546608i
$637$	15632.8	+	19290.3i	0.972361	+	1.19986i
$638$	−5534.04	−	6871.88i	−0.343409	−	0.426427i
$639$			1517.84i			0.0939671i
$640$	−232.746	−	6958.71i	−0.0143751	−	0.429793i
$641$	−13670.9			−0.842386			−0.421193	−	0.906971i	$-0.638388\pi$
$641$	−13670.9			−0.842386			−0.421193	+	0.906971i	$0.638388\pi$
$642$	11.4266	+	14.1889i	0.000702446	+	0.000872260i
$643$		−	20308.3i		−	1.24554i	−0.782405	−	0.622770i	$-0.786007\pi$
$643$		−	20308.3i		−	1.24554i	0.782405	−	0.622770i	$-0.213993\pi$
$644$	10919.8	−	14078.1i	0.668167	−	0.861420i
$645$		−	5294.51i		−	0.323211i
$646$	11666.9	−	9395.56i	0.710570	−	0.572235i
$647$	−23231.7			−1.41164			−0.705820	−	0.708391i	$-0.749421\pi$
$647$	−23231.7			−1.41164			−0.705820	+	0.708391i	$0.749421\pi$
$648$	818.810	+	1639.75i	0.0496387	+	0.0994066i
$649$		−	20153.1i		−	1.21892i
$650$	−16247.0	+	13084.0i	−0.980402	+	0.789535i
$651$	8366.28	+	3988.61i	0.503687	+	0.240132i
$652$	2420.90	−	11094.1i	0.145414	−	0.666379i
$653$		−	9477.68i		−	0.567979i	−0.958827	−	0.283990i	$-0.908342\pi$
$653$		−	9477.68i		−	0.567979i	0.958827	−	0.283990i	$-0.0916581\pi$
$654$	3455.13	−	2782.47i	0.206584	−	0.166366i
$655$			11724.7i			0.699424i
$656$	−13581.8	+	29638.5i	−0.808357	+	1.76401i
$657$		−	1672.38i		−	0.0993089i
$658$	3179.35	+	13391.5i	0.188365	+	0.793396i
$659$	−13928.5			−0.823334			−0.411667	−	0.911334i	$-0.635053\pi$
$659$	−13928.5			−0.823334			−0.411667	+	0.911334i	$0.635053\pi$
$660$	−5288.96	−	1154.13i	−0.311928	−	0.0680673i
$661$	−191.102			−0.0112451			−0.00562256	−	0.999984i	$-0.501790\pi$
$661$	−191.102			−0.0112451			−0.00562256	+	0.999984i	$0.501790\pi$
$662$	22088.7	−	17788.4i	1.29683	−	1.04436i
$663$	−11180.8			−0.654942
$664$	2822.26	−	1409.30i	0.164947	−	0.0823664i
$665$	−8268.20	−	3941.85i	−0.482146	−	0.229863i
$666$	−2499.82	−	3104.15i	−0.145445	−	0.180606i
$667$	7995.87			0.464170
$668$	−563.547	+	2582.54i	−0.0326412	+	0.149583i
$669$			7892.66i			0.456125i
$670$	−6180.49	+	4977.26i	−0.356378	+	0.286997i
$671$	35122.4			2.02069
$672$	9863.84	+	1964.54i	0.566229	+	0.112773i
$673$	−31526.8			−1.80575			−0.902874	−	0.429905i	$-0.858547\pi$
$673$	−31526.8			−1.80575			−0.902874	+	0.429905i	$0.858547\pi$
$674$	−14781.5	+	11903.8i	−0.844748	+	0.680290i
$675$			2750.87i			0.156861i
$676$	5190.38	−	23785.6i	0.295311	−	1.35330i
$677$	3711.82			0.210719			0.105360	−	0.994434i	$-0.466401\pi$
$677$	3711.82			0.210719			0.105360	+	0.994434i	$0.466401\pi$
$678$	11357.8	+	14103.6i	0.643356	+	0.798886i
$679$	−17615.0	−	8397.95i	−0.995587	−	0.474645i
$680$	5011.05	−	2502.27i	0.282596	−	0.141114i
$681$	8.87639			0.000499477
$682$	17240.0	−	13883.7i	0.967966	−	0.779520i
$683$	−8296.57			−0.464802			−0.232401	−	0.972620i	$-0.574658\pi$
$683$	−8296.57			−0.464802			−0.232401	+	0.972620i	$0.574658\pi$
$684$	7236.22	+	1579.05i	0.404508	+	0.0882697i
$685$	−8966.96			−0.500160
