LMFDB - Embedded newform 189.4.e.h.163.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(109,189)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("189.109");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 54 x^{14} - 12 x^{13} + 2361 x^{12} - 966 x^{11} + 29570 x^{10} - 65952 x^{9} + 300096 x^{8} + \cdots + 81 $ x^16 + 54x^14 - 12x^13 + 2361x^12 - 966x^11 + 29570x^10 - 65952x^9 + 300096x^8 - 356610x^7 + 531858x^6 + 80070x^5 + 77197x^4 - 216x^3 + 4878x^2 + 486x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{9}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.8
Root			$1.06000 + 1.83598i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.h.109.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73089 - 4.73004i) q^{2} +(-10.9155 - 18.9063i) q^{4} +(0.0995681 - 0.172457i) q^{5} +(-16.0061 - 9.31685i) q^{7} -75.5424 q^{8} +O(q^{10})$	\(q+(2.73089 - 4.73004i) q^{2} +(-10.9155 - 18.9063i) q^{4} +(0.0995681 - 0.172457i) q^{5} +(-16.0061 - 9.31685i) q^{7} -75.5424 q^{8} +(-0.543819 - 0.941923i) q^{10} +(14.2117 + 24.6153i) q^{11} +32.5809 q^{13} +(-87.7801 + 50.2664i) q^{14} +(-118.974 + 206.069i) q^{16} +(-57.7439 - 100.015i) q^{17} +(-10.5750 + 18.3164i) q^{19} -4.34736 q^{20} +155.242 q^{22} +(46.8828 - 81.2034i) q^{23} +(62.4802 + 108.219i) q^{25} +(88.9749 - 154.109i) q^{26} +(-1.43126 + 404.315i) q^{28} -231.571 q^{29} +(-140.871 - 243.996i) q^{31} +(347.640 + 602.130i) q^{32} -630.770 q^{34} +(-3.20045 + 1.83271i) q^{35} +(73.2770 - 126.919i) q^{37} +(57.7583 + 100.040i) q^{38} +(-7.52161 + 13.0278i) q^{40} +111.001 q^{41} +392.361 q^{43} +(310.256 - 537.380i) q^{44} +(-256.064 - 443.516i) q^{46} +(136.584 - 236.571i) q^{47} +(169.393 + 298.253i) q^{49} +682.506 q^{50} +(-355.638 - 615.984i) q^{52} +(-170.201 - 294.798i) q^{53} +5.66011 q^{55} +(1209.14 + 703.817i) q^{56} +(-632.395 + 1095.34i) q^{58} +(-348.408 - 603.461i) q^{59} +(185.001 - 320.431i) q^{61} -1538.81 q^{62} +1893.89 q^{64} +(3.24402 - 5.61880i) q^{65} +(-43.5681 - 75.4622i) q^{67} +(-1260.61 + 2183.45i) q^{68} +(-0.0713061 + 20.1432i) q^{70} +88.3772 q^{71} +(401.518 + 695.450i) q^{73} +(-400.223 - 693.207i) q^{74} +461.727 q^{76} +(1.86345 - 526.404i) q^{77} +(-182.308 + 315.766i) q^{79} +(23.6920 + 41.0357i) q^{80} +(303.132 - 525.040i) q^{82} -921.684 q^{83} -22.9978 q^{85} +(1071.50 - 1855.88i) q^{86} +(-1073.58 - 1859.50i) q^{88} +(-105.698 + 183.074i) q^{89} +(-521.494 - 303.551i) q^{91} -2047.01 q^{92} +(-745.993 - 1292.10i) q^{94} +(2.10586 + 3.64746i) q^{95} +845.718 q^{97} +(1873.35 + 13.2633i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 48 q^{4} - 60 q^{7}+O(q^{10}) $ 16 * q - 48 * q^4 - 60 * q^7	$ 16 q - 48 q^{4} - 60 q^{7} - 44 q^{10} - 168 q^{13} - 156 q^{16} - 12 q^{19} + 448 q^{22} - 408 q^{25} - 152 q^{28} - 800 q^{31} - 1896 q^{34} - 692 q^{37} - 96 q^{40} + 2912 q^{43} - 1524 q^{46} + 2020 q^{49} - 1972 q^{52} - 2560 q^{55} - 2372 q^{58} - 216 q^{61} + 9928 q^{64} - 684 q^{67} + 4316 q^{70} + 4564 q^{73} - 760 q^{76} - 556 q^{79} - 3340 q^{82} + 2592 q^{85} - 6696 q^{88} - 184 q^{91} + 492 q^{94} + 1168 q^{97}+O(q^{100}) $ 16 * q - 48 * q^4 - 60 * q^7 - 44 * q^10 - 168 * q^13 - 156 * q^16 - 12 * q^19 + 448 * q^22 - 408 * q^25 - 152 * q^28 - 800 * q^31 - 1896 * q^34 - 692 * q^37 - 96 * q^40 + 2912 * q^43 - 1524 * q^46 + 2020 * q^49 - 1972 * q^52 - 2560 * q^55 - 2372 * q^58 - 216 * q^61 + 9928 * q^64 - 684 * q^67 + 4316 * q^70 + 4564 * q^73 - 760 * q^76 - 556 * q^79 - 3340 * q^82 + 2592 * q^85 - 6696 * q^88 - 184 * q^91 + 492 * q^94 + 1168 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.73089	−	4.73004i	0.965516	−	1.67232i	0.257295	−	0.966333i	$-0.417169\pi$
$2$	2.73089	−	4.73004i	0.965516	−	1.67232i	0.708222	−	0.705990i	$-0.249498\pi$
$3$		0			0
$3$		0			0
$4$	−10.9155	−	18.9063i	−1.36444	−	2.36328i
$5$	0.0995681	−	0.172457i	0.00890564	−	0.0154250i	−0.861538	−	0.507693i	$-0.830499\pi$
$5$	0.0995681	−	0.172457i	0.00890564	−	0.0154250i	0.870444	+	0.492268i	$0.163832\pi$
$6$		0			0
$7$	−16.0061	−	9.31685i	−0.864250	−	0.503063i
$7$	−16.0061	−	9.31685i	−0.864250	−	0.503063i
$8$	−75.5424			−3.33854
$9$		0			0
$10$	−0.543819	−	0.941923i	−0.0171971	−	0.0297862i
$11$	14.2117	+	24.6153i	0.389544	+	0.674710i	0.992388	−	0.123149i	$-0.0392994\pi$
$11$	14.2117	+	24.6153i	0.389544	+	0.674710i	−0.602844	+	0.797859i	$0.705966\pi$
$12$		0			0
$13$	32.5809			0.695101			0.347551	−	0.937661i	$-0.387013\pi$
$13$	32.5809			0.695101			0.347551	+	0.937661i	$0.387013\pi$
$14$	−87.7801	+	50.2664i	−1.67573	+	0.959590i
$15$		0			0
$16$	−118.974	+	206.069i	−1.85897	+	3.21983i
$17$	−57.7439	−	100.015i	−0.823821	−	1.42690i	−0.902817	−	0.430026i	$-0.858505\pi$
$17$	−57.7439	−	100.015i	−0.823821	−	1.42690i	0.0789952	−	0.996875i	$-0.474829\pi$
$18$		0			0
$19$	−10.5750	+	18.3164i	−0.127688	+	0.221162i	−0.922780	−	0.385326i	$-0.874089\pi$
$19$	−10.5750	+	18.3164i	−0.127688	+	0.221162i	0.795093	+	0.606488i	$0.207422\pi$
$20$	−4.34736			−0.0486049
$21$		0			0
$22$	155.242			1.50444
$23$	46.8828	−	81.2034i	0.425032	−	0.736177i	−0.571391	−	0.820678i	$-0.693596\pi$
$23$	46.8828	−	81.2034i	0.425032	−	0.736177i	0.996423	+	0.0845003i	$0.0269294\pi$
$24$		0			0
$25$	62.4802	+	108.219i	0.499841	+	0.865751i
$26$	88.9749	−	154.109i	0.671132	−	1.16243i
$27$		0			0
$28$	−1.43126	+	404.315i	−0.00966007	+	2.72887i
$29$	−231.571			−1.48282			−0.741408	−	0.671055i	$-0.765841\pi$
$29$	−231.571			−1.48282			−0.741408	+	0.671055i	$0.765841\pi$
$30$		0			0
$31$	−140.871	−	243.996i	−0.816167	−	1.41364i	−0.908487	−	0.417913i	$-0.862762\pi$
$31$	−140.871	−	243.996i	−0.816167	−	1.41364i	0.0923206	−	0.995729i	$-0.470572\pi$
$32$	347.640	+	602.130i	1.92046	+	3.32633i
$33$		0			0
$34$	−630.770			−3.18165
$35$	−3.20045	+	1.83271i	−0.0154564	+	0.00885098i
$36$		0			0
$37$	73.2770	−	126.919i	0.325585	−	0.563931i	−0.656045	−	0.754722i	$-0.727772\pi$
