LMFDB - Embedded newform 189.4.e.e.163.1

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 40x^{10} + 1147x^{8} + 15564x^{6} + 154089x^{4} + 578934x^{2} + 1633284 $ x^12 + 40x^10 + 1147x^8 + 15564x^6 + 154089x^4 + 578934*x^2 + 1633284
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$2.35377 + 4.07684i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.e.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.35377 + 4.07684i) q^{2} +(-7.08042 - 12.2637i) q^{4} +(-0.415227 + 0.719194i) q^{5} +(16.4314 - 8.54463i) q^{7} +29.0024 q^{8} +O(q^{10})$	\(q+(-2.35377 + 4.07684i) q^{2} +(-7.08042 - 12.2637i) q^{4} +(-0.415227 + 0.719194i) q^{5} +(16.4314 - 8.54463i) q^{7} +29.0024 q^{8} +(-1.95469 - 3.38563i) q^{10} +(34.1251 + 59.1065i) q^{11} -35.7721 q^{13} +(-3.84045 + 87.1001i) q^{14} +(-11.6214 + 20.1289i) q^{16} +(-7.33893 - 12.7114i) q^{17} +(-43.3847 + 75.1445i) q^{19} +11.7599 q^{20} -321.290 q^{22} +(-29.2043 + 50.5834i) q^{23} +(62.1552 + 107.656i) q^{25} +(84.1991 - 145.837i) q^{26} +(-221.129 - 141.009i) q^{28} -67.1398 q^{29} +(34.7501 + 60.1889i) q^{31} +(61.3013 + 106.177i) q^{32} +69.0965 q^{34} +(-0.677492 + 15.3653i) q^{35} +(144.620 - 250.489i) q^{37} +(-204.235 - 353.745i) q^{38} +(-12.0426 + 20.8583i) q^{40} -357.750 q^{41} -235.801 q^{43} +(483.241 - 836.998i) q^{44} +(-137.480 - 238.123i) q^{46} +(-225.034 + 389.769i) q^{47} +(196.979 - 280.800i) q^{49} -585.195 q^{50} +(253.282 + 438.697i) q^{52} +(-86.2322 - 149.358i) q^{53} -56.6787 q^{55} +(476.548 - 247.815i) q^{56} +(158.031 - 273.718i) q^{58} +(222.928 + 386.123i) q^{59} +(-238.157 + 412.500i) q^{61} -327.174 q^{62} -763.099 q^{64} +(14.8535 - 25.7271i) q^{65} +(402.160 + 696.562i) q^{67} +(-103.925 + 180.004i) q^{68} +(-61.0471 - 38.9283i) q^{70} +353.412 q^{71} +(389.023 + 673.807i) q^{73} +(680.803 + 1179.19i) q^{74} +1228.73 q^{76} +(1065.77 + 679.613i) q^{77} +(37.0998 - 64.2587i) q^{79} +(-9.65105 - 16.7161i) q^{80} +(842.059 - 1458.49i) q^{82} -1168.49 q^{83} +12.1893 q^{85} +(555.020 - 961.324i) q^{86} +(989.711 + 1714.23i) q^{88} +(-757.361 + 1311.79i) q^{89} +(-587.784 + 305.659i) q^{91} +827.116 q^{92} +(-1059.35 - 1834.85i) q^{94} +(-36.0289 - 62.4039i) q^{95} +1631.46 q^{97} +(681.134 + 1463.99i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 32 q^{4} - 26 q^{7}+O(q^{10}) $ 12 * q - 32 * q^4 - 26 * q^7	$ 12 q - 32 q^{4} - 26 q^{7} + 20 q^{10} + 104 q^{13} + 148 q^{16} + 62 q^{19} - 712 q^{22} + 46 q^{25} - 348 q^{28} + 82 q^{31} + 840 q^{34} + 1132 q^{37} + 444 q^{40} - 3132 q^{43} + 888 q^{46} + 366 q^{49} + 72 q^{52} + 448 q^{55} - 4 q^{58} - 886 q^{61} - 1848 q^{64} + 2084 q^{67} - 4460 q^{70} + 2398 q^{73} + 6408 q^{76} - 984 q^{79} + 3892 q^{82} - 7200 q^{85} + 5796 q^{88} - 6492 q^{91} - 2772 q^{94} - 1364 q^{97}+O(q^{100}) $ 12 * q - 32 * q^4 - 26 * q^7 + 20 * q^10 + 104 * q^13 + 148 * q^16 + 62 * q^19 - 712 * q^22 + 46 * q^25 - 348 * q^28 + 82 * q^31 + 840 * q^34 + 1132 * q^37 + 444 * q^40 - 3132 * q^43 + 888 * q^46 + 366 * q^49 + 72 * q^52 + 448 * q^55 - 4 * q^58 - 886 * q^61 - 1848 * q^64 + 2084 * q^67 - 4460 * q^70 + 2398 * q^73 + 6408 * q^76 - 984 * q^79 + 3892 * q^82 - 7200 * q^85 + 5796 * q^88 - 6492 * q^91 - 2772 * q^94 - 1364 * 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 $

$2$	−2.35377	+	4.07684i	−0.832182	+	1.44138i	0.0641227	+	0.997942i	$0.479575\pi$
$2$	−2.35377	+	4.07684i	−0.832182	+	1.44138i	−0.896304	+	0.443439i	$0.853758\pi$
$3$		0			0
$3$		0			0
$4$	−7.08042	−	12.2637i	−0.885053	−	1.53296i
$5$	−0.415227	+	0.719194i	−0.0371390	+	0.0643266i	−0.883997	−	0.467492i	$-0.845158\pi$
$5$	−0.415227	+	0.719194i	−0.0371390	+	0.0643266i	0.846858	+	0.531818i	$0.178491\pi$
$6$		0			0
$7$	16.4314	−	8.54463i	0.887210	−	0.461367i
$7$	16.4314	−	8.54463i	0.887210	−	0.461367i
$8$	29.0024			1.28174
$9$		0			0
$10$	−1.95469	−	3.38563i	−0.0618128	−	0.107063i
$11$	34.1251	+	59.1065i	0.935374	+	1.62012i	0.773965	+	0.633229i	$0.218271\pi$
$11$	34.1251	+	59.1065i	0.935374	+	1.62012i	0.161410	+	0.986887i	$0.448396\pi$
$12$		0			0
$13$	−35.7721			−0.763184			−0.381592	−	0.924331i	$-0.624624\pi$
$13$	−35.7721			−0.763184			−0.381592	+	0.924331i	$0.624624\pi$
$14$	−3.84045	+	87.1001i	−0.0733146	+	1.66275i
$15$		0			0
$16$	−11.6214	+	20.1289i	−0.181585	+	0.314514i
$17$	−7.33893	−	12.7114i	−0.104703	−	0.181351i	0.808914	−	0.587927i	$-0.200056\pi$
$17$	−7.33893	−	12.7114i	−0.104703	−	0.181351i	−0.913617	+	0.406576i	$0.866723\pi$
$18$		0			0
$19$	−43.3847	+	75.1445i	−0.523849	+	0.907333i	0.475766	+	0.879572i	$0.342171\pi$
$19$	−43.3847	+	75.1445i	−0.523849	+	0.907333i	−0.999615	+	0.0277607i	$0.991162\pi$
$20$	11.7599			0.131480
$21$		0			0
$22$	−321.290			−3.11361
$23$	−29.2043	+	50.5834i	−0.264762	+	0.458581i	−0.967501	−	0.252866i	$-0.918627\pi$
$23$	−29.2043	+	50.5834i	−0.264762	+	0.458581i	0.702739	+	0.711447i	$0.251960\pi$
$24$		0			0
$25$	62.1552	+	107.656i	0.497241	+	0.861247i
$26$	84.1991	−	145.837i	0.635108	−	1.10004i
$27$		0			0
$28$	−221.129	−	141.009i	−1.49248	−	0.951720i
$29$	−67.1398			−0.429915			−0.214958	−	0.976623i	$-0.568961\pi$
$29$	−67.1398			−0.429915			−0.214958	+	0.976623i	$0.568961\pi$
$30$		0			0
$31$	34.7501	+	60.1889i	0.201332	+	0.348718i	0.948958	−	0.315403i	$-0.102140\pi$