$686$	10968.5	−	14231.0i	0.610466	−	0.792043i
$687$		−	1360.90i		−	0.0755774i
$688$	21356.8	+	9786.77i	1.18346	+	0.542321i
$689$		−	27066.0i		−	1.49657i
$690$	3820.88	−	3077.02i	0.210809	−	0.169768i
$691$		−	1001.26i		−	0.0551228i	−0.999620	−	0.0275614i	$-0.991226\pi$
$691$		−	1001.26i		−	0.0551228i	0.999620	−	0.0275614i	$-0.00877418\pi$
$692$	2043.48	−	9364.54i	0.112256	−	0.514431i
$693$	3365.19	−	7058.62i	0.184463	−	0.386919i
$694$	−6652.61	+	5357.46i	−0.363876	+	0.293035i
$695$		−	4321.25i		−	0.235848i
$696$	2016.49	+	4038.22i	0.109820	+	0.219926i
$697$	−26226.9			−1.42527
$698$	−2169.18	+	1746.88i	−0.117629	+	0.0947284i
$699$		−	13543.1i		−	0.732827i
$700$	11927.8	+	9251.88i	0.644040	+	0.499555i
$701$		−	19889.7i		−	1.07165i	−0.844330	−	0.535824i	$-0.820001\pi$
$701$		−	19889.7i		−	1.07165i	0.844330	−	0.535824i	$-0.179999\pi$
$702$	−3467.36	−	4305.59i	−0.186420	−	0.231487i
$703$	−16105.9			−0.864076
$704$	14432.0	−	19201.0i	0.772622	−	1.02794i
$705$			3789.85i			0.202460i
$706$	11697.6	+	14525.5i	0.623578	+	0.774325i
$707$	1494.36	−	3134.48i	0.0794926	−	0.166739i
$708$	−2198.03	+	10072.8i	−0.116676	+	0.534686i
$709$			33973.1i			1.79956i	0.436349	+	0.899778i	$0.356271\pi$
$709$			33973.1i			1.79956i	−0.436349	+	0.899778i	$0.643729\pi$
$710$	1438.48	+	1786.23i	0.0760355	+	0.0944168i
$711$			1363.50i			0.0719204i
$712$	−13851.8	+	6916.91i	−0.729099	+	0.364076i
$713$			20059.8i			1.05364i
$714$	1868.94	+	7872.01i	0.0979599	+	0.412608i
$715$	16328.0			0.854032
$716$	−6370.16	+	29192.2i	−0.332492	+	1.52369i
$717$	−9620.19			−0.501078
$718$	11253.8	+	13974.3i	0.584940	+	0.726347i
$719$	1323.81			0.0686644			0.0343322	−	0.999410i	$-0.489070\pi$
$719$	1323.81			0.0686644			0.0343322	+	0.999410i	$0.489070\pi$
$720$	2517.61	+	1153.69i	0.130313	+	0.0597161i
$721$	14276.4	−	29945.2i	0.737419	−	1.54677i
$722$	8201.07	−	6604.46i	0.422732	−	0.340433i
$723$	1972.27			0.101451
$724$	−4855.55	+	22251.2i	−0.249247	+	1.14221i
$725$			6774.57i			0.347036i
$726$	−4629.89	−	5749.16i	−0.236682	−	0.293900i
$727$	−334.178			−0.0170481			−0.00852406	−	0.999964i	$-0.502713\pi$
$727$	−334.178			−0.0170481			−0.00852406	+	0.999964i	$0.502713\pi$
$728$	−30330.7	+	553.705i	−1.54414	+	0.0281891i
$729$	−729.000			−0.0370370
$730$	−1584.94	−	1968.09i	−0.0803579	−	0.0997842i
$731$			18898.5i			0.956206i
$732$	−17554.6	−	3830.67i	−0.886388	−	0.193423i
$733$	2748.20			0.138482			0.0692409	−	0.997600i	$-0.477942\pi$
$733$	2748.20			0.138482			0.0692409	+	0.997600i	$0.477942\pi$
$734$	−22014.4	+	17728.6i	−1.10704	+	0.891517i
$735$	3843.66	−	3114.88i	0.192892	−	0.156319i
$736$	5349.18	+	21100.3i	0.267899	+	1.05675i
$737$	−27376.3			−1.36827
$738$	−8133.41	−	10099.6i	−0.405684	−	0.503757i
$739$	33184.3			1.65183			0.825916	−	0.563793i	$-0.190659\pi$
$739$	33184.3			1.65183			0.825916	+	0.563793i	$0.190659\pi$