$37$	73.2770	−	126.919i	0.325585	−	0.563931i	0.981631	+	0.190791i	$0.0611053\pi$
$38$	57.7583	+	100.040i	0.246569	+	0.427070i
$39$		0			0
$40$	−7.52161	+	13.0278i	−0.0297318	+	0.0514970i
$41$	111.001			0.422816			0.211408	−	0.977398i	$-0.432195\pi$
$41$	111.001			0.422816			0.211408	+	0.977398i	$0.432195\pi$
$42$		0			0
$43$	392.361			1.39150			0.695750	−	0.718284i	$-0.255072\pi$
$43$	392.361			1.39150			0.695750	+	0.718284i	$0.255072\pi$
$44$	310.256	−	537.380i	1.06302	−	1.84121i
$45$		0			0
$46$	−256.064	−	443.516i	−0.820751	−	1.42158i
$47$	136.584	−	236.571i	0.423890	−	0.734199i	−0.572426	−	0.819956i	$-0.693998\pi$
$47$	136.584	−	236.571i	0.423890	−	0.734199i	0.996316	+	0.0857573i	$0.0273310\pi$
$48$		0			0
$49$	169.393	+	298.253i	0.493856	+	0.869544i
$50$	682.506			1.93042
$51$		0			0
$52$	−355.638	−	615.984i	−0.948426	−	1.64272i
$53$	−170.201	−	294.798i	−0.441113	−	0.764030i	0.556660	−	0.830741i	$-0.312083\pi$
$53$	−170.201	−	294.798i	−0.441113	−	0.764030i	−0.997772	+	0.0667111i	$0.978749\pi$
$54$		0			0
$55$	5.66011			0.0138765
$56$	1209.14	+	703.817i	2.88533	+	1.67949i
$57$		0			0
$58$	−632.395	+	1095.34i	−1.43168	+	2.47975i
$59$	−348.408	−	603.461i	−0.768795	−	1.33159i	−0.938217	−	0.346049i	$-0.887523\pi$
$59$	−348.408	−	603.461i	−0.768795	−	1.33159i	0.169421	−	0.985544i	$-0.445810\pi$
$60$		0			0
$61$	185.001	−	320.431i	0.388311	−	0.672574i	−0.603912	−	0.797051i	$-0.706392\pi$
$61$	185.001	−	320.431i	0.388311	−	0.672574i	0.992222	+	0.124477i	$0.0397254\pi$
$62$	−1538.81			−3.15209
$63$		0			0
$64$	1893.89			3.69900
$65$	3.24402	−	5.61880i	0.00619032	−	0.0107220i
$66$		0			0
$67$	−43.5681	−	75.4622i	−0.0794431	−	0.137600i	0.823567	−	0.567219i	$-0.191981\pi$
$67$	−43.5681	−	75.4622i	−0.0794431	−	0.137600i	−0.903010	+	0.429620i	$0.858648\pi$
$68$	−1260.61	+	2183.45i	−2.24812	+	3.89385i
$69$		0			0
$70$	−0.0713061	+	20.1432i	−0.000121753	+	0.0343939i
$71$	88.3772			0.147725			0.0738623	−	0.997268i	$-0.476467\pi$
$71$	88.3772			0.147725			0.0738623	+	0.997268i	$0.476467\pi$
$72$		0			0
$73$	401.518	+	695.450i	0.643755	+	1.11502i	0.984587	+	0.174893i	$0.0559579\pi$
$73$	401.518	+	695.450i	0.643755	+	1.11502i	−0.340832	+	0.940124i	$0.610709\pi$
$74$	−400.223	−	693.207i	−0.628716	−	1.08897i
$75$		0			0
$76$	461.727			0.696891
$77$	1.86345	−	526.404i	0.00275792	−	0.779083i
$78$		0			0
$79$	−182.308	+	315.766i	−0.259636	+	0.449702i	−0.966144	−	0.258002i	$-0.916936\pi$
$79$	−182.308	+	315.766i	−0.259636	+	0.449702i	0.706509	+	0.707705i	$0.250269\pi$
$80$	23.6920	+	41.0357i	0.0331106	+	0.0573492i
$81$		0			0
$82$	303.132	−	525.040i	0.408236	−	0.707085i
$83$	−921.684			−1.21889			−0.609446	−	0.792828i	$-0.708608\pi$
$83$	−921.684			−1.21889			−0.609446	+	0.792828i	$0.708608\pi$
$84$		0			0
$85$	−22.9978			−0.0293466
$86$	1071.50	−	1855.88i	1.34351	−	2.32704i
$87$		0			0
$88$	−1073.58	−	1859.50i	−1.30051	−	2.25254i
$89$	−105.698	+	183.074i	−0.125887	+	0.218043i	−0.922079	−	0.387001i	$-0.873511\pi$
$89$	−105.698	+	183.074i	−0.125887	+	0.218043i	0.796192	+	0.605044i	$0.206844\pi$
$90$		0			0
$91$	−521.494	−	303.551i	−0.600741	−	0.349679i
$92$	−2047.01			−2.31973
$93$		0			0
$94$	−745.993	−	1292.10i	−0.818545	−	1.41776i
$95$	2.10586	+	3.64746i	0.00227428	+	0.00393917i
$96$		0			0
$97$	845.718			0.885254			0.442627	−	0.896706i	$-0.354047\pi$
$97$	845.718			0.885254			0.442627	+	0.896706i	$0.354047\pi$
$98$	1873.35	+	13.2633i	1.93098	+	0.0136714i
$99$		0			0
$100$	1364.01	−	2362.54i	1.36401	−	2.36254i
$101$	−78.4758	−	135.924i	−0.0773132	−	0.133910i	0.824777	−	0.565459i	$-0.191301\pi$
$101$	−78.4758	−	135.924i	−0.0773132	−	0.133910i	−0.902090	+	0.431548i	$0.857967\pi$
$102$		0			0
$103$	69.6626	−	120.659i	0.0666414	−	0.115426i	−0.830780	−	0.556602i	$-0.812105\pi$
$103$	69.6626	−	120.659i	0.0666414	−	0.115426i	0.897421	+	0.441175i	$0.145438\pi$
$104$	−2461.24			−2.32062
$105$		0			0
$106$	−1859.21			−1.70361
$107$	−207.738	+	359.813i	−0.187690	+	0.325088i	−0.944480	−	0.328570i	$-0.893433\pi$
$107$	−207.738	+	359.813i	−0.187690	+	0.325088i	0.756790	+	0.653658i	$0.226767\pi$
$108$		0			0
$109$	422.040	+	730.995i	0.370863	+	0.642354i	0.989699	−	0.143167i	$-0.0457285\pi$
$109$	422.040	+	730.995i	0.370863	+	0.642354i	−0.618835	+	0.785521i	$0.712395\pi$
$110$	15.4572	−	26.7726i	0.0133980	−	0.0232061i
$111$		0			0
$112$	3824.22	−	2189.90i	3.22639	−	1.84756i
$113$	1342.21			1.11738			0.558692	−	0.829375i	$-0.311303\pi$
$113$	1342.21			1.11738			0.558692	+	0.829375i	$0.311303\pi$
$114$		0			0
$115$	−9.33606	−	16.1705i	−0.00757037	−	0.0131123i
$116$	2527.72	+	4378.14i	2.02322	+	3.50431i
$117$		0			0
$118$	−3805.86			−2.96914
$119$	−7.57144	+	2138.85i	−0.00583254	+	1.64763i
$120$		0			0
$121$	261.557	−	453.029i	0.196511	−	0.340368i
$122$	−1010.44	−	1750.13i	−0.749841	−	1.29876i
$123$		0			0
$124$	−3075.37	+	5326.69i	−2.22723	+	3.85767i
$125$	49.7761			0.0356169
$126$		0			0
$127$	978.750			0.683858			0.341929	−	0.939726i	$-0.388920\pi$
$127$	978.750			0.683858			0.341929	+	0.939726i	$0.388920\pi$
$128$	2390.88	−	4141.13i	1.65099	−	2.85959i
$129$		0			0
$130$	−17.7181	−	30.6887i	−0.0119537	−	0.0207044i
$131$	1186.40	−	2054.91i	0.791271	−	1.37052i	−0.133909	−	0.990994i	$-0.542753\pi$
$131$	1186.40	−	2054.91i	0.791271	−	1.37052i	0.925180	−	0.379528i	$-0.123914\pi$
$132$		0			0
$133$	339.916	−	194.649i	0.221612	−	0.126904i
$134$	−475.919			−0.306815
$135$		0			0
$136$	4362.12	+	7555.41i	2.75036	+	4.76376i
$137$	801.337	+	1387.96i	0.499729	+	0.865556i	1.00000		0.000312974i	$-9.96229e-5\pi$
$137$	801.337	+	1387.96i	0.499729	+	0.865556i	−0.500271	+	0.865869i	$0.666766\pi$
$138$		0			0
$139$	2101.78			1.28252			0.641262	−	0.767322i	$-0.278411\pi$
$139$	2101.78			1.28252			0.641262	+	0.767322i	$0.278411\pi$
$140$	69.5844	+	40.5037i	0.0420068	+	0.0244513i
$141$		0			0
$142$	241.349	−	418.028i	0.142631	−	0.247043i