$31$	34.7501	+	60.1889i	0.201332	+	0.348718i	−0.747626	+	0.664120i	$0.768806\pi$
$32$	61.3013	+	106.177i	0.338645	+	0.586551i
$33$		0			0
$34$	69.0965			0.348528
$35$	−0.677492	+	15.3653i	−0.00327192	+	0.0742059i
$36$		0			0
$37$	144.620	−	250.489i	0.642578	−	1.11298i	−0.342277	−	0.939599i	$-0.611198\pi$
$37$	144.620	−	250.489i	0.642578	−	1.11298i	0.984855	−	0.173379i	$-0.0554685\pi$
$38$	−204.235	−	353.745i	−0.871875	−	1.51013i
$39$		0			0
$40$	−12.0426	+	20.8583i	−0.0476024	+	0.0824498i
$41$	−357.750			−1.36271			−0.681355	−	0.731953i	$-0.738609\pi$
$41$	−357.750			−1.36271			−0.681355	+	0.731953i	$0.738609\pi$
$42$		0			0
$43$	−235.801			−0.836263			−0.418132	−	0.908386i	$-0.637315\pi$
$43$	−235.801			−0.836263			−0.418132	+	0.908386i	$0.637315\pi$
$44$	483.241	−	836.998i	1.65571	−	2.86778i
$45$		0			0
$46$	−137.480	−	238.123i	−0.440660	−	0.763246i
$47$	−225.034	+	389.769i	−0.698394	+	1.20965i	0.270629	+	0.962684i	$0.412768\pi$
$47$	−225.034	+	389.769i	−0.698394	+	1.20965i	−0.969023	+	0.246970i	$0.920565\pi$
$48$		0			0
$49$	196.979	−	280.800i	0.574282	−	0.818658i
$50$	−585.195			−1.65518
$51$		0			0
$52$	253.282	+	438.697i	0.675458	+	1.16993i
$53$	−86.2322	−	149.358i	−0.223489	−	0.387094i	0.732376	−	0.680900i	$-0.238411\pi$
$53$	−86.2322	−	149.358i	−0.223489	−	0.387094i	−0.955865	+	0.293806i	$0.905078\pi$
$54$		0			0
$55$	−56.6787			−0.138955
$56$	476.548	−	247.815i	1.13717	−	0.591350i
$57$		0			0
$58$	158.031	−	273.718i	0.357768	−	0.619672i
$59$	222.928	+	386.123i	0.491912	+	0.852016i	0.999957	−	0.00931467i	$-0.00296499\pi$
$59$	222.928	+	386.123i	0.491912	+	0.852016i	−0.508045	+	0.861330i	$0.669632\pi$
$60$		0			0
$61$	−238.157	+	412.500i	−0.499883	+	0.865823i	−1.00000		0.000134725i	$-0.999957\pi$
$61$	−238.157	+	412.500i	−0.499883	+	0.865823i	0.500117	+	0.865958i	$0.333290\pi$
$62$	−327.174			−0.670180
$63$		0			0
$64$	−763.099			−1.49043
$65$	14.8535	−	25.7271i	0.0283439	−	0.0490931i
$66$		0			0
$67$	402.160	+	696.562i	0.733309	+	1.27013i	0.955461	+	0.295116i	$0.0953583\pi$
$67$	402.160	+	696.562i	0.733309	+	1.27013i	−0.222153	+	0.975012i	$0.571308\pi$
$68$	−103.925	+	180.004i	−0.185336	+	0.321011i
$69$		0			0
$70$	−61.0471	−	38.9283i	−0.104236	−	0.0664689i
$71$	353.412			0.590737			0.295368	−	0.955383i	$-0.404558\pi$
$71$	353.412			0.590737			0.295368	+	0.955383i	$0.404558\pi$
$72$		0			0
$73$	389.023	+	673.807i	0.623721	+	1.08032i	0.988787	+	0.149335i	$0.0477133\pi$
$73$	389.023	+	673.807i	0.623721	+	1.08032i	−0.365065	+	0.930982i	$0.618953\pi$
$74$	680.803	+	1179.19i	1.06948	+	1.85240i
$75$		0			0
$76$	1228.73			1.85454
$77$	1065.77	+	679.613i	1.57734	+	1.00583i
$78$		0			0
$79$	37.0998	−	64.2587i	0.0528361	−	0.0915149i	−0.838398	−	0.545059i	$-0.816507\pi$
$79$	37.0998	−	64.2587i	0.0528361	−	0.0915149i	0.891234	+	0.453544i	$0.149841\pi$
$80$	−9.65105	−	16.7161i	−0.0134878	−	0.0233615i
$81$		0			0
$82$	842.059	−	1458.49i	1.13402	−	1.96418i
$83$	−1168.49			−1.54529			−0.772643	−	0.634840i	$-0.781066\pi$
$83$	−1168.49			−1.54529			−0.772643	+	0.634840i	$0.781066\pi$
$84$		0			0
$85$	12.1893			0.0155543
$86$	555.020	−	961.324i	0.695923	−	1.20537i
$87$		0			0
$88$	989.711	+	1714.23i	1.19890	+	2.07656i
$89$	−757.361	+	1311.79i	−0.902023	+	1.56235i	−0.0771598	+	0.997019i	$0.524585\pi$
$89$	−757.361	+	1311.79i	−0.902023	+	1.56235i	−0.824864	+	0.565332i	$0.808748\pi$
$90$		0			0
$91$	−587.784	+	305.659i	−0.677104	+	0.352108i
$92$	827.116			0.937313
$93$		0			0
$94$	−1059.35	−	1834.85i	−1.16238	−	2.01330i
$95$	−36.0289	−	62.4039i	−0.0389104	−	0.0673948i
$96$		0			0
$97$	1631.46			1.70772			0.853862	−	0.520499i	$-0.174254\pi$
$97$	1631.46			1.70772			0.853862	+	0.520499i	$0.174254\pi$
$98$	681.134	+	1463.99i	0.702091	+	1.50903i
$99$		0			0
$100$	880.170	−	1524.50i	0.880170	−	1.52450i
$101$	−602.865	−	1044.19i	−0.593934	−	1.02872i	−0.993696	−	0.112105i	$-0.964241\pi$
$101$	−602.865	−	1044.19i	−0.593934	−	1.02872i	0.399762	−	0.916619i	$-0.369093\pi$
$102$		0			0
$103$	242.681	−	420.336i	0.232156	−	0.402106i	−0.726286	−	0.687392i	$-0.758755\pi$
$103$	242.681	−	420.336i	0.232156	−	0.402106i	0.958442	+	0.285286i	$0.0920886\pi$
$104$	−1037.48			−0.978201
$105$		0			0
$106$	811.881			0.743933
$107$	129.050	−	223.522i	0.116596	−	0.201950i	−0.801821	−	0.597565i	$-0.796135\pi$
$107$	129.050	−	223.522i	0.116596	−	0.201950i	0.918417	+	0.395615i	$0.129468\pi$
$108$		0			0
$109$	−290.623	−	503.374i	−0.255382	−	0.442335i	0.709617	−	0.704587i	$-0.248868\pi$
$109$	−290.623	−	503.374i	−0.255382	−	0.442335i	−0.964999	+	0.262253i	$0.915535\pi$
$110$	133.408	−	231.070i	0.115636	−	0.200288i
$111$		0			0
$112$	−18.9618	+	430.046i	−0.0159975	+	0.362817i
$113$	708.244			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$113$	708.244			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$114$		0			0
$115$	−24.2528	−	42.0071i	−0.0196660	−	0.0340625i
$116$	475.378	+	823.379i	0.380498	+	0.659042i
$117$		0			0
$118$	−2098.88			−1.63744
$119$	−229.203	−	146.157i	−0.176563	−	0.112590i
$120$		0			0
$121$	−1663.55	+	2881.36i	−1.24985	+	2.16481i
$122$	−1121.13	−	1941.86i	−0.831988	−	1.44104i
$123$		0			0
$124$	492.091	−	852.326i	0.356380	−	0.617267i
$125$	−207.041			−0.148146
$126$		0			0