$740$	−5883.68	−	1283.91i	−0.292282	−	0.0637802i
$741$	−22339.6			−1.10751
$742$	−19056.2	+	4524.25i	−0.942824	+	0.223842i
$743$			35492.4i			1.75248i	0.481877	+	0.876239i	$0.339955\pi$
$743$			35492.4i			1.75248i	−0.481877	+	0.876239i	$0.660045\pi$
$744$	−10131.0	+	5058.91i	−0.499220	+	0.249286i
$745$		−	6406.80i		−	0.315070i
$746$	−222.124	−	275.822i	−0.0109015	−	0.0135369i
$747$			1254.72i			0.0614562i
$748$	18878.7	+	4119.61i	0.922825	+	0.201374i
$749$	−17.1118	+	35.8926i	−0.000834780	+	0.00175098i
$750$	5805.57	+	7209.04i	0.282652	+	0.350983i
$751$			2319.93i			0.112723i	0.998410	+	0.0563617i	$0.0179500\pi$
$751$			2319.93i			0.112723i	−0.998410	+	0.0563617i	$0.982050\pi$
$752$	−15287.4	−	7005.44i	−0.741320	−	0.339710i
$753$	3577.95			0.173158
$754$	−8539.09	−	10603.4i	−0.412434	−	0.512138i
$755$			11455.4i			0.552194i
$756$	−2451.82	+	3160.95i	−0.117952	+	0.152067i
$757$		−	22007.9i		−	1.05666i	−0.849040	−	0.528329i	$-0.822819\pi$
$757$		−	22007.9i		−	1.05666i	0.849040	−	0.528329i	$-0.177181\pi$
$758$	609.225	−	490.619i	0.0291927	−	0.0235094i
$759$	16924.5			0.809379
$760$	10012.2	−	4999.60i	0.477870	−	0.238625i
$761$			14464.1i			0.688991i	0.938788	+	0.344495i	$0.111950\pi$
$761$			14464.1i			0.688991i	−0.938788	+	0.344495i	$0.888050\pi$
$762$	−11682.8	+	9408.39i	−0.555413	+	0.447284i
$763$	8740.19	+	4166.88i	0.414700	+	0.197708i
$764$	−3985.52	−	869.700i	−0.188732	−	0.0411841i
$765$			2227.81i			0.105290i
$766$	−3361.87	+	2707.37i	−0.158576	+	0.127704i
$767$		−	31096.5i		−	1.46392i
$768$	−9307.46	+	8022.86i	−0.437310	+	0.376953i
$769$			3889.51i			0.182392i	0.995833	+	0.0911960i	$0.0290690\pi$
$769$			3889.51i			0.182392i	−0.995833	+	0.0911960i	$0.970931\pi$
$770$	−2729.33	−	11496.0i	−0.127738	−	0.538033i
$771$	−2910.93			−0.135972
$772$	4277.29	−	19601.3i	0.199408	−	0.913816i
$773$	−16998.7			−0.790946			−0.395473	−	0.918478i	$-0.629419\pi$
$773$	−16998.7			−0.790946			−0.395473	+	0.918478i	$0.629419\pi$
$774$	−7277.57	+	5860.75i	−0.337968	+	0.272171i
$775$	−16995.9			−0.787754
$776$	21330.6	−	10651.4i	0.986757	−	0.492738i
$777$	3743.59	−	7852.34i	0.172845	−	0.362549i
$778$	12574.2	+	15613.9i	0.579442	+	0.719520i
$779$	−52402.0			−2.41014
$780$	−8160.92	−	1780.83i	−0.374626	−	0.0817488i
$781$			7912.03i			0.362503i
$782$	−13638.4	+	10983.3i	−0.623670	+	0.502252i
$783$	−1795.31			−0.0819402
$784$	5459.80	+	21262.2i	0.248716	+	0.968577i
$785$	14617.9			0.664633
$786$	16116.2	−	12978.7i	0.731356	−	0.588973i
$787$		−	11983.2i		−	0.542763i	−0.962472	−	0.271381i	$-0.912520\pi$
$787$		−	11983.2i		−	0.542763i	0.962472	−	0.271381i	$-0.0874805\pi$
$788$	22683.9	+	4949.95i	1.02548	+	0.223775i
$789$	6135.62			0.276849
$790$	1292.21	+	1604.60i	0.0581959	+	0.0722646i
$791$	−17008.9	+	35676.8i	−0.764558	+	1.60369i
$792$	4268.20	+	8547.50i	0.191495	+	0.383487i
$793$	54194.3			2.42685
$794$	12685.2	−	10215.6i	0.566979	−	0.456598i