$143$	463.029	+	801.990i	0.270772	+	0.468992i
$144$		0			0
$145$	−23.0571	+	39.9360i	−0.0132054	+	0.0228724i
$146$	4386.01			2.48623
$147$		0			0
$148$	−3199.43			−1.77697
$149$	262.200	−	454.144i	0.144163	−	0.249697i	−0.784897	−	0.619626i	$-0.787284\pi$
$149$	262.200	−	454.144i	0.144163	−	0.249697i	0.929060	+	0.369928i	$0.120618\pi$
$150$		0			0
$151$	433.833	+	751.420i	0.233807	+	0.404965i	0.958925	−	0.283659i	$-0.0915484\pi$
$151$	433.833	+	751.420i	0.233807	+	0.404965i	−0.725119	+	0.688624i	$0.758215\pi$
$152$	798.860	−	1383.67i	0.426290	−	0.738356i
$153$		0			0
$154$	−2484.83	−	1446.37i	−1.30022	−	0.756829i
$155$	−56.1050			−0.0290739
$156$		0			0
$157$	2.96000	+	5.12687i	0.00150467	+	0.00260617i	0.866777	−	0.498696i	$-0.166188\pi$
$157$	2.96000	+	5.12687i	0.00150467	+	0.00260617i	−0.865272	+	0.501303i	$0.832854\pi$
$158$	995.726	+	1724.65i	0.501365	+	0.868390i
$159$		0			0
$160$	138.455			0.0684116
$161$	−1506.97	+	862.953i	−0.737677	+	0.422424i
$162$		0			0
$163$	416.480	−	721.364i	0.200130	−	0.346636i	−0.748440	−	0.663202i	$-0.769197\pi$
$163$	416.480	−	721.364i	0.200130	−	0.346636i	0.948570	+	0.316567i	$0.102530\pi$
$164$	−1211.64	−	2098.62i	−0.576909	−	0.999235i
$165$		0			0
$166$	−2517.02	+	4359.61i	−1.17686	+	2.03838i
$167$	566.798			0.262636			0.131318	−	0.991340i	$-0.458079\pi$
$167$	566.798			0.262636			0.131318	+	0.991340i	$0.458079\pi$
$168$		0			0
$169$	−1135.48			−0.516834
$170$	−62.8045	+	108.781i	−0.0283346	+	0.0490770i
$171$		0			0
$172$	−4282.83	−	7418.08i	−1.89862	−	3.28851i
$173$	−2062.88	+	3573.02i	−0.906579	+	1.57024i	−0.0877960	+	0.996138i	$0.527982\pi$
$173$	−2062.88	+	3573.02i	−0.906579	+	1.57024i	−0.818783	+	0.574103i	$0.805351\pi$
$174$		0			0
$175$	8.19246	−	2314.28i	0.00353881	−	0.999676i
$176$	−6763.27			−2.89660
$177$		0			0
$178$	577.299	+	999.912i	0.243092	+	0.421048i
$179$	463.823	+	803.365i	0.193675	+	0.335454i	0.946465	−	0.322806i	$-0.104626\pi$
$179$	463.823	+	803.365i	0.193675	+	0.335454i	−0.752791	+	0.658260i	$0.771293\pi$
$180$		0			0
$181$	1211.67			0.497585			0.248792	−	0.968557i	$-0.419966\pi$
$181$	1211.67			0.497585			0.248792	+	0.968557i	$0.419966\pi$
$182$	−2859.96	+	1637.73i	−1.16480	+	0.667013i
$183$		0			0
$184$	−3541.64	+	6134.30i	−1.41899	+	2.45775i
$185$	−14.5921	−	25.2742i	−0.00579909	−	0.0100443i
$186$		0			0
$187$	1641.28	−	2842.77i	0.641829	−	1.11168i
$188$	−5963.56			−2.31350
$189$		0			0
$190$	23.0035			0.00878342
$191$	−913.746	+	1582.65i	−0.346159	+	0.599565i	−0.985564	−	0.169306i	$-0.945848\pi$
$191$	−913.746	+	1582.65i	−0.346159	+	0.599565i	0.639405	+	0.768870i	$0.279181\pi$
$192$		0			0
$193$	411.115	+	712.072i	0.153330	+	0.265576i	0.932450	−	0.361300i	$-0.117667\pi$
$193$	411.115	+	712.072i	0.153330	+	0.265576i	−0.779120	+	0.626875i	$0.784334\pi$
$194$	2309.56	−	4000.28i	0.854727	−	1.48043i
$195$		0			0
$196$	3789.85	−	6458.18i	1.38114	−	2.35357i
$197$	4873.12			1.76241			0.881207	−	0.472731i	$-0.156732\pi$
$197$	4873.12			1.76241			0.881207	+	0.472731i	$0.156732\pi$
$198$		0			0
$199$	741.113	+	1283.65i	0.264001	+	0.457262i	0.967301	−	0.253630i	$-0.0816246\pi$
$199$	741.113	+	1283.65i	0.264001	+	0.457262i	−0.703301	+	0.710892i	$0.748291\pi$
$200$	−4719.90	−	8175.11i	−1.66874	−	2.89034i
$201$		0			0
$202$	−857.236			−0.298589
$203$	3706.56	+	2157.51i	1.28152	+	0.745949i
$204$		0			0
$205$	11.0522	−	19.1429i	0.00376545	−	0.00652195i
$206$	−380.482	−	659.015i	−0.128687	−	0.222892i
$207$		0			0
$208$	−3876.28	+	6713.91i	−1.29217	+	2.23810i
$209$	−601.153			−0.198960
$210$		0			0
$211$	−4359.21			−1.42228			−0.711138	−	0.703053i	$-0.751820\pi$
$211$	−4359.21			−1.42228			−0.711138	+	0.703053i	$0.751820\pi$
$212$	−3715.68	+	6435.75i	−1.20375	+	2.08495i
$213$		0			0
$214$	1134.62	+	1965.22i	0.362435	+	0.627755i
$215$	39.0666	−	67.6653i	0.0123922	−	0.0214639i
$216$		0			0
$217$	−18.4711	+	5217.90i	−0.00577835	+	1.63232i
$218$	4610.18			1.43230
$219$		0			0
$220$	−61.7832	−	107.012i	−0.0189338	−	0.0327942i
$221$	−1881.35	−	3258.59i	−0.572639	−	0.991841i
$222$		0			0
$223$	−3312.73			−0.994784			−0.497392	−	0.867526i	$-0.665709\pi$
$223$	−3312.73			−0.994784			−0.497392	+	0.867526i	$0.665709\pi$
$224$	45.5829	−	12876.7i	0.0135966	−	3.84089i
$225$		0			0
$226$	3665.43	−	6348.71i	1.07885	−	1.86863i
$227$	−399.161	−	691.366i	−0.116710	−	0.202148i	0.801752	−	0.597657i	$-0.203902\pi$
$227$	−399.161	−	691.366i	−0.116710	−	0.202148i	−0.918462	+	0.395509i	$0.870568\pi$
$228$		0			0
$229$	177.457	−	307.365i	0.0512083	−	0.0886954i	−0.839285	−	0.543692i	$-0.817026\pi$
$229$	177.457	−	307.365i	0.0512083	−	0.0886954i	0.890493	+	0.454996i	$0.150359\pi$
$230$	−101.983			−0.0292372
$231$		0			0
$232$	17493.4			4.95043
$233$	−2236.95	+	3874.52i	−0.628960	+	1.08939i	0.358801	+	0.933414i	$0.383186\pi$
$233$	−2236.95	+	3874.52i	−0.628960	+	1.08939i	−0.987761	+	0.155977i	$0.950148\pi$
$234$		0			0
$235$	−27.1988	−	47.1097i	−0.00755002	−	0.0130770i
$236$	−7606.14	+	13174.2i	−2.09795	+	3.63376i
$237$		0			0
$238$	10096.2	+	5876.79i	2.74974	+	1.60057i
$239$	1494.65			0.404523			0.202262	−	0.979332i	$-0.435171\pi$
$239$	1494.65			0.404523			0.202262	+	0.979332i	$0.435171\pi$
$240$		0			0
$241$	78.4424	+	135.866i	0.0209665	+	0.0363150i	0.876318	−	0.481733i	$-0.159992\pi$
$241$	78.4424	+	135.866i	0.0209665	+	0.0363150i	−0.855352	+	0.518048i	$0.826659\pi$
$242$	−1428.57	−	2474.35i	−0.379470	−	0.657261i
$243$		0			0
$244$	−8077.55			−2.11931
$245$	68.3020	+	0.483578i	0.0178108	+	0.000126101i
$246$		0			0
$247$	−344.543	+	596.765i	−0.0887559	+	0.153730i
$248$	10641.7	+	18432.0i	2.72480	+	4.71949i
$249$		0			0
$250$	135.933	−	235.443i	0.0343887	−	0.0595630i
$251$	−3498.68			−0.879819			−0.439909	−	0.898042i	$-0.644989\pi$
$251$	−3498.68			−0.879819			−0.439909	+	0.898042i	$0.644989\pi$
$252$		0			0
$253$	2665.13			0.662275