$127$	2348.04			1.64059			0.820296	−	0.571939i	$-0.193809\pi$
$127$	2348.04			1.64059			0.820296	+	0.571939i	$0.193809\pi$
$128$	1305.74	−	2261.62i	0.901661	−	1.56172i
$129$		0			0
$130$	69.9234	+	121.111i	0.0471745	+	0.0817087i
$131$	1202.91	−	2083.50i	0.802279	−	1.38959i	−0.115834	−	0.993269i	$-0.536954\pi$
$131$	1202.91	−	2083.50i	0.802279	−	1.38959i	0.918113	−	0.396320i	$-0.129713\pi$
$132$		0			0
$133$	−70.7873	+	1605.43i	−0.0461507	+	1.04668i
$134$	−3786.36			−2.44098
$135$		0			0
$136$	−212.846	−	368.661i	−0.134202	−	0.232444i
$137$	593.775	+	1028.45i	0.370289	+	0.641360i	0.989610	−	0.143778i	$-0.0459252\pi$
$137$	593.775	+	1028.45i	0.370289	+	0.641360i	−0.619320	+	0.785138i	$0.712592\pi$
$138$		0			0
$139$	−712.439			−0.434736			−0.217368	−	0.976090i	$-0.569747\pi$
$139$	−712.439			−0.434736			−0.217368	+	0.976090i	$0.569747\pi$
$140$	193.231	−	100.484i	0.116650	−	0.0606604i
$141$		0			0
$142$	−831.849	+	1440.81i	−0.491600	+	0.851477i
$143$	−1220.73	−	2114.36i	−0.713863	−	1.23645i
$144$		0			0
$145$	27.8782	−	48.2865i	0.0159666	−	0.0276550i
$146$	−3662.67			−2.07620
$147$		0			0
$148$	−4095.89			−2.27486
$149$	1104.62	−	1913.26i	0.607342	−	1.05195i	−0.384335	−	0.923194i	$-0.625569\pi$
$149$	1104.62	−	1913.26i	0.607342	−	1.05195i	0.991677	−	0.128753i	$-0.0410975\pi$
$150$		0			0
$151$	273.491	+	473.701i	0.147394	+	0.255293i	0.930263	−	0.366892i	$-0.119578\pi$
$151$	273.491	+	473.701i	0.147394	+	0.255293i	−0.782870	+	0.622185i	$0.786245\pi$
$152$	−1258.26	+	2179.37i	−0.671436	+	1.16296i
$153$		0			0
$154$	−5279.24	+	2745.31i	−2.76242	+	1.43651i
$155$	−57.7166			−0.0299091
$156$		0			0
$157$	−935.096	−	1619.63i	−0.475343	−	0.823318i	0.524258	−	0.851559i	$-0.324343\pi$
$157$	−935.096	−	1619.63i	−0.475343	−	0.823318i	−0.999601	+	0.0282414i	$0.991009\pi$
$158$	174.648	+	302.500i	0.0879385	+	0.152314i
$159$		0			0
$160$	−101.816			−0.0503078
$161$	−47.6504	+	1080.69i	−0.0233253	+	0.529010i
$162$		0			0
$163$	1518.70	−	2630.46i	0.729777	−	1.26401i	−0.227200	−	0.973848i	$-0.572957\pi$
$163$	1518.70	−	2630.46i	0.729777	−	1.26401i	0.956977	−	0.290163i	$-0.0937096\pi$
$164$	2533.02	+	4387.32i	1.20607	+	2.08898i
$165$		0			0
$166$	2750.36	−	4763.76i	1.28596	−	2.22735i
$167$	2967.09			1.37485			0.687426	−	0.726255i	$-0.258741\pi$
$167$	2967.09			1.37485			0.687426	+	0.726255i	$0.258741\pi$
$168$		0			0
$169$	−917.358			−0.417550
$170$	−28.6907	+	49.6937i	−0.0129440	+	0.0224196i
$171$		0			0
$172$	1669.57	+	2891.78i	0.740138	+	1.28196i
$173$	1933.41	−	3348.76i	0.849677	−	1.47168i	−0.0318190	−	0.999494i	$-0.510130\pi$
$173$	1933.41	−	3348.76i	0.849677	−	1.47168i	0.881496	−	0.472191i	$-0.156537\pi$
$174$		0			0
$175$	1941.17	+	1237.84i	0.838508	+	0.534696i
$176$	−1586.33			−0.679399
$177$		0			0
$178$	−3565.30	−	6175.28i	−1.50129	−	2.60032i
$179$	−167.363	−	289.881i	−0.0698844	−	0.121043i	0.828966	−	0.559299i	$-0.188930\pi$
$179$	−167.363	−	289.881i	−0.0698844	−	0.121043i	−0.898850	+	0.438256i	$0.855596\pi$
$180$		0			0
$181$	−1564.56			−0.642502			−0.321251	−	0.946994i	$-0.604103\pi$
$181$	−1564.56			−0.642502			−0.321251	+	0.946994i	$0.604103\pi$
$182$	137.381	−	3115.75i	0.0559525	−	1.26898i
$183$		0			0
$184$	−846.995	+	1467.04i	−0.339355	+	0.587780i
$185$	120.100	+	208.020i	0.0477294	+	0.0826698i
$186$		0			0
$187$	500.884	−	867.557i	0.195873	−	0.339262i
$188$	6373.33			2.47246
$189$		0			0
$190$	339.215			0.129522
$191$	−1533.57	+	2656.22i	−0.580971	+	1.00627i	0.414394	+	0.910098i	$0.363994\pi$
$191$	−1533.57	+	2656.22i	−0.580971	+	1.00627i	−0.995365	+	0.0961730i	$0.969340\pi$
$192$		0			0
$193$	1111.80	+	1925.69i	0.414658	+	0.718209i	0.995392	−	0.0958843i	$-0.0305679\pi$
$193$	1111.80	+	1925.69i	0.414658	+	0.718209i	−0.580734	+	0.814093i	$0.697235\pi$
$194$	−3840.07	+	6651.19i	−1.42114	+	2.46148i
$195$		0			0
$196$	−4838.32	−	427.498i	−1.76324	−	0.155794i
$197$	1856.18			0.671306			0.335653	−	0.941986i	$-0.391043\pi$
$197$	1856.18			0.671306			0.335653	+	0.941986i	$0.391043\pi$
$198$		0			0
$199$	496.801	+	860.485i	0.176971	+	0.306523i	0.940842	−	0.338846i	$-0.110037\pi$
$199$	496.801	+	860.485i	0.176971	+	0.306523i	−0.763870	+	0.645370i	$0.776703\pi$
$200$	1802.65	+	3122.28i	0.637333	+	1.10389i
$201$		0			0
$202$	5676.02			1.97704
$203$	−1103.20	+	573.684i	−0.381425	+	0.198349i
$204$		0			0
$205$	148.547	−	257.291i	0.0506097	−	0.0876585i
$206$	1142.43	+	1978.75i	0.386392	+	0.669251i
$207$		0			0
$208$	415.723	−	720.053i	0.138583	−	0.240032i
$209$	−5922.03			−1.95998
$210$		0			0
$211$	−545.079			−0.177843			−0.0889213	−	0.996039i	$-0.528342\pi$
$211$	−545.079			−0.177843			−0.0889213	+	0.996039i	$0.528342\pi$
$212$	−1221.12	+	2115.04i	−0.395599	+	0.685197i
$213$		0			0
$214$	607.509	+	1052.24i	0.194058	+	0.336118i
$215$	97.9109	−	169.587i	0.0310580	−	0.0537940i
$216$		0			0
$217$	1085.28	+	692.059i	0.339511	+	0.216498i
$218$	2736.23			0.850097
$219$		0			0
$220$	401.309	+	695.088i	0.122983	+	0.213013i
$221$	262.529	+	454.713i	0.0799077	+	0.138404i
$222$		0			0
$223$	−3446.72			−1.03502			−0.517510	−	0.855677i	$-0.673141\pi$
$223$	−3446.72			−1.03502			−0.517510	+	0.855677i	$0.673141\pi$
$224$	1914.51	+	1220.83i	0.571064	+	0.364154i
$225$		0			0
$226$	−1667.04	+	2887.40i	−0.490663	+	0.849853i