$795$	−5392.99			−0.240591
$796$	69.4017	−	318.043i	0.00309030	−	0.0141617i
$797$	−14904.3			−0.662405			−0.331203	−	0.943560i	$-0.607454\pi$
$797$	−14904.3			−0.662405			−0.331203	+	0.943560i	$0.607454\pi$
$798$	3734.19	+	15728.5i	0.165650	+	0.697722i
$799$		−	13527.7i		−	0.598967i
$800$	−17877.4	+	4532.14i	−0.790079	+	0.200294i
$801$		−	6158.23i		−	0.271648i
$802$	−20458.1	+	16475.2i	−0.900747	+	0.725387i
$803$		−	8717.60i		−	0.383110i
$804$	13683.0	+	2985.83i	0.600200	+	0.130973i
$805$	9665.40	+	4607.97i	0.423181	+	0.201751i
$806$	26601.5	−	21422.6i	1.16253	−	0.936204i
$807$			20586.8i			0.898003i
$808$	1895.36	+	3795.64i	0.0825227	+	0.165260i
$809$	7044.51			0.306146			0.153073	−	0.988215i	$-0.451083\pi$
$809$	7044.51			0.306146			0.153073	+	0.988215i	$0.451083\pi$
$810$	−857.902	+	690.883i	−0.0372143	+	0.0299693i
$811$		−	15142.8i		−	0.655656i	−0.944737	−	0.327828i	$-0.893683\pi$
$811$		−	15142.8i		−	0.655656i	0.944737	−	0.327828i	$-0.106317\pi$
$812$	−6038.10	+	7784.48i	−0.260955	+	0.336431i
$813$		−	6352.94i		−	0.274056i
$814$	−13030.8	−	16180.9i	−0.561092	−	0.696734i
$815$	6824.35			0.293308
$816$	−8986.47	−	4118.05i	−0.385526	−	0.176668i
$817$			37759.7i			1.61695i
$818$	21002.2	+	26079.4i	0.897708	+	1.11473i
$819$	5192.52	−	10891.5i	0.221540	−	0.464690i
$820$	−19143.1	−	4177.31i	−0.815252	−	0.177900i
$821$		−	20471.5i		−	0.870232i	−0.900374	−	0.435116i	$-0.856707\pi$
$821$		−	20471.5i		−	0.870232i	0.900374	−	0.435116i	$-0.143293\pi$
$822$	9925.96	+	12325.5i	0.421177	+	0.522995i
$823$		−	1542.13i		−	0.0653165i	−0.999467	−	0.0326582i	$-0.989603\pi$
$823$		−	1542.13i		−	0.0653165i	0.999467	−	0.0326582i	$-0.0103973\pi$
$824$	18107.2	+	36261.6i	0.765529	+	1.53305i
$825$			14339.4i			0.605132i
$826$	−21893.9	+	5197.97i	−0.922261	+	0.218960i
$827$	−11150.2			−0.468842			−0.234421	−	0.972135i	$-0.575319\pi$
$827$	−11150.2			−0.468842			−0.234421	+	0.972135i	$0.575319\pi$
$828$	−8459.03	−	1845.89i	−0.355038	−	0.0774746i
$829$	23834.5			0.998562			0.499281	−	0.866440i	$-0.333598\pi$
$829$	23834.5			0.998562			0.499281	+	0.866440i	$0.333598\pi$
$830$	1189.11	+	1476.58i	0.0497286	+	0.0617503i
$831$	22004.9			0.918581
$832$	22268.7	−	29627.4i	0.927919	−	1.23455i
$833$	−13719.8	+	11118.4i	−0.570662	+	0.462462i
$834$	−5939.78	+	4783.40i	−0.246616	+	0.198604i
$835$	−1588.60			−0.0658392
$836$	37720.1	+	8231.08i	1.56050	+	0.340524i
$837$		−	4504.03i		−	0.186000i
$838$	27016.6	+	33547.7i	1.11369	+	1.38292i
$839$	−36842.7			−1.51603			−0.758015	−	0.652237i	$-0.773831\pi$
$839$	−36842.7			−1.51603			−0.758015	+	0.652237i	$0.773831\pi$
$840$	110.327	+	6043.49i	0.00453173	+	0.248238i
$841$	19967.7			0.818717
$842$	15094.4	+	18743.4i	0.617798	+	0.767149i
$843$			115.981i			0.00473853i
$844$	−1871.46	+	8576.24i	−0.0763251	+	0.349770i
$845$	14631.3			0.595659
$846$	5209.33	−	4195.17i	0.211703	−	0.170488i