$254$	2672.86	−	4629.53i	0.660276	−	1.14363i
$255$		0			0
$256$	−5482.93	−	9496.72i	−1.33861	−	2.31853i
$257$	2369.55	−	4104.18i	0.575130	−	0.996155i	−0.420897	−	0.907108i	$-0.638285\pi$
$257$	2369.55	−	4104.18i	0.575130	−	0.996155i	0.996027	−	0.0890463i	$-0.0283819\pi$
$258$		0			0
$259$	−2355.37	+	1348.78i	−0.565080	+	0.323587i
$260$	−141.641			−0.0337854
$261$		0			0
$262$	−6479.88	−	11223.5i	−1.52797	−	2.64652i
$263$	−1682.22	−	2913.69i	−0.394411	−	0.683141i	0.598614	−	0.801037i	$-0.295718\pi$
$263$	−1682.22	−	2913.69i	−0.394411	−	0.683141i	−0.993026	+	0.117897i	$0.962385\pi$
$264$		0			0
$265$	−67.7865			−0.0157136
$266$	7.57332	−	2139.38i	0.00174568	−	0.493135i
$267$		0			0
$268$	−951.139	+	1647.42i	−0.216791	+	0.375494i
$269$	−2603.64	−	4509.63i	−0.590136	−	1.02215i	−0.994214	−	0.107421i	$-0.965741\pi$
$269$	−2603.64	−	4509.63i	−0.590136	−	1.02215i	0.404078	−	0.914725i	$-0.367592\pi$
$270$		0			0
$271$	1156.00	−	2002.25i	0.259122	−	0.448813i	−0.706885	−	0.707329i	$-0.749900\pi$
$271$	1156.00	−	2002.25i	0.259122	−	0.448813i	0.966007	+	0.258516i	$0.0832334\pi$
$272$	27480.1			6.12583
$273$		0			0
$274$	8753.46			1.92999
$275$	−1775.90	+	3075.94i	−0.389420	+	0.674495i
$276$		0			0
$277$	−1303.36	−	2257.49i	−0.282713	−	0.489673i	0.689339	−	0.724439i	$-0.257901\pi$
$277$	−1303.36	−	2257.49i	−0.282713	−	0.489673i	−0.972052	+	0.234766i	$0.924568\pi$
$278$	5739.74	−	9941.52i	1.23830	−	2.14479i
$279$		0			0
$280$	241.770	−	138.447i	0.0516019	−	0.0295493i
$281$	5271.62			1.11914			0.559570	−	0.828783i	$-0.310966\pi$
$281$	5271.62			1.11914			0.559570	+	0.828783i	$0.310966\pi$
$282$		0			0
$283$	−2904.11	−	5030.06i	−0.610004	−	1.05656i	−0.991239	−	0.132080i	$-0.957834\pi$
$283$	−2904.11	−	5030.06i	−0.610004	−	1.05656i	0.381235	−	0.924478i	$-0.375499\pi$
$284$	−964.686	−	1670.88i	−0.201562	−	0.349115i
$285$		0			0
$286$	5057.93			1.04574
$287$	−1776.70	−	1034.18i	−0.365419	−	0.212703i
$288$		0			0
$289$	−4212.23	+	7295.79i	−0.857364	+	1.48500i
$290$	125.933	+	218.122i	0.0255001	+	0.0441674i
$291$		0			0
$292$	8765.58	−	15182.4i	1.75674	−	3.04275i
$293$	1979.70			0.394729			0.197364	−	0.980330i	$-0.436762\pi$
$293$	1979.70			0.394729			0.197364	+	0.980330i	$0.436762\pi$
$294$		0			0
$295$	−138.761			−0.0273864
$296$	−5535.52	+	9587.81i	−1.08698	+	1.88270i
$297$		0			0
$298$	−1432.08	−	2480.43i	−0.278383	−	0.482174i
$299$	1527.48	−	2645.68i	0.295441	−	0.511718i
$300$		0			0
$301$	−6280.18	−	3655.57i	−1.20260	−	0.700011i
$302$	4739.00			0.902977
$303$		0			0
$304$	−2516.29	−	4358.35i	−0.474735	−	0.822264i
$305$	−36.8404	−	63.8094i	−0.00691631	−	0.0119794i
$306$		0			0
$307$	924.005			0.171778			0.0858888	−	0.996305i	$-0.472627\pi$
$307$	924.005			0.171778			0.0858888	+	0.996305i	$0.472627\pi$
$308$	−9972.69	+	5710.76i	−1.84496	+	1.05650i
$309$		0			0
$310$	−153.217	+	265.379i	−0.0280714	+	0.0486210i
$311$	−5054.30	−	8754.31i	−0.921554	−	1.59618i	−0.797012	−	0.603964i	$-0.793587\pi$
$311$	−5054.30	−	8754.31i	−0.921554	−	1.59618i	−0.124542	−	0.992214i	$-0.539746\pi$
$312$		0			0
$313$	−3415.26	+	5915.40i	−0.616747	+	1.06824i	0.373328	+	0.927699i	$0.378217\pi$
$313$	−3415.26	+	5915.40i	−0.616747	+	1.06824i	−0.990075	+	0.140538i	$0.955117\pi$
$314$	32.3337			0.00581114
$315$		0			0
$316$	7959.96			1.41703
$317$	−3811.81	+	6602.25i	−0.675371	+	1.16978i	0.300989	+	0.953627i	$0.402683\pi$
$317$	−3811.81	+	6602.25i	−0.675371	+	1.16978i	−0.976360	+	0.216149i	$0.930650\pi$
$318$		0			0
$319$	−3291.01	−	5700.20i	−0.577621	−	1.00047i
$320$	188.571	−	326.614i	0.0329419	−	0.0570571i
$321$		0			0
$322$	−33.5753	+	9484.68i	−0.00581081	+	1.64149i
$323$	2442.56			0.420768
$324$		0			0
$325$	2035.66	+	3525.87i	0.347440	+	0.601784i
$326$	−2274.72	−	3939.94i	−0.386458	−	0.669364i
$327$		0			0
$328$	−8385.30			−1.41159
$329$	−4390.27	+	2514.05i	−0.735695	+	0.421288i
$330$		0			0
$331$	−1241.60	+	2150.52i	−0.206177	+	0.357110i	−0.950507	−	0.310702i	$-0.899436\pi$
$331$	−1241.60	+	2150.52i	−0.206177	+	0.357110i	0.744330	+	0.667812i	$0.232769\pi$
$332$	10060.7	+	17425.6i	1.66311	+	2.88059i
$333$		0			0
$334$	1547.86	−	2680.98i	0.253579	−	0.439211i
$335$	−17.3520			−0.00282997
$336$		0			0
$337$	7895.47			1.27624			0.638121	−	0.769936i	$-0.279712\pi$
$337$	7895.47			1.27624			0.638121	+	0.769936i	$0.279712\pi$
$338$	−3100.89	+	5370.89i	−0.499012	+	0.864314i
$339$		0			0
$340$	251.034	+	434.803i	0.0400418	+	0.0693544i
$341$	4004.02	−	6935.17i	0.635865	−	1.10135i
$342$		0			0
$343$	67.4606	−	6352.09i	0.0106196	−	0.999944i
$344$	−29639.9			−4.64557
$345$		0			0
$346$	11267.0	+	19515.1i	1.75063	+	3.03219i
$347$	444.712	+	770.263i	0.0687994	+	0.119164i	0.898373	−	0.439233i	$-0.144750\pi$
$347$	444.712	+	770.263i	0.0687994	+	0.119164i	−0.829574	+	0.558397i	$0.811417\pi$
$348$		0			0
$349$	6962.20			1.06785			0.533923	−	0.845533i	$-0.320717\pi$
$349$	6962.20			1.06785			0.533923	+	0.845533i	$0.320717\pi$
$350$	−10924.3	−	6358.81i	−1.66837	−	0.971122i
$351$		0			0
$352$	−9881.09	+	17114.6i	−1.49620	+	2.59150i
$353$	−5780.30	−	10011.8i	−0.871542	−	1.50956i	−0.860401	−	0.509617i	$-0.829787\pi$
$353$	−5780.30	−	10011.8i	−0.871542	−	1.50956i	−0.0111411	−	0.999938i	$-0.503546\pi$
$354$		0			0
$355$	8.79955	−	15.2413i	0.00131558	−	0.00227865i
$356$	4615.00			0.687064
$357$		0			0
$358$	5066.60			0.747984
$359$	4228.51	−	7323.99i	0.621649	−	1.07673i	−0.367529	−	0.930012i	$-0.619796\pi$
$359$	4228.51	−	7323.99i	0.621649	−	1.07673i	0.989179	−	0.146716i	$-0.0468705\pi$
$360$		0			0
$361$	3205.84	+	5552.68i	0.467392	+	0.809546i
$362$	3308.95	−	5731.26i	0.480426	−	0.832123i
$363$		0			0
$364$	−46.6316	+	13172.9i	−0.00671473	+	1.89684i
$365$	159.914			0.0229322
$366$		0			0
$367$	−3456.46	−	5986.77i	−0.491623	−	0.851517i	0.508330	−	0.861162i	$-0.330263\pi$
$367$	−3456.46	−	5986.77i	−0.491623	−	0.851517i	−0.999953	+	0.00964558i	$0.996930\pi$
$368$	11155.7	+	19322.2i	1.58024	+	2.73706i