$227$	243.149	+	421.146i	0.0710940	+	0.123138i	0.899381	−	0.437166i	$-0.144018\pi$
$227$	243.149	+	421.146i	0.0710940	+	0.123138i	−0.828287	+	0.560304i	$0.810684\pi$
$228$		0			0
$229$	−2107.34	+	3650.02i	−0.608109	+	1.05328i	0.383442	+	0.923565i	$0.374738\pi$
$229$	−2107.34	+	3650.02i	−0.608109	+	1.05328i	−0.991552	+	0.129712i	$0.958595\pi$
$230$	228.342			0.0654627
$231$		0			0
$232$	−1947.21			−0.551038
$233$	549.671	−	952.058i	0.154550	−	0.267688i	−0.778345	−	0.627837i	$-0.783941\pi$
$233$	549.671	−	952.058i	0.154550	−	0.267688i	0.932895	+	0.360148i	$0.117274\pi$
$234$		0			0
$235$	−186.880	−	323.685i	−0.0518753	−	0.0898506i
$236$	3156.85	−	5467.83i	0.870736	−	1.50816i
$237$		0			0
$238$	1135.35	−	590.404i	0.309217	−	0.160799i
$239$	4558.99			1.23388			0.616939	−	0.787011i	$-0.288373\pi$
$239$	4558.99			1.23388			0.616939	+	0.787011i	$0.288373\pi$
$240$		0			0
$241$	544.702	+	943.452i	0.145591	+	0.252171i	0.929593	−	0.368587i	$-0.120158\pi$
$241$	544.702	+	943.452i	0.145591	+	0.252171i	−0.784002	+	0.620758i	$0.786825\pi$
$242$	−7831.22	−	13564.1i	−2.08021	−	3.60302i
$243$		0			0
$244$	6745.01			1.76969
$245$	120.158	+	258.261i	0.0313332	+	0.0673457i
$246$		0			0
$247$	1551.96	−	2688.07i	0.399793	−	0.692462i
$248$	1007.84	+	1745.62i	0.258055	+	0.446964i
$249$		0			0
$250$	487.325	−	844.072i	0.123285	−	0.213535i
$251$	6356.75			1.59855			0.799273	−	0.600969i	$-0.205218\pi$
$251$	6356.75			1.59855			0.799273	+	0.600969i	$0.205218\pi$
$252$		0			0
$253$	−3986.41			−0.990606
$254$	−5526.75	+	9572.60i	−1.36527	+	2.36472i
$255$		0			0
$256$	3094.44	+	5359.73i	0.755478	+	1.30853i
$257$	531.716	−	920.959i	0.129056	−	0.223532i	−0.794255	−	0.607585i	$-0.792138\pi$
$257$	531.716	−	920.959i	0.129056	−	0.223532i	0.923311	+	0.384052i	$0.125472\pi$
$258$		0			0
$259$	235.965	−	5351.60i	0.0566106	−	1.28391i
$260$	−420.677			−0.100343
$261$		0			0
$262$	5662.73	+	9808.13i	1.33528	+	2.31278i
$263$	−1837.29	−	3182.29i	−0.430770	−	0.746115i	0.566170	−	0.824288i	$-0.308425\pi$
$263$	−1837.29	−	3182.29i	−0.430770	−	0.746115i	−0.996940	+	0.0781735i	$0.975091\pi$
$264$		0			0
$265$	143.224			0.0332006
$266$	−6378.47	−	4067.40i	−1.47026	−	0.937549i
$267$		0			0
$268$	5694.93	−	9863.91i	1.29803	−	2.24826i
$269$	−3479.97	−	6027.48i	−0.788764	−	1.36618i	−0.926725	−	0.375741i	$-0.877388\pi$
$269$	−3479.97	−	6027.48i	−0.788764	−	1.36618i	0.137961	−	0.990438i	$-0.455945\pi$
$270$		0			0
$271$	3297.89	−	5712.11i	0.739235	−	1.28039i	−0.213606	−	0.976920i	$-0.568521\pi$
$271$	3297.89	−	5712.11i	0.739235	−	1.28039i	0.952840	−	0.303472i	$-0.0981459\pi$
$272$	341.155			0.0760499
$273$		0			0
$274$	−5590.43			−1.23259
$275$	−4242.11	+	7347.55i	−0.930214	+	1.61118i
$276$		0			0
$277$	1560.53	+	2702.92i	0.338495	+	0.586290i	0.984150	−	0.177339i	$-0.0567489\pi$
$277$	1560.53	+	2702.92i	0.338495	+	0.586290i	−0.645655	+	0.763629i	$0.723416\pi$
$278$	1676.91	−	2904.50i	0.361779	−	0.626620i
$279$		0			0
$280$	−19.6489	+	445.630i	−0.00419374	+	0.0951124i
$281$	1662.38			0.352915			0.176457	−	0.984308i	$-0.443536\pi$
$281$	1662.38			0.352915			0.176457	+	0.984308i	$0.443536\pi$
$282$		0			0
$283$	−226.639	−	392.551i	−0.0476053	−	0.0824548i	0.841241	−	0.540661i	$-0.181826\pi$
$283$	−226.639	−	392.551i	−0.0476053	−	0.0824548i	−0.888846	+	0.458206i	$0.848492\pi$
$284$	−2502.31	−	4334.12i	−0.522833	−	0.905574i
$285$		0			0
$286$	11493.2			2.37625
$287$	−5878.31	+	3056.84i	−1.20901	+	0.628709i
$288$		0			0
$289$	2348.78	−	4068.21i	0.478075	−	0.828049i
$290$	131.238	+	227.310i	0.0265743	+	0.0460280i
$291$		0			0
$292$	5508.89	−	9541.68i	1.10405	−	1.91228i
$293$	−772.774			−0.154082			−0.0770408	−	0.997028i	$-0.524547\pi$
$293$	−772.774			−0.154082			−0.0770408	+	0.997028i	$0.524547\pi$
$294$		0			0
$295$	−370.263			−0.0730764
$296$	4194.33	−	7264.79i	0.823616	−	1.42654i
$297$		0			0
$298$	5200.03	+	9006.72i	1.01084	+	1.75082i
$299$	1044.70	−	1809.47i	0.202062	−	0.349982i
$300$		0			0
$301$	−3874.53	+	2014.83i	−0.741941	+	0.385824i
$302$	−2574.94			−0.490633
$303$		0			0
$304$	−1008.38	−	1746.57i	−0.190246	−	0.329516i
$305$	−197.778	−	342.562i	−0.0371303	−	0.0643116i
$306$		0			0
$307$	4193.64			0.779621			0.389810	−	0.920895i	$-0.372541\pi$
$307$	4193.64			0.779621			0.389810	+	0.920895i	$0.372541\pi$
$308$	788.466	−	17882.1i	0.145867	−	3.30821i
$309$		0			0
$310$	135.851	−	235.302i	0.0248898	−	0.0431104i
$311$	199.870	+	346.185i	0.0364424	+	0.0631201i	0.883671	−	0.468108i	$-0.155064\pi$
$311$	199.870	+	346.185i	0.0364424	+	0.0631201i	−0.847229	+	0.531228i	$0.821731\pi$
$312$		0			0
$313$	−1865.24	+	3230.69i	−0.336836	+	0.583417i	−0.983836	−	0.179073i	$-0.942690\pi$
$313$	−1865.24	+	3230.69i	−0.336836	+	0.583417i	0.647000	+	0.762490i	$0.276023\pi$
$314$	8803.99			1.58229
$315$		0			0
$316$	−1050.73			−0.187051
$317$	−4186.74	+	7251.64i	−0.741800	+	1.28483i	0.209875	+	0.977728i	$0.432694\pi$
$317$	−4186.74	+	7251.64i	−0.741800	+	1.28483i	−0.951675	+	0.307107i	$0.900639\pi$
$318$		0			0
$319$	−2291.15	−	3968.40i	−0.402132	−	0.696513i
$320$	316.859	−	548.816i	0.0553530	−	0.0958741i
$321$		0			0
$322$	−4293.66	−	2737.96i	−0.743094	−	0.473853i
$323$	1273.59			0.219394
$324$		0			0
$325$	−2223.42	−	3851.08i	−0.379487	−	0.657290i
$326$	7149.32	+	12383.0i	1.21461	+	2.10377i