$847$	6933.46	−	14543.2i	0.281271	−	0.589977i
$848$	9968.80	−	21754.1i	0.403691	−	0.880940i
$849$	11948.4			0.483000
$850$	−9305.68	−	11555.3i	−0.375508	−	0.466286i
$851$	18827.5			0.758402
$852$	862.936	−	3954.52i	0.0346992	−	0.159014i
$853$	1901.29			0.0763175			0.0381587	−	0.999272i	$-0.487851\pi$
$853$	1901.29			0.0763175			0.0381587	+	0.999272i	$0.487851\pi$
$854$	−9058.91	−	38156.2i	−0.362985	−	1.52890i
$855$			4451.23i			0.178045i
$856$	−21.7035	−	43.4634i	−0.000866601	−	0.00173546i
$857$		−	4434.92i		−	0.176772i	−0.996086	−	0.0883862i	$-0.971829\pi$
$857$		−	4434.92i		−	0.176772i	0.996086	−	0.0883862i	$-0.0281710\pi$
$858$	−18074.3	−	22443.6i	−0.719167	−	0.893023i
$859$		−	7098.21i		−	0.281941i	−0.990014	−	0.140971i	$-0.954978\pi$
$859$		−	7098.21i		−	0.281941i	0.990014	−	0.140971i	$-0.0450223\pi$
$860$	−3010.08	+	13794.1i	−0.119352	+	0.546948i
$861$	12180.1	−	25548.3i	0.482111	−	1.01125i
$862$	5681.47	+	7054.95i	0.224492	+	0.278762i
$863$		−	27367.3i		−	1.07948i	−0.841830	−	0.539742i	$-0.818522\pi$
$863$		−	27367.3i		−	1.07948i	0.841830	−	0.539742i	$-0.181478\pi$
$864$	−1201.05	−	4737.65i	−0.0472923	−	0.186549i
$865$	5760.42			0.226428
$866$	−12038.2	−	14948.4i	−0.472374	−	0.586568i
$867$			6786.93i			0.265855i
$868$	−19529.5	−	15148.2i	−0.763680	−	0.592355i
$869$			7107.51i			0.277452i
$870$	−2112.76	+	1701.44i	−0.0823324	+	0.0663037i
$871$	−42241.9			−1.64330
$872$	−10583.8	+	5285.01i	−0.411022	+	0.205244i
$873$			9483.15i			0.367647i
$874$	−27250.0	+	21944.9i	−1.05463	+	0.849310i
$875$	−8694.08	+	18236.2i	−0.335901	+	0.704566i
$876$	−950.796	+	4357.16i	−0.0366717	+	0.168053i
$877$			14135.7i			0.544273i	0.962259	+	0.272137i	$0.0877303\pi$
$877$			14135.7i			0.544273i	−0.962259	+	0.272137i	$0.912270\pi$
$878$	40164.6	−	32345.2i	1.54384	−	1.24328i
$879$			14023.1i			0.538097i
$880$	13123.5	+	6013.84i	0.502718	+	0.230371i
$881$			28867.0i			1.10392i	0.833870	+	0.551960i	$0.186120\pi$
$881$			28867.0i			1.10392i	−0.833870	+	0.551960i	$0.813880\pi$
$882$	−8536.29	−	1835.28i	−0.325887	−	0.0700648i
$883$	20027.1			0.763268			0.381634	−	0.924314i	$-0.375361\pi$
$883$	20027.1			0.763268			0.381634	+	0.924314i	$0.375361\pi$
$884$	29130.0	+	6356.60i	1.10831	+	0.241850i
$885$	−6196.08			−0.235343
$886$	−23106.7	+	18608.2i	−0.876168	+	0.705593i
$887$	42737.7			1.61780			0.808902	−	0.587943i	$-0.200062\pi$
$887$	42737.7			1.61780			0.808902	+	0.587943i	$0.200062\pi$
$888$	4748.14	+	9508.63i	0.179434	+	0.359334i
$889$	−29553.2	−	14089.5i	−1.11494	−	0.531547i
$890$	−5836.24	−	7247.13i	−0.219810	−	0.272949i
$891$	−3800.04			−0.142880
$892$	4487.19	−	20563.2i	0.168433	−	0.771868i
$893$		−	27028.7i		−	1.01286i
$894$	−8806.47	+	7092.00i	−0.329455	+	0.265315i
$895$	−17957.0			−0.670656
$896$	−24581.9	−	10726.2i	−0.916546	−	0.399930i
$897$	26114.6			0.972064