$369$		0			0
$370$	−159.398			−0.0223965
$371$	−22.3170	+	6304.31i	−0.00312302	+	0.882220i
$372$		0			0
$373$	−211.956	+	367.118i	−0.0294226	+	0.0509615i	−0.880362	−	0.474303i	$-0.842700\pi$
$373$	−211.956	+	367.118i	−0.0294226	+	0.0509615i	0.850939	+	0.525264i	$0.176034\pi$
$374$	−8964.30	−	15526.6i	−1.23939	−	2.14669i
$375$		0			0
$376$	−10317.9	+	17871.1i	−1.41517	+	2.45115i
$377$	−7544.79			−1.03071
$378$		0			0
$379$	−9714.33			−1.31660			−0.658300	−	0.752756i	$-0.728724\pi$
$379$	−9714.33			−1.31660			−0.658300	+	0.752756i	$0.728724\pi$
$380$	45.9732	−	79.6280i	0.00620626	−	0.0107496i
$381$		0			0
$382$	4990.68	+	8644.12i	0.668444	+	1.15778i
$383$	−1107.08	+	1917.51i	−0.147699	+	0.255823i	−0.930377	−	0.366605i	$-0.880520\pi$
$383$	−1107.08	+	1917.51i	−0.147699	+	0.255823i	0.782677	+	0.622428i	$0.213854\pi$
$384$		0			0
$385$	−90.5966	−	52.7344i	−0.0119928	−	0.00698077i
$386$	4490.84			0.592171
$387$		0			0
$388$	−9231.47	−	15989.4i	−1.20788	−	2.09211i
$389$	−3832.73	−	6638.48i	−0.499556	−	0.865256i	0.500444	−	0.865769i	$-0.333170\pi$
$389$	−3832.73	−	6638.48i	−0.499556	−	0.865256i	−1.00000		0.000513038i	$0.999837\pi$
$390$		0			0
$391$	−10828.8			−1.40060
$392$	−12796.3	−	22530.8i	−1.64876	−	2.90300i
$393$		0			0
$394$	13308.0	−	23050.1i	1.70164	−	2.94732i
$395$	36.3041	+	62.8805i	0.00462444	+	0.00800977i
$396$		0			0
$397$	−2489.10	+	4311.24i	−0.314671	+	0.545026i	−0.979367	−	0.202088i	$-0.935227\pi$
$397$	−2489.10	+	4311.24i	−0.314671	+	0.545026i	0.664697	+	0.747113i	$0.268561\pi$
$398$	8095.60			1.01959
$399$		0			0
$400$	−29734.0			−3.71675
$401$	−2385.10	+	4131.12i	−0.297023	+	0.514460i	−0.975454	−	0.220205i	$-0.929327\pi$
$401$	−2385.10	+	4131.12i	−0.297023	+	0.514460i	0.678430	+	0.734665i	$0.262661\pi$
$402$		0			0
$403$	−4589.70	−	7949.60i	−0.567319	−	0.982625i
$404$	−1713.21	+	2967.37i	−0.210979	+	0.365426i
$405$		0			0
$406$	20327.3	−	11640.2i	2.48480	−	1.42290i
$407$	4165.56			0.507319
$408$		0			0
$409$	298.629	+	517.240i	0.0361033	+	0.0625327i	0.883512	−	0.468408i	$-0.155172\pi$
$409$	298.629	+	517.240i	0.0361033	+	0.0625327i	−0.847409	+	0.530940i	$0.821839\pi$
$410$	−60.3646	−	104.554i	−0.00727120	−	0.0125941i
$411$		0			0
$412$	−3041.62			−0.363714
$413$	−45.6836	+	12905.1i	−0.00544296	+	1.53758i
$414$		0			0
$415$	−91.7703	+	158.951i	−0.0108550	+	0.0188014i
$416$	11326.4	+	19617.9i	1.33491	+	2.31214i
$417$		0			0
$418$	−1641.68	+	2843.48i	−0.192099	+	0.332725i
$419$	−9571.90			−1.11603			−0.558016	−	0.829830i	$-0.688437\pi$
$419$	−9571.90			−1.11603			−0.558016	+	0.829830i	$0.688437\pi$
$420$		0			0
$421$	−5954.33			−0.689303			−0.344651	−	0.938731i	$-0.612003\pi$
$421$	−5954.33			−0.689303			−0.344651	+	0.938731i	$0.612003\pi$
$422$	−11904.5	+	20619.2i	−1.37323	+	2.37850i
$423$		0			0
$424$	12857.4	+	22269.7i	1.47267	+	2.55074i
$425$	7215.70	−	12498.0i	0.823560	−	1.42645i
$426$		0			0
$427$	−5946.56	+	3405.24i	−0.673944	+	0.385927i
$428$	9070.29			1.02437
$429$		0			0
$430$	−213.373	−	369.573i	−0.0239297	−	0.0414475i
$431$	−1271.72	−	2202.69i	−0.142127	−	0.246171i	0.786170	−	0.618010i	$-0.212061\pi$
$431$	−1271.72	−	2202.69i	−0.142127	−	0.246171i	−0.928297	+	0.371839i	$0.878727\pi$
$432$		0			0
$433$	9781.07			1.08556			0.542781	−	0.839874i	$-0.317371\pi$
$433$	9781.07			1.08556			0.542781	+	0.839874i	$0.317371\pi$
$434$	24630.5	+	14336.9i	2.72419	+	1.58570i
$435$		0			0
$436$	9213.59	−	15958.4i	1.01204	−	1.75291i
$437$	991.570	+	1717.45i	0.108543	+	0.188002i
$438$		0			0
$439$	8410.13	−	14566.8i	0.914336	−	1.58368i	0.106465	−	0.994316i	$-0.466047\pi$
$439$	8410.13	−	14566.8i	0.914336	−	1.58368i	0.807871	−	0.589360i	$-0.200620\pi$
$440$	−427.579			−0.0463273
$441$		0			0
$442$	−20551.1			−2.21157
$443$	1863.37	−	3227.46i	0.199846	−	0.346143i	−0.748633	−	0.662985i	$-0.769289\pi$
$443$	1863.37	−	3227.46i	0.199846	−	0.346143i	0.948478	+	0.316842i	$0.102623\pi$
$444$		0			0
$445$	21.0483	+	36.4567i	0.00224221	+	0.00388362i
$446$	−9046.71	+	15669.4i	−0.960480	+	1.66360i
$447$		0			0
$448$	−30313.8	−	17645.1i	−3.19686	−	1.86083i
$449$	9287.05			0.976131			0.488065	−	0.872807i	$-0.337703\pi$
$449$	9287.05			0.976131			0.488065	+	0.872807i	$0.337703\pi$
$450$		0			0
$451$	1577.51	+	2732.33i	0.164705	+	0.285278i
$452$	−14650.9	−	25376.2i	−1.52461	−	2.64070i
$453$		0			0
$454$	−4360.26			−0.450742
$455$	−104.274	+	59.7113i	−0.0107438	+	0.00615233i
$456$		0			0
$457$	−6009.70	+	10409.1i	−0.615147	+	1.06547i	0.375212	+	0.926939i	$0.377570\pi$
$457$	−6009.70	+	10409.1i	−0.615147	+	1.06547i	−0.990359	+	0.138526i	$0.955764\pi$
$458$	−969.233	−	1678.76i	−0.0988849	−	0.171274i
$459$		0			0
$460$	−203.816	+	353.020i	−0.0206587	+	0.0357819i
$461$	9571.71			0.967026			0.483513	−	0.875337i	$-0.339361\pi$
$461$	9571.71			0.967026			0.483513	+	0.875337i	$0.339361\pi$
$462$		0			0
$463$	2265.15			0.227366			0.113683	−	0.993517i	$-0.463735\pi$
$463$	2265.15			0.227366			0.113683	+	0.993517i	$0.463735\pi$
$464$	27550.9	−	47719.5i	2.75650	−	4.77441i
$465$		0			0
$466$	12217.8	+	21161.8i	1.21454	+	2.10365i
$467$	−2660.47	+	4608.07i	−0.263623	+	0.456609i	−0.967202	−	0.254009i	$-0.918251\pi$
$467$	−2660.47	+	4608.07i	−0.263623	+	0.456609i	0.703579	+	0.710617i	$0.251584\pi$
$468$		0			0
$469$	−5.71269	+	1613.77i	−0.000562447	+	0.158885i
$470$	−297.108			−0.0291587
$471$		0			0
$472$	26319.6	+	45586.9i	2.56665	+	4.44557i
$473$	5576.10	+	9658.10i	0.542050	+	0.938858i
$474$		0			0
$475$	−2642.91			−0.255294
$476$	40520.4	−	23203.6i	3.90178	−	2.23432i
$477$		0			0
$478$	4081.74	−	7069.78i	0.390574	−	0.676494i
$479$	1883.49	+	3262.30i	0.179663	+	0.311186i	0.941765	−	0.336271i	$-0.109166\pi$
$479$	1883.49	+	3262.30i	0.179663	+	0.311186i	−0.762102	+	0.647457i	$0.775832\pi$
$480$		0			0
$481$	2387.43	−	4135.15i	0.226315	−	0.391989i
$482$	856.871			0.0809739
$483$		0			0