$327$		0			0
$328$	−10375.6			−1.74664
$329$	−367.169	+	8327.27i	−0.0615280	+	1.39543i
$330$		0			0
$331$	674.858	−	1168.89i	0.112065	−	0.194102i	−0.804538	−	0.593902i	$-0.797587\pi$
$331$	674.858	−	1168.89i	0.112065	−	0.194102i	0.916603	+	0.399799i	$0.130920\pi$
$332$	8273.43	+	14330.0i	1.36766	+	2.36886i
$333$		0			0
$334$	−6983.83	+	12096.4i	−1.14413	+	1.98169i
$335$	−667.950			−0.108937
$336$		0			0
$337$	−6629.72			−1.07164			−0.535822	−	0.844331i	$-0.679998\pi$
$337$	−6629.72			−1.07164			−0.535822	+	0.844331i	$0.679998\pi$
$338$	2159.25	−	3739.92i	0.347478	−	0.601849i
$339$		0			0
$340$	−86.3052	−	149.485i	−0.0137663	−	0.0238440i
$341$	−2371.70	+	4107.91i	−0.376642	+	0.652363i
$342$		0			0
$343$	837.297	−	6297.03i	0.131807	−	0.991275i
$344$	−6838.79			−1.07187
$345$		0			0
$346$	9101.57	+	15764.4i	1.41417	+	2.44942i
$347$	−2476.47	−	4289.37i	−0.383123	−	0.663589i	0.608384	−	0.793643i	$-0.291818\pi$
$347$	−2476.47	−	4289.37i	−0.383123	−	0.663589i	−0.991507	+	0.130054i	$0.958485\pi$
$348$		0			0
$349$	−4498.12			−0.689911			−0.344955	−	0.938619i	$-0.612106\pi$
$349$	−4498.12			−0.689911			−0.344955	+	0.938619i	$0.612106\pi$
$350$	−9615.54	+	5000.27i	−1.46849	+	0.763645i
$351$		0			0
$352$	−4183.83	+	7246.61i	−0.633520	+	1.09729i
$353$	806.677	+	1397.21i	0.121629	+	0.210668i	0.920410	−	0.390954i	$-0.127855\pi$
$353$	806.677	+	1397.21i	0.121629	+	0.210668i	−0.798781	+	0.601622i	$0.794521\pi$
$354$		0			0
$355$	−146.746	+	254.172i	−0.0219394	+	0.0380001i
$356$	21449.7			3.19335
$357$		0			0
$358$	1575.73			0.232626
$359$	−6593.45	+	11420.2i	−0.969328	+	1.67893i	−0.271821	+	0.962348i	$0.587626\pi$
$359$	−6593.45	+	11420.2i	−0.969328	+	1.67893i	−0.697507	+	0.716578i	$0.745708\pi$
$360$		0			0
$361$	−334.959	−	580.167i	−0.0488350	−	0.0845847i
$362$	3682.61	−	6378.47i	0.534679	−	0.926091i
$363$		0			0
$364$	7910.26	+	5044.18i	1.13904	+	0.726338i
$365$	−646.130			−0.0926575
$366$		0			0
$367$	−2551.69	−	4419.66i	−0.362936	−	0.628623i	0.625507	−	0.780219i	$-0.284892\pi$
$367$	−2551.69	−	4419.66i	−0.362936	−	0.628623i	−0.988443	+	0.151596i	$0.951559\pi$
$368$	−678.792	−	1175.70i	−0.0961535	−	0.166543i
$369$		0			0
$370$	−1130.75			−0.158878
$371$	−2693.12	−	1717.34i	−0.376873	−	0.240323i
$372$		0			0
$373$	729.593	−	1263.69i	0.101279	−	0.175420i	−0.810933	−	0.585139i	$-0.801040\pi$
$373$	729.593	−	1263.69i	0.101279	−	0.175420i	0.912212	+	0.409719i	$0.134373\pi$
$374$	2357.93	+	4084.05i	0.326004	+	0.564656i
$375$		0			0
$376$	−6526.51	+	11304.2i	−0.895157	+	1.55046i
$377$	2401.73			0.328104
$378$		0			0
$379$	2332.75			0.316162			0.158081	−	0.987426i	$-0.449469\pi$
$379$	2332.75			0.316162			0.158081	+	0.987426i	$0.449469\pi$
$380$	−510.200	+	883.693i	−0.0688756	+	0.119296i
$381$		0			0
$382$	−7219.34	−	12504.3i	−0.966946	−	1.67480i
$383$	2825.55	−	4894.00i	0.376969	−	0.652929i	−0.613651	−	0.789578i	$-0.710300\pi$
$383$	2825.55	−	4894.00i	0.376969	−	0.652929i	0.990620	+	0.136648i	$0.0436330\pi$
$384$		0			0
$385$	−931.307	+	484.298i	−0.123283	+	0.0641094i
$386$	−10467.7			−1.38028
$387$		0			0
$388$	−11551.4	−	20007.6i	−1.51143	−	2.61787i
$389$	4520.41	+	7829.58i	0.589188	+	1.02050i	0.994339	+	0.106253i	$0.0338854\pi$
$389$	4520.41	+	7829.58i	0.589188	+	1.02050i	−0.405152	+	0.914250i	$0.632781\pi$
$390$		0			0
$391$	857.314			0.110886
$392$	5712.85	−	8143.86i	0.736078	−	1.04930i
$393$		0			0
$394$	−4369.01	+	7567.35i	−0.558649	+	0.967608i
$395$	30.8097	+	53.3639i	0.00392456	+	0.00679754i
$396$		0			0
$397$	−1762.18	+	3052.18i	−0.222774	+	0.385855i	−0.955649	−	0.294507i	$-0.904844\pi$
$397$	−1762.18	+	3052.18i	−0.222774	+	0.385855i	0.732876	+	0.680363i	$0.238178\pi$
$398$	−4677.41			−0.589089
$399$		0			0
$400$	−2889.33			−0.361166
$401$	2234.91	−	3870.97i	0.278319	−	0.482062i	−0.692648	−	0.721276i	$-0.743556\pi$
$401$	2234.91	−	3870.97i	0.278319	−	0.482062i	0.970967	+	0.239213i	$0.0768895\pi$
$402$		0			0
$403$	−1243.08	−	2153.08i	−0.153654	−	0.266136i
$404$	−8537.09	+	14786.7i	−1.05133	+	1.82095i
$405$		0			0
$406$	257.847	−	5847.88i	0.0315191	−	0.714841i
$407$	19740.7			2.40420
$408$		0			0
$409$	3766.18	+	6523.22i	0.455320	+	0.788637i	0.998707	−	0.0508458i	$-0.0161917\pi$
$409$	3766.18	+	6523.22i	0.455320	+	0.788637i	−0.543387	+	0.839482i	$0.682858\pi$
$410$	699.290	+	1211.21i	0.0842329	+	0.145896i
$411$		0			0
$412$	−6873.15			−0.821882
$413$	6962.29	+	4439.68i	0.829520	+	0.528965i
$414$		0			0
$415$	485.189	−	840.373i	0.0573904	−	0.0994031i
$416$	−2192.88	−	3798.17i	−0.258449	−	0.447646i
$417$		0			0
$418$	13939.1	−	24143.2i	1.63106	−	2.82508i
$419$	−15486.4			−1.80563			−0.902814	−	0.430031i	$-0.858502\pi$
$419$	−15486.4			−1.80563			−0.902814	+	0.430031i	$0.858502\pi$
$420$		0			0
$421$	4408.87			0.510393			0.255196	−	0.966889i	$-0.417860\pi$
$421$	4408.87			0.510393			0.255196	+	0.966889i	$0.417860\pi$
$422$	1282.99	−	2222.20i	0.147997	−	0.256339i
$423$		0			0
$424$	−2500.94	−	4331.75i	−0.286454	−	0.496152i
$425$	912.305	−	1580.16i	0.104125	−	0.180350i
$426$		0			0
$427$	−388.582	+	8812.90i	−0.0440393	+	0.998796i
$428$	−3654.93			−0.412774
$429$		0			0
$430$	460.918	+	798.334i	0.0516918	+	0.0895328i
$431$	−5178.32	−	8969.11i	−0.578726	−	1.00238i	−0.995626	−	0.0934300i	$-0.970217\pi$