$898$	−3529.75	+	2842.57i	−0.131168	+	0.105632i
$899$		−	11092.1i		−	0.411504i
$900$	1563.94	−	7166.99i	0.0579238	−	0.265444i
$901$	19250.0			0.711777
$902$	−42396.9	−	52646.2i	−1.56504	−	1.94338i
$903$	−18409.5	−	8776.73i	−0.678440	−	0.323445i
$904$	−21573.0	−	43202.1i	−0.793702	−	1.58947i
$905$	−13687.4			−0.502747
$906$	15746.1	−	12680.6i	0.577404	−	0.464994i
$907$	−14324.5			−0.524406			−0.262203	−	0.965013i	$-0.584449\pi$
$907$	−14324.5			−0.524406			−0.262203	+	0.965013i	$0.584449\pi$
$908$	−23.1262	−	5.04647i	−0.000845230	−	0.000184442i
$909$	−1687.47			−0.0615728
$910$	−4211.38	−	17738.4i	−0.153413	−	0.646178i
$911$			39329.0i			1.43033i	0.698956	+	0.715164i	$0.253648\pi$
$911$			39329.0i			1.43033i	−0.698956	+	0.715164i	$0.746352\pi$
$912$	−17955.2	−	8227.98i	−0.651926	−	0.298745i
$913$			6540.45i			0.237084i
$914$	12970.6	−	10445.4i	0.469396	−	0.378012i
$915$		−	10798.4i		−	0.390146i
$916$	−773.711	+	3545.64i	−0.0279084	+	0.127894i
$917$	40768.0	+	19436.1i	1.46813	+	0.699930i
$918$	3062.24	−	2466.07i	0.110097	−	0.0886629i
$919$			22629.0i			0.812256i	0.913816	+	0.406128i	$0.133121\pi$
$919$			22629.0i			0.812256i	−0.913816	+	0.406128i	$0.866879\pi$
$920$	−11704.1	+	5844.46i	−0.419428	+	0.209442i
$921$	20746.5			0.742260
$922$	16536.2	−	13316.9i	0.590663	−	0.475671i
$923$			12208.4i			0.435366i
$924$	−12780.5	+	16477.0i	−0.455031	+	0.586639i
$925$			15951.8i			0.567019i
$926$	17384.6	+	21587.3i	0.616948	+	0.766093i
$927$	−16121.2			−0.571185
$928$	−2957.83	−	11667.4i	−0.104629	−	0.412718i
$929$			27943.8i			0.986876i	0.869781	+	0.493438i	$0.164260\pi$
$929$			27943.8i			0.986876i	−0.869781	+	0.493438i	$0.835740\pi$
$930$	−4268.53	−	5300.43i	−0.150506	−	0.186890i
$931$	−27412.4	+	22214.9i	−0.964990	+	0.782024i
$932$	−7699.60	+	35284.5i	−0.270610	+	1.24011i
$933$		−	19376.1i		−	0.679897i
$934$	−24197.9	−	30047.7i	−0.847730	−	1.05267i
$935$			11612.9i			0.406184i
$936$	6585.88	+	13188.9i	0.229985	+	0.460569i
$937$			53676.0i			1.87142i	0.352775	+	0.935708i	$0.385238\pi$
$937$			53676.0i			1.87142i	−0.352775	+	0.935708i	$0.614762\pi$
$938$	7060.99	+	29741.0i	0.245788	+	1.03526i
$939$	−2463.22			−0.0856061
$940$	2154.63	−	9873.91i	0.0747621	−	0.342608i
$941$	−10563.7			−0.365957			−0.182978	−	0.983117i	$-0.558574\pi$
$941$	−10563.7			−0.365957			−0.182978	+	0.983117i	$0.558574\pi$
$942$	−16181.3	−	20093.1i	−0.559677	−	0.694976i
$943$	61257.2			2.11539
$944$	11453.3	−	24993.5i	0.394887	−	0.861727i
$945$	−2170.17	−	1034.63i	−0.0747044	−	0.0356153i
$946$	−37935.7	+	30550.2i	−1.30380	+	1.04997i
$947$	25873.4			0.887827			0.443913	−	0.896070i	$-0.353590\pi$
$947$	25873.4			0.887827			0.443913	+	0.896070i	$0.353590\pi$
$948$	775.189	−	3552.42i	0.0265580	−	0.121706i
$949$		−	13451.4i		−	0.460116i
$950$	−18593.0	−	23087.8i	−0.634986	−	0.788491i
$951$	5654.12			0.192794
$952$	−393.808	−	21571.9i	−0.0134069	−	0.734402i