$484$	−11420.1			−1.07251
$485$	84.2065	−	145.850i	0.00788375	−	0.0136551i
$486$		0			0
$487$	−4428.96	−	7671.18i	−0.412105	−	0.713787i	0.583014	−	0.812462i	$-0.301873\pi$
$487$	−4428.96	−	7671.18i	−0.412105	−	0.713787i	−0.995120	+	0.0986744i	$0.968540\pi$
$488$	−13975.4	+	24206.2i	−1.29639	+	2.24541i
$489$		0			0
$490$	188.813	−	321.751i	0.0174075	−	0.0296637i
$491$	17311.1			1.59112			0.795560	−	0.605874i	$-0.207177\pi$
$491$	17311.1			1.59112			0.795560	+	0.605874i	$0.207177\pi$
$492$		0			0
$493$	13371.8	+	23160.7i	1.22157	+	2.11583i
$494$	1881.82	+	3259.40i	0.171391	+	0.296857i
$495$		0			0
$496$	67039.8			6.06891
$497$	−1414.58	−	823.397i	−0.127671	−	0.0743147i
$498$		0			0
$499$	3515.22	−	6088.55i	0.315357	−	0.546214i	−0.664157	−	0.747594i	$-0.731209\pi$
$499$	3515.22	−	6088.55i	0.315357	−	0.546214i	0.979513	+	0.201380i	$0.0645425\pi$
$500$	−543.334	−	941.081i	−0.0485972	−	0.0841729i
$501$		0			0
$502$	−9554.51	+	16548.9i	−0.849479	+	1.47134i
$503$	−1519.74			−0.134716			−0.0673578	−	0.997729i	$-0.521457\pi$
$503$	−1519.74			−0.134716			−0.0673578	+	0.997729i	$0.521457\pi$
$504$		0			0
$505$	−31.2547			−0.00275409
$506$	7278.19	−	12606.2i	0.639437	−	1.10754i
$507$		0			0
$508$	−10683.6	−	18504.5i	−0.933086	−	1.61615i
$509$	−9727.68	+	16848.8i	−0.847096	+	1.46721i	0.0366920	+	0.999327i	$0.488318\pi$
$509$	−9727.68	+	16848.8i	−0.847096	+	1.46721i	−0.883788	+	0.467887i	$0.845015\pi$
$510$		0			0
$511$	52.6474	−	14872.3i	0.00455770	−	1.28750i
$512$	−21639.1			−1.86782
$513$		0			0
$514$	−12942.0	−	22416.1i	−1.11059	−	1.92361i
$515$	−13.8723	−	24.0276i	−0.00118697	−	0.00205589i
$516$		0			0
$517$	7764.35			0.660495
$518$	−52.4776	+	14824.4i	−0.00445122	+	1.25742i
$519$		0			0
$520$	−245.061	+	424.458i	−0.0206666	+	0.0357956i
$521$	5111.98	+	8854.21i	0.429866	+	0.744549i	0.996861	−	0.0791720i	$-0.0252276\pi$
$521$	5111.98	+	8854.21i	0.429866	+	0.744549i	−0.566995	+	0.823721i	$0.691894\pi$
$522$		0			0
$523$	−8303.48	+	14382.1i	−0.694237	+	1.20245i	0.276200	+	0.961100i	$0.410925\pi$
$523$	−8303.48	+	14382.1i	−0.694237	+	1.20245i	−0.970437	+	0.241354i	$0.922409\pi$
$524$	−51801.0			−4.31858
$525$		0			0
$526$	−18375.9			−1.52324
$527$	−16268.9	+	28178.5i	−1.34475	+	2.32918i
$528$		0			0
$529$	1687.50	+	2922.84i	0.138695	+	0.240227i
$530$	−185.118	+	320.633i	−0.0151717	+	0.0262781i
$531$		0			0
$532$	−7390.46	−	4301.84i	−0.602288	−	0.350580i
$533$	3616.52			0.293900
$534$		0			0
$535$	41.3681	+	71.6517i	0.00334299	+	0.00579023i
$536$	3291.24	+	5700.59i	0.265224	+	0.459381i
$537$		0			0
$538$	−28441.0			−2.27914
$539$	−4934.26	+	8408.34i	−0.394311	+	0.671935i
$540$		0			0
$541$	−3291.27	+	5700.65i	−0.261558	+	0.453032i	−0.966656	−	0.256078i	$-0.917570\pi$
$541$	−3291.27	+	5700.65i	−0.261558	+	0.453032i	0.705098	+	0.709110i	$0.250903\pi$
$542$	−6313.83	−	10935.9i	−0.500373	−	0.866672i
$543$		0			0
$544$	40148.2	−	69538.7i	3.16423	−	5.48060i
$545$	168.087			0.0132111
$546$		0			0
$547$	3407.73			0.266369			0.133185	−	0.991091i	$-0.457480\pi$
$547$	3407.73			0.266369			0.133185	+	0.991091i	$0.457480\pi$
$548$	17494.1	−	30300.6i	1.36370	−	2.36200i
$549$		0			0
$550$	9699.56	+	16800.1i	0.751983	+	1.30247i
$551$	2448.86	−	4241.55i	0.189337	−	0.327942i
$552$		0			0
$553$	5859.99	−	3355.66i	0.450619	−	0.258042i
$554$	−14237.4			−1.09185
$555$		0			0
$556$	−22942.1	−	39736.9i	−1.74993	−	3.03097i
$557$	−4740.05	−	8210.02i	−0.360579	−	0.624541i	0.627477	−	0.778635i	$-0.284088\pi$
$557$	−4740.05	−	8210.02i	−0.360579	−	0.624541i	−0.988056	+	0.154094i	$0.950754\pi$
$558$		0			0
$559$	12783.5			0.967233
$560$	3.10652	−	877.558i	0.000234418	−	0.0662207i
$561$		0			0
$562$	14396.2	−	24935.0i	1.08055	−	1.87156i
$563$	−10932.2	−	18935.2i	−0.818363	−	1.41745i	−0.906888	−	0.421372i	$-0.861549\pi$
$563$	−10932.2	−	18935.2i	−0.818363	−	1.41745i	0.0885250	−	0.996074i	$-0.471785\pi$
$564$		0			0
$565$	133.641	−	231.473i	0.00995101	−	0.0172357i
$566$	−31723.2			−2.35588
$567$		0			0
$568$	−6676.23			−0.493184
$569$	−571.695	+	990.204i	−0.0421207	+	0.0729552i	−0.886317	−	0.463079i	$-0.846745\pi$
$569$	−571.695	+	990.204i	−0.0421207	+	0.0729552i	0.844196	+	0.536034i	$0.180078\pi$
$570$		0			0
$571$	−5235.55	−	9068.24i	−0.383715	−	0.664613i	0.607875	−	0.794032i	$-0.292022\pi$
$571$	−5235.55	−	9068.24i	−0.383715	−	0.664613i	−0.991590	+	0.129419i	$0.958689\pi$
$572$	10108.4	−	17508.3i	0.738907	−	1.27982i
$573$		0			0
$574$	−9743.70	+	5579.63i	−0.708526	+	0.405730i
$575$	11717.0			0.849795
$576$		0			0
$577$	−2379.80	−	4121.94i	−0.171703	−	0.297398i	0.767313	−	0.641273i	$-0.221594\pi$
$577$	−2379.80	−	4121.94i	−0.171703	−	0.297398i	−0.939015	+	0.343876i	$0.888260\pi$
$578$	23006.3	+	39848.0i	1.65560	+	2.86758i
$579$		0			0
$580$	1006.72			0.0720721
$581$	14752.6	+	8587.19i	1.05343	+	0.613179i
$582$		0			0
$583$	4837.70	−	8379.14i	0.343665	−	0.595246i
$584$	−30331.7	−	52536.0i	−2.14920	−	3.72252i
$585$		0			0
$586$	5406.36	−	9364.08i	0.381117	−	0.660114i
$587$	6307.45			0.443503			0.221751	−	0.975103i	$-0.428823\pi$
$587$	6307.45			0.443503			0.221751	+	0.975103i	$0.428823\pi$
$588$		0			0
$589$	5958.83			0.416858
$590$	−378.942	+	656.348i	−0.0264421	+	0.0457990i
$591$		0			0
$592$	17436.1	+	30200.2i	1.21051	+	2.09666i
$593$	8865.93	−	15356.2i	0.613963	−	1.06342i	−0.376602	−	0.926375i	$-0.622908\pi$
$593$	8865.93	−	15356.2i	0.613963	−	1.06342i	0.990565	−	0.137041i	$-0.0437591\pi$
$594$		0			0
$595$	368.106	+	214.267i	0.0253628	+	0.0147632i
$596$	−11448.2			−0.786808
$597$		0			0
$598$	−8342.79	−	14450.1i	−0.570505	−	0.988144i
$599$	9555.03	+	16549.8i	0.651766	+	1.12889i	0.982694	+	0.185236i	$0.0593050\pi$
$599$	9555.03	+	16549.8i	0.651766	+	1.12889i	−0.330928	+	0.943656i	$0.607362\pi$
$600$		0			0
$601$	−13118.3			−0.890357			−0.445179	−	0.895442i	$-0.646860\pi$
$601$	−13118.3			−0.890357			−0.445179	+	0.895442i	$0.646860\pi$