$431$	−5178.32	−	8969.11i	−0.578726	−	1.00238i	0.416900	−	0.908952i	$-0.363116\pi$
$432$		0			0
$433$	−1398.15			−0.155175			−0.0775875	−	0.996986i	$-0.524722\pi$
$433$	−1398.15			−0.155175			−0.0775875	+	0.996986i	$0.524722\pi$
$434$	−5375.92	+	2795.58i	−0.594590	+	0.309199i
$435$		0			0
$436$	−4115.47	+	7128.20i	−0.452053	+	0.782979i
$437$	−2534.04	−	4389.09i	−0.277390	−	0.480454i
$438$		0			0
$439$	1724.66	−	2987.20i	0.187502	−	0.324763i	−0.756915	−	0.653514i	$-0.773294\pi$
$439$	1724.66	−	2987.20i	0.187502	−	0.324763i	0.944417	+	0.328750i	$0.106627\pi$
$440$	−1643.82			−0.178104
$441$		0			0
$442$	−2471.73			−0.265991
$443$	1122.33	−	1943.93i	0.120369	−	0.208485i	−0.799544	−	0.600607i	$-0.794926\pi$
$443$	1122.33	−	1943.93i	0.120369	−	0.208485i	0.919913	+	0.392122i	$0.128259\pi$
$444$		0			0
$445$	−628.953	−	1089.38i	−0.0670005	−	0.116048i
$446$	8112.78	−	14051.7i	0.861325	−	1.49186i
$447$		0			0
$448$	−12538.7	+	6520.39i	−1.32232	+	0.687633i
$449$	7639.18			0.802929			0.401465	−	0.915875i	$-0.368501\pi$
$449$	7639.18			0.802929			0.401465	+	0.915875i	$0.368501\pi$
$450$		0			0
$451$	−12208.3	−	21145.3i	−1.27464	−	2.20775i
$452$	−5014.66	−	8685.65i	−0.521836	−	0.903847i
$453$		0			0
$454$	−2289.26			−0.236652
$455$	24.2353	−	549.648i	0.00249707	−	0.0566327i
$456$		0			0
$457$	−270.412	+	468.367i	−0.0276790	+	0.0479415i	−0.879533	−	0.475838i	$-0.842145\pi$
$457$	−270.412	+	468.367i	−0.0276790	+	0.0479415i	0.851854	+	0.523779i	$0.175478\pi$
$458$	−9920.38	−	17182.6i	−1.01212	−	1.75304i
$459$		0			0
$460$	−343.441	+	594.857i	−0.0348109	+	0.0602942i
$461$	−8627.25			−0.871608			−0.435804	−	0.900042i	$-0.643536\pi$
$461$	−8627.25			−0.871608			−0.435804	+	0.900042i	$0.643536\pi$
$462$		0			0
$463$	4497.71			0.451461			0.225730	−	0.974190i	$-0.427523\pi$
$463$	4497.71			0.451461			0.225730	+	0.974190i	$0.427523\pi$
$464$	780.260	−	1351.45i	0.0780661	−	0.135214i
$465$		0			0
$466$	2587.59	+	4481.84i	0.257227	+	0.445531i
$467$	−1246.53	+	2159.06i	−0.123518	+	0.213939i	−0.921153	−	0.389202i	$-0.872751\pi$
$467$	−1246.53	+	2159.06i	−0.123518	+	0.213939i	0.797635	+	0.603141i	$0.206084\pi$
$468$		0			0
$469$	12559.9	+	8009.14i	1.23659	+	0.788546i
$470$	1759.48			0.172679
$471$		0			0
$472$	6465.45	+	11198.5i	0.630501	+	1.09206i
$473$	−8046.75	−	13937.4i	−0.782219	−	1.35484i
$474$		0			0
$475$	−10786.3			−1.04192
$476$	−169.567	+	3845.72i	−0.0163279	+	0.370311i
$477$		0			0
$478$	−10730.8	+	18586.3i	−1.02681	+	1.77849i
$479$	−4169.63	−	7222.02i	−0.397736	−	0.688899i	0.595710	−	0.803199i	$-0.296871\pi$
$479$	−4169.63	−	7222.02i	−0.397736	−	0.688899i	−0.993446	+	0.114301i	$0.963537\pi$
$480$		0			0
$481$	−5173.36	+	8960.52i	−0.490405	+	0.849407i
$482$	−5128.41			−0.484632
$483$		0			0
$484$	47114.6			4.42474
$485$	−677.424	+	1173.33i	−0.0634232	+	0.109852i
$486$		0			0
$487$	1552.42	+	2688.88i	0.144450	+	0.250194i	0.929167	−	0.369659i	$-0.120525\pi$
$487$	1552.42	+	2688.88i	0.144450	+	0.250194i	−0.784718	+	0.619853i	$0.787192\pi$
$488$	−6907.12	+	11963.5i	−0.640719	+	1.10976i
$489$		0			0
$490$	−1335.71	−	118.019i	−0.123146	−	0.0108807i
$491$	496.579			0.0456421			0.0228211	−	0.999740i	$-0.492735\pi$
$491$	496.579			0.0456421			0.0228211	+	0.999740i	$0.492735\pi$
$492$		0			0
$493$	492.734	+	853.440i	0.0450134	+	0.0779656i
$494$	7305.90	+	12654.2i	0.665401	+	1.15251i
$495$		0			0
$496$	−1615.38			−0.146236
$497$	5807.04	−	3019.78i	0.524107	−	0.272546i
$498$		0			0
$499$	6626.79	−	11477.9i	0.594501	−	1.02971i	−0.399116	−	0.916900i	$-0.630683\pi$
$499$	6626.79	−	11477.9i	0.594501	−	1.02971i	0.993617	−	0.112805i	$-0.0359836\pi$
$500$	1465.94	+	2539.07i	0.131117	+	0.227102i
$501$		0			0
$502$	−14962.3	+	25915.5i	−1.33028	+	2.30411i
$503$	1625.59			0.144099			0.0720493	−	0.997401i	$-0.477046\pi$
$503$	1625.59			0.144099			0.0720493	+	0.997401i	$0.477046\pi$
$504$		0			0
$505$	1001.30			0.0882325
$506$	9383.07	−	16252.0i	0.824364	−	1.42784i
$507$		0			0
$508$	−16625.2	−	28795.6i	−1.45201	−	2.51496i
$509$	−3541.52	+	6134.10i	−0.308399	+	0.534163i	−0.978012	−	0.208547i	$-0.933127\pi$
$509$	−3541.52	+	6134.10i	−0.308399	+	0.534163i	0.669613	+	0.742710i	$0.266460\pi$
$510$		0			0
$511$	12149.6	+	7747.50i	1.05179	+	0.670703i
$512$	−8242.42			−0.711459
$513$		0			0
$514$	2503.07	+	4335.44i	0.214797	+	0.372039i
$515$	201.535	+	349.070i	0.0172441	+	0.0298677i
$516$		0			0
$517$	−30717.2			−2.61304
$518$	21262.2	+	13558.4i	1.80349	+	1.15004i
$519$		0			0
$520$	430.788	−	746.146i	0.0363294	−	0.0629244i
$521$	−8282.67	−	14346.0i	−0.696489	−	1.20635i	−0.969676	−	0.244393i	$-0.921411\pi$
$521$	−8282.67	−	14346.0i	−0.696489	−	1.20635i	0.273188	−	0.961961i	$-0.411922\pi$
$522$		0			0
$523$	3236.34	−	5605.51i	0.270584	−	0.468665i	−0.698428	−	0.715681i	$-0.746117\pi$
$523$	3236.34	−	5605.51i	0.270584	−	0.468665i	0.969011	+	0.247016i	$0.0794499\pi$
$524$	−34068.4			−2.84024
$525$		0			0
$526$	17298.2			1.43391
$527$	510.057	−	883.445i	0.0421602	−	0.0730236i
$528$		0			0
$529$	4377.71	+	7582.42i	0.359802	+	0.623196i
$530$	−337.115	+	583.900i	−0.0276289	+	0.0478547i
$531$		0			0
$532$	20189.7	−	10499.0i	1.64536	−	0.855621i
$533$	12797.5			1.04000
$534$		0			0
$535$	107.170	+	185.624i	0.00866051	+	0.0150005i
$536$	11663.6	+	20202.0i	0.939909	+	1.62797i