$953$	−38689.7			−1.31509			−0.657546	−	0.753414i	$-0.728406\pi$
$953$	−38689.7			−1.31509			−0.657546	+	0.753414i	$0.728406\pi$
$954$	5969.76	+	7412.93i	0.202598	+	0.251575i
$955$		−	2451.62i		−	0.0830708i
$956$	25064.0	+	5469.34i	0.847938	+	0.185033i
$957$	−9358.38			−0.316106
$958$	−28545.0	+	22987.8i	−0.962680	+	0.775262i
$959$	−14864.6	+	31179.0i	−0.500523	+	1.04987i
$960$	−5903.36	−	4437.11i	−0.198469	−	0.149174i
$961$	−1963.46			−0.0659079
$962$	−20106.6	−	24967.4i	−0.673871	−	0.836777i
$963$	19.3230			0.000646598
$964$	−5138.46	−	1121.29i	−0.171679	−	0.0374629i
$965$	12057.4			0.402218
$966$	−4365.22	−	18386.4i	−0.145392	−	0.612393i
$967$		−	33968.4i		−	1.12963i	−0.825219	−	0.564813i	$-0.808948\pi$
$967$		−	33968.4i		−	1.12963i	0.825219	−	0.564813i	$-0.191052\pi$
$968$	8793.98	+	17610.8i	0.291993	+	0.584745i
$969$		−	15888.4i		−	0.526739i
$970$	8987.31	+	11160.0i	0.297490	+	0.369407i
$971$			5733.66i			0.189497i	0.995501	+	0.0947486i	$0.0302047\pi$
$971$			5733.66i			0.189497i	−0.995501	+	0.0947486i	$0.969795\pi$
$972$	1899.31	+	414.457i	0.0626752	+	0.0136766i
$973$	−15025.4	−	7163.35i	−0.495059	−	0.236019i
$974$	−28619.4	−	35538.0i	−0.941504	−	1.16911i
$975$			22125.8i			0.726763i
$976$	43558.1	+	19960.5i	1.42855	+	0.654632i
$977$	60487.2			1.98071			0.990357	−	0.138536i	$-0.0442396\pi$
$977$	60487.2			1.98071			0.990357	+	0.138536i	$0.0442396\pi$
$978$	−7554.20	−	9380.40i	−0.246990	−	0.306700i
$979$		−	32100.9i		−	1.04796i
$980$	−11785.0	+	5930.16i	−0.384141	+	0.193298i
$981$		−	4705.33i		−	0.153139i
$982$	−27823.2	+	22406.5i	−0.904149	+	0.728127i
$983$	−55135.5			−1.78896			−0.894481	−	0.447107i	$-0.852454\pi$
$983$	−55135.5			−1.78896			−0.894481	+	0.447107i	$0.852454\pi$
$984$	15448.5	+	30937.2i	0.500489	+	1.00228i
$985$			13953.6i			0.451368i
$986$	7541.38	−	6073.21i	0.243577	−	0.196156i
$987$	13177.7	+	6282.44i	0.424975	+	0.202606i
$988$	58202.5	+	12700.7i	1.87416	+	0.408969i
$989$		−	44140.6i		−	1.41920i
$990$	−4471.97	+	3601.35i	−0.143564	+	0.115615i
$991$		−	40791.1i		−	1.30754i	−0.756693	−	0.653771i	$-0.773186\pi$
$991$		−	40791.1i		−	1.30754i	0.756693	−	0.653771i	$-0.226814\pi$
$992$	29270.9	−	7420.53i	0.936848	−	0.237502i
$993$		−	30081.2i		−	0.961328i
$994$	8595.46	−	2040.70i	0.274277	−	0.0651178i
$995$	195.638			0.00623332
$996$	713.342	−	3268.99i	0.0226939	−	0.103998i
$997$	17582.4			0.558515			0.279257	−	0.960216i	$-0.409912\pi$
$997$	17582.4			0.558515			0.279257	+	0.960216i	$0.409912\pi$
$998$	−4049.81	+	3261.38i	−0.128451	+	0.103444i
$999$	−4227.35			−0.133881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.p.a.139.12	yes	48
4.3	odd	2		672.4.p.a.559.31		48
7.6	odd	2	inner	168.4.p.a.139.11	yes	48
8.3	odd	2	inner	168.4.p.a.139.10	yes	48
8.5	even	2		672.4.p.a.559.45		48
28.27	even	2		672.4.p.a.559.46		48
56.13	odd	2		672.4.p.a.559.32		48