$602$	−34441.5	+	19722.6i	−2.33178	+	1.33527i
$603$		0			0
$604$	9471.04	−	16404.3i	0.638032	−	1.10510i
$605$	−52.0854	−	90.2145i	−0.00350012	−	0.00606238i
$606$		0			0
$607$	−8736.71	+	15132.4i	−0.584204	+	1.01187i	0.410770	+	0.911739i	$0.365260\pi$
$607$	−8736.71	+	15132.4i	−0.584204	+	1.01187i	−0.994974	+	0.100133i	$0.968073\pi$
$608$	−14705.1			−0.980876
$609$		0			0
$610$	−402.429			−0.0267112
$611$	4450.03	−	7707.68i	0.294647	−	0.510343i
$612$		0			0
$613$	−1547.70	−	2680.69i	−0.101975	−	0.176626i	0.810523	−	0.585707i	$-0.199183\pi$
$613$	−1547.70	−	2680.69i	−0.101975	−	0.176626i	−0.912498	+	0.409080i	$0.865850\pi$
$614$	2523.36	−	4370.58i	0.165854	−	0.287268i
$615$		0			0
$616$	−140.769	+	39765.9i	−0.00920740	+	2.60099i
$617$	−26334.8			−1.71831			−0.859157	−	0.511712i	$-0.829011\pi$
$617$	−26334.8			−1.71831			−0.859157	+	0.511712i	$0.829011\pi$
$618$		0			0
$619$	1343.02	+	2326.18i	0.0872061	+	0.151045i	0.906329	−	0.422572i	$-0.138873\pi$
$619$	1343.02	+	2326.18i	0.0872061	+	0.151045i	−0.819123	+	0.573618i	$0.805539\pi$
$620$	612.416	+	1060.74i	0.0396697	+	0.0687100i
$621$		0			0
$622$	−55211.0			−3.55910
$623$	3397.49	−	1945.54i	0.218487	−	0.125115i
$624$		0			0
$625$	−7805.07	+	13518.8i	−0.499524	+	0.865201i
$626$	18653.4	+	32308.7i	1.19096	+	2.06280i
$627$		0			0
$628$	64.6200	−	111.925i	0.00410608	−	0.00711194i
$629$	−16925.2			−1.07290
$630$		0			0
$631$	22414.2			1.41409			0.707047	−	0.707167i	$-0.250027\pi$
$631$	22414.2			1.41409			0.707047	+	0.707167i	$0.250027\pi$
$632$	13772.0	−	23853.8i	0.866803	−	1.50135i
$633$		0			0
$634$	20819.3	+	36060.1i	1.30416	+	2.25888i
$635$	97.4522	−	168.792i	0.00609019	−	0.0105485i
$636$		0			0
$637$	5518.97	+	9717.37i	0.343280	+	0.604421i
$638$	−35949.6			−2.23081
$639$		0			0
$640$	−476.111	−	824.648i	−0.0294062	−	0.0509329i
$641$	11069.5	+	19173.0i	0.682092	+	1.18142i	0.974341	+	0.225076i	$0.0722630\pi$
$641$	11069.5	+	19173.0i	0.682092	+	1.18142i	−0.292249	+	0.956342i	$0.594404\pi$
$642$		0			0
$643$	22523.7			1.38141			0.690707	−	0.723134i	$-0.257299\pi$
$643$	22523.7			1.38141			0.690707	+	0.723134i	$0.257299\pi$
$644$	32764.6	+	19071.6i	2.00483	+	1.16697i
$645$		0			0
$646$	6670.38	−	11553.4i	0.406258	−	0.703659i
$647$	5761.75	+	9979.64i	0.350105	+	0.606399i	0.986267	−	0.165156i	$-0.0528127\pi$
$647$	5761.75	+	9979.64i	0.350105	+	0.606399i	−0.636163	+	0.771555i	$0.719479\pi$
$648$		0			0
$649$	9902.93	−	17152.4i	0.598959	−	1.03743i
$650$	22236.7			1.34184
$651$		0			0
$652$	−18184.4			−1.09226
$653$	230.968	−	400.049i	0.0138415	−	0.0239742i	−0.859022	−	0.511939i	$-0.828927\pi$
$653$	230.968	−	400.049i	0.0138415	−	0.0239742i	0.872863	+	0.487965i	$0.162261\pi$
$654$		0			0
$655$	−236.256	−	409.207i	−0.0140936	−	0.0244107i
$656$	−13206.2	+	22873.9i	−0.786001	+	1.36139i
$657$		0			0
$658$	−97.8152	+	27631.8i	−0.00579519	+	1.63708i
$659$	14373.3			0.849627			0.424813	−	0.905281i	$-0.360340\pi$
$659$	14373.3			0.849627			0.424813	+	0.905281i	$0.360340\pi$
$660$		0			0
$661$	−33.9245	−	58.7589i	−0.00199623	−	0.00345758i	0.865026	−	0.501728i	$-0.167302\pi$
$661$	−33.9245	−	58.7589i	−0.00199623	−	0.00345758i	−0.867022	+	0.498270i	$0.833969\pi$
$662$	6781.38	+	11745.7i	0.398135	+	0.689591i
$663$		0			0
$664$	69626.3			4.06931
$665$	0.276122	−	78.0017i	1.61016e−5	−	0.00454853i
$666$		0			0
$667$	−10856.7	+	18804.3i	−0.630244	+	1.09162i
$668$	−6186.91	−	10716.0i	−0.358351	−	0.620683i
$669$		0			0
$670$	−47.3863	+	82.0755i	−0.00273238	+	0.00473262i
$671$	10516.7			0.605056
$672$		0			0
$673$	21970.2			1.25838			0.629190	−	0.777252i	$-0.283387\pi$
$673$	21970.2			1.25838			0.629190	+	0.777252i	$0.283387\pi$
$674$	21561.7	−	37345.9i	1.23223	−	2.13429i
$675$		0			0
$676$	12394.4	+	21467.8i	0.705191	+	1.22143i
$677$	−1496.65	+	2592.27i	−0.0849642	+	0.147162i	−0.905376	−	0.424611i	$-0.860411\pi$
$677$	−1496.65	+	2592.27i	−0.0849642	+	0.147162i	0.820412	+	0.571773i	$0.193744\pi$
$678$		0			0
$679$	−13536.7	−	7879.43i	−0.765081	−	0.445338i
$680$	1737.31			0.0979747
$681$		0			0
$682$	−21869.1	−	37878.4i	−1.22788	−	2.12674i
$683$	−2730.95	−	4730.14i	−0.152997	−	0.264998i	0.779331	−	0.626612i	$-0.215559\pi$
$683$	−2730.95	−	4730.14i	−0.152997	−	0.264998i	−0.932328	+	0.361614i	$0.882226\pi$
$684$		0			0
$685$	319.150			0.0178016
$686$	−29861.4	−	17666.0i	−1.66198	−	0.983221i
$687$		0			0
$688$	−46680.7	+	80853.3i	−2.58675	+	4.48038i
$689$	−5545.32	−	9604.77i	−0.306618	−	0.531078i
$690$		0			0
$691$	7889.49	−	13665.0i	0.434342	−	0.752303i	−0.562899	−	0.826525i	$-0.690314\pi$
$691$	7889.49	−	13665.0i	0.434342	−	0.752303i	0.997242	+	0.0742225i	$0.0236475\pi$
$692$	90070.0			4.94790
$693$		0			0
$694$	4857.84			0.265708
$695$	209.270	−	362.467i	0.0114217	−	0.0197829i
$696$		0			0
$697$	−6409.64	−	11101.8i	−0.348325	−	0.603317i
$698$	19013.0	−	32931.5i	1.03102	−	1.78578i
$699$		0			0
$700$	−43843.9	+	25106.8i	−2.36735	+	1.35564i
$701$	8058.91			0.434209			0.217105	−	0.976148i	$-0.430339\pi$
$701$	8058.91			0.434209			0.217105	+	0.976148i	$0.430339\pi$
$702$		0			0
$703$	1549.81	+	2684.34i	0.0831466	+	0.144014i
$704$	26915.3	+	46618.7i	1.44092	+	2.49575i
$705$		0			0
$706$	−63141.5			−3.36595
$707$	−10.2898	+	2906.77i	−0.000547367	+	0.154626i
$708$		0			0
$709$	−13009.5	+	22533.1i	−0.689113	+	1.19358i	0.283013	+	0.959116i	$0.408666\pi$
$709$	−13009.5	+	22533.1i	−0.689113	+	1.19358i	−0.972125	+	0.234462i	$0.924667\pi$
$710$	−48.0612	−	83.2445i	−0.00254043	−	0.00440016i
$711$		0			0
$712$	7984.68	−	13829.9i	0.420279	−	0.727944i
$713$	−26417.7			−1.38759
$714$		0			0
$715$	184.412			0.00964560
$716$	10125.8	−	17538.3i	0.528516	−	0.915416i
$717$		0			0
$718$	−23095.2	−	40002.1i	−1.20043	−	2.07920i
$719$	−2331.73	+	4038.68i	−0.120944	+	0.209482i	−0.920140	−	0.391589i	$-0.871926\pi$
$719$	−2331.73	+	4038.68i	−0.120944	+	0.209482i	0.799196	+	0.601070i	$0.205259\pi$
$720$		0			0