$537$		0			0
$538$	32764.1			2.62558
$539$	23319.0	+	2060.39i	1.86349	+	0.164652i
$540$		0			0
$541$	1694.46	−	2934.89i	0.134659	−	0.233236i	−0.790808	−	0.612064i	$-0.790339\pi$
$541$	1694.46	−	2934.89i	0.134659	−	0.233236i	0.925467	+	0.378828i	$0.123673\pi$
$542$	15524.9	+	26890.0i	1.23036	+	2.13104i
$543$		0			0
$544$	899.772	−	1558.45i	0.0709144	−	0.122827i
$545$	482.698			0.0379385
$546$		0			0
$547$	10055.2			0.785980			0.392990	−	0.919543i	$-0.371441\pi$
$547$	10055.2			0.785980			0.392990	+	0.919543i	$0.371441\pi$
$548$	8408.36	−	14563.7i	0.655452	−	1.13528i
$549$		0			0
$550$	−19969.9	−	34588.8i	−1.54821	−	2.68159i
$551$	2912.84	−	5045.18i	0.225211	−	0.390076i
$552$		0			0
$553$	60.5328	−	1372.86i	0.00465482	−	0.105570i
$554$	−14692.5			−1.12676
$555$		0			0
$556$	5044.37	+	8737.11i	0.384764	+	0.666431i
$557$	2816.25	+	4877.90i	0.214234	+	0.371065i	0.953035	−	0.302859i	$-0.0979410\pi$
$557$	2816.25	+	4877.90i	0.214234	+	0.371065i	−0.738801	+	0.673924i	$0.764608\pi$
$558$		0			0
$559$	8435.10			0.638223
$560$	−301.413	−	192.204i	−0.0227447	−	0.0145037i
$561$		0			0
$562$	−3912.84	+	6777.24i	−0.293689	+	0.508684i
$563$	−725.207	−	1256.10i	−0.0542874	−	0.0940286i	0.837605	−	0.546277i	$-0.183955\pi$
$563$	−725.207	−	1256.10i	−0.0542874	−	0.0940286i	−0.891892	+	0.452248i	$0.850622\pi$
$564$		0			0
$565$	−294.082	+	509.364i	−0.0218975	+	0.0379276i
$566$	2133.82			0.158465
$567$		0			0
$568$	10249.8			0.757169
$569$	8015.20	−	13882.7i	0.590536	−	1.02284i	−0.403625	−	0.914925i	$-0.632250\pi$
$569$	8015.20	−	13882.7i	0.590536	−	1.02284i	0.994160	−	0.107913i	$-0.0344168\pi$
$570$		0			0
$571$	8270.39	+	14324.7i	0.606139	+	1.04986i	0.991870	+	0.127252i	$0.0406157\pi$
$571$	8270.39	+	14324.7i	0.606139	+	1.04986i	−0.385732	+	0.922611i	$0.626051\pi$
$572$	−17286.5	+	29941.2i	−1.26361	+	2.18864i
$573$		0			0
$574$	1373.92	−	31160.0i	0.0999065	−	2.26584i
$575$	−7260.80			−0.526602
$576$		0			0
$577$	1019.63	+	1766.06i	0.0735666	+	0.127421i	0.900462	−	0.434935i	$-0.143229\pi$
$577$	1019.63	+	1766.06i	0.0735666	+	0.127421i	−0.826895	+	0.562356i	$0.809895\pi$
$578$	11057.0	+	19151.2i	0.795690	+	1.37818i
$579$		0			0
$580$	−789.558			−0.0565252
$581$	−19199.9	+	9984.34i	−1.37099	+	0.712944i
$582$		0			0
$583$	5885.37	−	10193.8i	0.418091	−	0.724155i
$584$	11282.6	+	19542.0i	0.799446	+	1.38468i
$585$		0			0
$586$	1818.93	−	3150.48i	0.128224	−	0.222090i
$587$	20392.1			1.43385			0.716927	−	0.697148i	$-0.245548\pi$
$587$	20392.1			1.43385			0.716927	+	0.697148i	$0.245548\pi$
$588$		0			0
$589$	−6030.49			−0.421871
$590$	871.512	−	1509.50i	0.0608129	−	0.105331i
$591$		0			0
$592$	3361.38	+	5822.09i	0.233365	+	0.404200i
$593$	10134.5	−	17553.4i	0.701810	−	1.21557i	−0.266020	−	0.963967i	$-0.585709\pi$
$593$	10134.5	−	17553.4i	0.701810	−	1.21557i	0.967830	−	0.251604i	$-0.0809579\pi$
$594$		0			0
$595$	200.286	−	104.153i	0.0137999	−	0.00717622i
$596$	−31284.7			−2.15012
$597$		0			0
$598$	4917.96	+	8518.15i	0.336305	+	0.582497i
$599$	11158.9	+	19327.8i	0.761169	+	1.31838i	0.942248	+	0.334915i	$0.108708\pi$
$599$	11158.9	+	19327.8i	0.761169	+	1.31838i	−0.181079	+	0.983468i	$0.557959\pi$
$600$		0			0
$601$	1880.78			0.127652			0.0638259	−	0.997961i	$-0.479670\pi$
$601$	1880.78			0.127652			0.0638259	+	0.997961i	$0.479670\pi$
$602$	905.583	−	20538.3i	0.0613103	−	1.39050i
$603$		0			0
$604$	3872.87	−	6708.01i	0.260902	−	0.451896i
$605$	−1381.50	−	2392.83i	−0.0928364	−	0.160797i
$606$		0			0
$607$	8180.82	−	14169.6i	0.547033	−	0.947489i	−0.451443	−	0.892300i	$-0.649090\pi$
$607$	8180.82	−	14169.6i	0.547033	−	0.947489i	0.998476	−	0.0551891i	$-0.0175762\pi$
$608$	−10638.2			−0.709595
$609$		0			0
$610$	1862.09			0.123597
$611$	8049.92	−	13942.9i	0.533003	−	0.923188i
$612$		0			0
$613$	7960.70	+	13788.3i	0.524518	+	0.908492i	0.999592	+	0.0285467i	$0.00908792\pi$
$613$	7960.70	+	13788.3i	0.524518	+	0.908492i	−0.475074	+	0.879946i	$0.657579\pi$
$614$	−9870.84	+	17096.8i	−0.648786	+	1.12373i
$615$		0			0
$616$	30909.7	+	19710.4i	2.02174	+	1.28921i
$617$	7690.80			0.501815			0.250908	−	0.968011i	$-0.419271\pi$
$617$	7690.80			0.501815			0.250908	+	0.968011i	$0.419271\pi$
$618$		0			0
$619$	302.006	+	523.089i	0.0196101	+	0.0339657i	0.875664	−	0.482921i	$-0.160424\pi$
$619$	302.006	+	523.089i	0.0196101	+	0.0339657i	−0.856054	+	0.516887i	$0.827091\pi$
$620$	408.658	+	707.817i	0.0264712	+	0.0458494i
$621$		0			0
$622$	−1881.79			−0.121307
$623$	−1235.73	+	28025.8i	−0.0794676	+	1.80230i
$624$		0			0
$625$	−7683.43	+	13308.1i	−0.491739	+	0.851718i
$626$	−8780.67	−	15208.6i	−0.560617	−	0.971017i
$627$		0			0
$628$	−13241.8	+	22935.4i	−0.841407	+	1.45736i
$629$	−4245.43			−0.269120
$630$		0			0
$631$	−10806.1			−0.681752			−0.340876	−	0.940108i	$-0.610724\pi$
$631$	−10806.1			−0.681752			−0.340876	+	0.940108i	$0.610724\pi$
$632$	1075.98	−	1863.66i	0.0677220	−	0.117298i
$633$		0			0
$634$	−19709.2	−	34137.3i	−1.23462	−	2.13843i
$635$	−974.970	+	1688.70i	−0.0609300	+	0.105534i
$636$		0			0
$637$	−7046.34	+	10044.8i	−0.438283	+	0.624786i
$638$	21571.4			1.33859
$639$		0			0
$640$	1084.36	+	1878.17i	0.0669736	+	0.116002i
$641$	2223.81	+	3851.76i	0.137029	+	0.237340i	0.926371	−	0.376613i	$-0.122911\pi$