56.27	even	2	inner	168.4.p.a.139.9	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.p.a.139.9	✓	48	56.27	even	2	inner
168.4.p.a.139.10	yes	48	8.3	odd	2	inner
168.4.p.a.139.11	yes	48	7.6	odd	2	inner
168.4.p.a.139.12	yes	48	1.1	even	1	trivial
672.4.p.a.559.31		48	4.3	odd	2
672.4.p.a.559.32		48	56.13	odd	2
672.4.p.a.559.45		48	8.5	even	2
672.4.p.a.559.46		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+(-2.20291 + 1.77404i) q^{2} +3.00000i q^{3} +(1.70558 - 7.81607i) q^{4} +4.80791 q^{5} +(-5.32211 - 6.60872i) q^{6} +(7.97009 - 16.7176i) q^{7} +(10.1088 + 20.2438i) q^{8} -9.00000 q^{9} +(-10.5914 + 8.52942i) q^{10} -46.9141 q^{11} +(23.4482 + 5.11675i) q^{12} -72.3890 q^{13} +(12.1003 + 50.9665i) q^{14} +14.4237i q^{15} +(-58.1820 - 26.6619i) q^{16} -51.4848i q^{17} +(19.8261 - 15.9663i) q^{18} -102.868i q^{19} +(8.20029 - 37.5790i) q^{20} +(50.1528 + 23.9103i) q^{21} +(103.347 - 83.2274i) q^{22} +120.251i q^{23} +(-60.7315 + 30.3263i) q^{24} -101.884 q^{25} +(159.466 - 128.421i) q^{26} -27.0000i q^{27} +(-117.072 - 90.8080i) q^{28} -66.4930i q^{29} +(-25.5883 - 31.7741i) q^{30} +166.816 q^{31} +(175.469 - 44.4833i) q^{32} -140.742i q^{33} +(91.3360 + 113.416i) q^{34} +(38.3195 - 80.3767i) q^{35} +(-15.3502 + 70.3447i) q^{36} -156.568i q^{37} +(182.492 + 226.609i) q^{38} -217.167i q^{39} +(48.6021 + 97.3306i) q^{40} -509.410i q^{41} +(-152.899 + 36.3008i) q^{42} -367.069 q^{43} +(-80.0159 + 366.684i) q^{44} -43.2712 q^{45} +(-213.330 - 264.902i) q^{46} +262.751 q^{47} +(79.9857 - 174.546i) q^{48} +(-215.955 - 266.481i) q^{49} +(224.441 - 180.746i) q^{50} +154.455 q^{51} +(-123.465 + 565.798i) q^{52} +373.897i q^{53} +(47.8990 + 59.4784i) q^{54} -225.559 q^{55} +(418.996 - 7.64901i) q^{56} +308.604 q^{57} +(117.961 + 146.478i) q^{58} +429.575i q^{59} +(112.737 + 24.6009i) q^{60} -748.653 q^{61} +(-367.480 + 295.938i) q^{62} +(-71.7308 + 150.458i) q^{63} +(-307.626 + 409.280i) q^{64} -348.040 q^{65} +(249.682 + 310.042i) q^{66} +583.540 q^{67} +(-402.409 - 87.8116i) q^{68} -360.754 q^{69} +(58.1770 + 245.043i) q^{70} -168.649i q^{71} +(-90.9789 - 182.195i) q^{72} +185.820i q^{73} +(277.758 + 344.905i) q^{74} -305.652i q^{75} +(-804.024 - 175.450i) q^{76} +(-373.910 + 784.291i) q^{77} +(385.263 + 478.399i) q^{78} -151.500i q^{79} +(-279.734 - 128.188i) q^{80} +81.0000 q^{81} +(903.713 + 1122.18i) q^{82} -139.413i q^{83} +(272.424 - 351.217i) q^{84} -247.535i q^{85} +(808.619 - 651.195i) q^{86} +199.479 q^{87} +(-474.244 - 949.722i) q^{88} +684.248i q^{89} +(95.3224 - 76.7648i) q^{90} +(-576.947 + 1210.17i) q^{91} +(939.893 + 205.098i) q^{92} +500.448i q^{93} +(-578.815 + 466.130i) q^{94} -494.581i q^{95} +(133.450 + 526.406i) q^{96} -1053.68i q^{97} +(948.477 + 203.920i) q^{98} +422.227 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

L-functions

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