$721$	−2239.19	+	1282.25i	−0.115661	+	0.0662324i
$722$	35019.2			1.80510
$723$		0			0
$724$	−13226.1	−	22908.2i	−0.678926	−	1.17593i
$725$	−14468.6	−	25060.3i	−0.741172	−	1.28375i
$726$		0			0
$727$	35484.5			1.81024			0.905121	−	0.425154i	$-0.139780\pi$
$727$	35484.5			1.81024			0.905121	+	0.425154i	$0.139780\pi$
$728$	39395.0	+	22931.0i	2.00560	+	1.16742i
$729$		0			0
$730$	436.707	−	756.398i	0.0221414	−	0.0383501i
$731$	−22656.5	−	39242.1i	−1.14635	−	1.98553i
$732$		0			0
$733$	7628.55	−	13213.0i	0.384402	−	0.665804i	−0.607284	−	0.794485i	$-0.707741\pi$
$733$	7628.55	−	13213.0i	0.384402	−	0.665804i	0.991686	+	0.128681i	$0.0410742\pi$
$734$	−37756.9			−1.89868
$735$		0			0
$736$	65193.4			3.26503
$737$	1238.35	−	2144.89i	0.0618932	−	0.107202i
$738$		0			0
$739$	−12876.9	−	22303.4i	−0.640978	−	1.11021i	−0.985215	−	0.171324i	$-0.945195\pi$
$739$	−12876.9	−	22303.4i	−0.640978	−	1.11021i	0.344236	−	0.938883i	$-0.388138\pi$
$740$	−318.561	+	551.764i	−0.0158251	+	0.0274098i
$741$		0			0
$742$	29758.7	+	17322.0i	1.47234	+	0.857020i
$743$	−5703.55			−0.281619			−0.140809	−	0.990037i	$-0.544971\pi$
$743$	−5703.55			−0.281619			−0.140809	+	0.990037i	$0.544971\pi$
$744$		0			0
$745$	−52.2135	−	90.4364i	−0.00256772	−	0.00444743i
$746$	1157.66	+	2005.12i	0.0568160	+	0.0984083i
$747$		0			0
$748$	−71661.7			−3.50296
$749$	6677.40	−	3823.75i	0.325750	−	0.186538i
$750$		0			0
$751$	−7725.44	+	13380.9i	−0.375373	+	0.650166i	−0.990383	−	0.138354i	$-0.955819\pi$
$751$	−7725.44	+	13380.9i	−0.375373	+	0.650166i	0.615010	+	0.788520i	$0.289152\pi$
$752$	32499.9	+	56291.4i	1.57600	+	2.72970i
$753$		0			0
$754$	−20604.0	+	35687.2i	−0.995164	+	1.72368i
$755$	172.784			0.00832879
$756$		0			0
$757$	12434.7			0.597025			0.298513	−	0.954406i	$-0.403509\pi$
$757$	12434.7			0.597025			0.298513	+	0.954406i	$0.403509\pi$
$758$	−26528.8	+	45949.2i	−1.27120	+	2.20178i
$759$		0			0
$760$	−159.082	−	275.538i	−0.00759277	−	0.0131511i
$761$	1159.31	−	2007.98i	0.0552234	−	0.0956497i	−0.837092	−	0.547062i	$-0.815746\pi$
$761$	1159.31	−	2007.98i	0.0552234	−	0.0956497i	0.892316	+	0.451412i	$0.149080\pi$
$762$		0			0
$763$	55.3383	−	15632.5i	0.00262566	−	0.741722i
$764$	39896.1			1.88926
$765$		0			0
$766$	6046.61	+	10473.0i	0.285212	+	0.494003i
$767$	−11351.5	−	19661.3i	−0.534391	−	0.925592i
$768$		0			0
$769$	23104.3			1.08344			0.541718	−	0.840560i	$-0.317774\pi$
$769$	23104.3			1.08344			0.541718	+	0.840560i	$0.317774\pi$
$770$	−496.846	+	284.514i	−0.0232533	+	0.0133158i
$771$		0			0
$772$	8975.09	−	15545.3i	0.418420	−	0.724725i
$773$	6216.80	+	10767.8i	0.289266	+	0.501024i	0.973635	−	0.228112i	$-0.0732554\pi$
$773$	6216.80	+	10767.8i	0.289266	+	0.501024i	−0.684369	+	0.729136i	$0.739922\pi$
$774$		0			0
$775$	17603.3	−	30489.8i	0.815908	−	1.41319i
$776$	−63887.6			−2.95545
$777$		0			0
$778$	−41867.1			−1.92932
$779$	−1173.84	+	2033.14i	−0.0539885	+	0.0935108i
$780$	<

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.73089 - 4.73004i) q^{2} +(-10.9155 - 18.9063i) q^{4} +(0.0995681 - 0.172457i) q^{5} +(-16.0061 - 9.31685i) q^{7} -75.5424 q^{8} +O(q^{10})\)	\(q+(2.73089 - 4.73004i) q^{2} +(-10.9155 - 18.9063i) q^{4} +(0.0995681 - 0.172457i) q^{5} +(-16.0061 - 9.31685i) q^{7} -75.5424 q^{8} +(-0.543819 - 0.941923i) q^{10} +(14.2117 + 24.6153i) q^{11} +32.5809 q^{13} +(-87.7801 + 50.2664i) q^{14} +(-118.974 + 206.069i) q^{16} +(-57.7439 - 100.015i) q^{17} +(-10.5750 + 18.3164i) q^{19} -4.34736 q^{20} +155.242 q^{22} +(46.8828 - 81.2034i) q^{23} +(62.4802 + 108.219i) q^{25} +(88.9749 - 154.109i) q^{26} +(-1.43126 + 404.315i) q^{28} -231.571 q^{29} +(-140.871 - 243.996i) q^{31} +(347.640 + 602.130i) q^{32} -630.770 q^{34} +(-3.20045 + 1.83271i) q^{35} +(73.2770 - 126.919i) q^{37} +(57.7583 + 100.040i) q^{38} +(-7.52161 + 13.0278i) q^{40} +111.001 q^{41} +392.361 q^{43} +(310.256 - 537.380i) q^{44} +(-256.064 - 443.516i) q^{46} +(136.584 - 236.571i) q^{47} +(169.393 + 298.253i) q^{49} +682.506 q^{50} +(-355.638 - 615.984i) q^{52} +(-170.201 - 294.798i) q^{53} +5.66011 q^{55} +(1209.14 + 703.817i) q^{56} +(-632.395 + 1095.34i) q^{58} +(-348.408 - 603.461i) q^{59} +(185.001 - 320.431i) q^{61} -1538.81 q^{62} +1893.89 q^{64} +(3.24402 - 5.61880i) q^{65} +(-43.5681 - 75.4622i) q^{67} +(-1260.61 + 2183.45i) q^{68} +(-0.0713061 + 20.1432i) q^{70} +88.3772 q^{71} +(401.518 + 695.450i) q^{73} +(-400.223 - 693.207i) q^{74} +461.727 q^{76} +(1.86345 - 526.404i) q^{77} +(-182.308 + 315.766i) q^{79} +(23.6920 + 41.0357i) q^{80} +(303.132 - 525.040i) q^{82} -921.684 q^{83} -22.9978 q^{85} +(1071.50 - 1855.88i) q^{86} +(-1073.58 - 1859.50i) q^{88} +(-105.698 + 183.074i) q^{89} +(-521.494 - 303.551i) q^{91} -2047.01 q^{92} +(-745.993 - 1292.10i) q^{94} +(2.10586 + 3.64746i) q^{95} +845.718 q^{97} +(1873.35 + 13.2633i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 48 q^{4} - 60 q^{7}+O(q^{10}) \) 16 * q - 48 * q^4 - 60 * q^7	\( 16 q - 48 q^{4} - 60 q^{7} - 44 q^{10} - 168 q^{13} - 156 q^{16} - 12 q^{19} + 448 q^{22} - 408 q^{25} - 152 q^{28} - 800 q^{31} - 1896 q^{34} - 692 q^{37} - 96 q^{40} + 2912 q^{43} - 1524 q^{46} + 2020 q^{49} - 1972 q^{52} - 2560 q^{55} - 2372 q^{58} - 216 q^{61} + 9928 q^{64} - 684 q^{67} + 4316 q^{70} + 4564 q^{73} - 760 q^{76} - 556 q^{79} - 3340 q^{82} + 2592 q^{85} - 6696 q^{88} - 184 q^{91} + 492 q^{94} + 1168 q^{97}+O(q^{100}) \) 16 * q - 48 * q^4 - 60 * q^7 - 44 * q^10 - 168 * q^13 - 156 * q^16 - 12 * q^19 + 448 * q^22 - 408 * q^25 - 152 * q^28 - 800 * q^31 - 1896 * q^34 - 692 * q^37 - 96 * q^40 + 2912 * q^43 - 1524 * q^46 + 2020 * q^49 - 1972 * q^52 - 2560 * q^55 - 2372 * q^58 - 216 * q^61 + 9928 * q^64 - 684 * q^67 + 4316 * q^70 + 4564 * q^73 - 760 * q^76 - 556 * q^79 - 3340 * q^82 + 2592 * q^85 - 6696 * q^88 - 184 * q^91 + 492 * q^94 + 1168 * q^97

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