$641$	2223.81	+	3851.76i	0.137029	+	0.237340i	−0.789342	+	0.613954i	$0.789578\pi$
$642$		0			0
$643$	13531.3			0.829897			0.414949	−	0.909845i	$-0.363800\pi$
$643$	13531.3			0.829897			0.414949	+	0.909845i	$0.363800\pi$
$644$	13590.6	−	7067.40i	0.831593	−	0.432445i
$645$		0			0
$646$	−2997.73	+	5192.22i	−0.182576	+	0.316231i
$647$	−9488.46	−	16434.5i	−0.576553	−	0.998620i	−0.995871	−	0.0907801i	$-0.971064\pi$
$647$	−9488.46	−	16434.5i	−0.576553	−	0.998620i	0.419318	−	0.907840i	$-0.362269\pi$
$648$		0			0
$649$	−15214.9	+	26353.0i	−0.920243	+	1.59391i
$650$	20933.6			1.26321
$651$		0			0
$652$	−43012.1			−2.58357
$653$	4398.36	−	7618.19i	0.263585	−	0.456543i	−0.703607	−	0.710590i	$-0.748428\pi$
$653$	4398.36	−	7618.19i	0.263585	−	0.456543i	0.967192	+	0.254046i	$0.0817616\pi$
$654$		0			0
$655$	998.959	+	1730.25i	0.0595917	+	0.103216i
$656$	4157.56	−	7201.11i	0.247447	−	0.428592i
$657$		0			0
$658$	−33084.7	−	21097.3i	−1.96015	−	1.24994i
$659$	−24279.6			−1.43520			−0.717601	−	0.696455i	$-0.754760\pi$
$659$	−24279.6			−1.43520			−0.717601	+	0.696455i	$0.754760\pi$
$660$		0			0
$661$	12817.7	+	22200.8i	0.754234	+	1.30637i	0.945754	+	0.324883i	$0.105325\pi$
$661$	12817.7	+	22200.8i	0.754234	+	1.30637i	−0.191520	+	0.981489i	$0.561342\pi$
$662$	3176.91	+	5502.58i	0.186517	+	0.323057i
$663$		0			0
$664$	−33889.1			−1.98065
$665$	−1125.22	−	717.527i	−0.0656154	−	0.0418414i
$666$		0			0
$667$	1960.77	−	3396.16i	0.113825	−	0.197151i
$668$	−21008.2	−	36387.4i	−1.21682	−	2.10759i
$669$		0			0
$670$	1572.20	−	2723.13i	0.0906557	−	0.157020i
$671$	−32508.6			−1.87031
$672$		0			0
$673$	−23355.1			−1.33770			−0.668852	−	0.743396i	$-0.733214\pi$
$673$	−23355.1			−1.33770			−0.668852	+	0.743396i	$0.733214\pi$
$674$	15604.8	−	27028.3i	0.891803	−	1.54465i
$675$		0			0
$676$	6495.28	+	11250.2i	0.369554	+	0.640086i
$677$	8996.86	−	15583.0i	0.510750	−	0.884644i	−0.489173	−	0.872187i	$-0.662701\pi$
$677$	8996.86	−	15583.0i	0.510750	−	0.884644i	0.999922	−	0.0124573i	$-0.00396539\pi$
$678$		0			0
$679$	26807.0	−	13940.2i	1.51511	−	0.787887i
$680$	353.518			0.0199365
$681$		0			0
$682$	−11164.9	−	19338.1i	−0.626870	−	1.08577i
$683$	8965.46	+	15528.6i	0.502275	+	0.869966i	0.999997	+	0.00262913i	$0.000836880\pi$
$683$	8965.46	+	15528.6i	0.502275	+	0.869966i	−0.497721	+	0.867337i	$0.665830\pi$
$684$		0			0
$685$	−986.205			−0.0550087
$686$	23701.2	+	18235.3i	1.31912	+	1.01491i
$687$		0			0
$688$	2740.35	−	4746.42i	0.151853	−	0.263017i
$689$	3084.70	+	5342.86i	0.170563	+	0.295424i
$690$		0			0
$691$	−12909.0	+	22359.1i	−0.710683	+	1.23094i	0.253918	+	0.967226i	$0.418281\pi$
$691$	−12909.0	+	22359.1i	−0.710683	+	1.23094i	−0.964601	+	0.263714i	$0.915053\pi$
$692$	−54757.4			−3.00804
$693$		0			0
$694$	23316.1			1.27531
$695$	295.824	−	512.382i	0.0161457	−	0.0279651i
$696$		0			0
$697$	2625.50	+	4547.50i	0.142680	+	0.247129i
$698$	10587.5	−	18338.1i	0.574131	−	0.994424i
$699$		0			0
$700$	1436.10	−	32570.3i	0.0775423	−	1.75863i
$701$	−16727.2			−0.901250			−0.450625	−	0.892713i	$-0.648799\pi$
$701$	−16727.2			−0.901250			−0.450625	+	0.892713i	$0.648799\pi$
$702$		0			0
$703$	12548.6	+	21734.8i	0.673228	+	1.16606i
$704$	−26040.9	−	45104.1i	−1.39411	−	2.41466i
$705$		0			0
$706$	−7594.92			−0.404870
$707$	−18828.1	−	12006.3i	−1.00156	−	0.638673i
$708$		0			0
$709$	3445.71	−	5968.14i	0.182519	−	0.316133i	−0.760218	−	0.649667i	$-0.774908\pi$
$709$	3445.71	−	5968.14i	0.182519	−	0.316133i	0.942738	+	0.333535i	$0.108241\pi$
$710$	−690.812	−	1196.52i	−0.0365151	−	0.0632460i
$711$		0			0
$712$	−21965.3	+	38045.0i	−1.15616	+	2.00252i
$713$	−4059.41			−0.213220
$714$		0			0
$715$	2027.51			0.106049
$716$	−2370.00	+	4104.97i	−0.123703	+	0.214260i
$717$		0			0
$718$	−31038.9	−	53760.9i	−1.61331	−	2.79434i
$719$	5203.19	−	9012.19i	0.269884	−	0.467452i	−0.698948	−	0.715172i	$-0.746348\pi$
$719$	5203.19	−	9012.19i	0.269884	−	0.467452i	0.968832	+	0.247721i	$0.0796815\pi$
$720$		0			0
$721$	395.964	−	8980.31i	0.0204528	−	0.463862i
$722$	3153.66			0.162558
$723$		0			0
$724$	11077.8	+	19187.2i	0.568649	+	0.984929i
$725$	−4173.08	−	7227.99i	−0.213772	−	0.370263i
$726$		0			0
$727$	2203.46			0.112410			0.0562049	−	0.998419i	$-0.482100\pi$
$727$	2203.46			0.112410			0.0562049	+	0.998419i	$0.482100\pi$
$728$	−17047.1	+	8864.85i	−0.867869	+	0.451309i
$729$		0			0
$730$	1520.84	−	2634.17i	0.0771079	−	0.133555i
$731$	1730.53	+	2997.36i	0.0875593	+	0.151657i
$732$		0			0
$733$	4386.85	−	7598.24i	0.221053	−	0.382875i	−0.734075	−	0.679069i	$-0.762384\pi$
$733$	4386.85	−	7598.24i	0.221053	−	0.382875i	0.955128	+	0.296193i	$0.0957172\pi$
$734$	24024.4			1.20811
$735$		0			0
$736$	−7161.06			−0.358641
$737$	−27447.6	+	47540.6i	−1.37184	+	2.37609i
$738$		0			0
$739$	−13692.9	−	23716.9i	−0.681601	−	1.18057i	−0.974492	−	0.224422i	$-0.927951\pi$
$739$	−13692.9	−	23716.9i	−0.681601	−	1.18057i	0.292891	−	0.956146i	$-0.405383\pi$
$740$	1700.72	−	2945.73i	0.0844861	−	0.146334i
$741$		0			0
$742$	13340.3	−	6937.22i	0.660024	−	0.343226i
$743$	28890.0			1.42648			0.713239	−	0.700921i	$-0.247228\pi$
$743$	28890.0			1.42648			0.713239	+	0.700921i	$0.247228\pi$
$744$		0			0
$745$	917.335	+	1588.87i	0.0451121	+	0.0781365i
$746$	3434.58	+	5948.87i	0.168564	+	0.291962i
$747$		0			0
$748$	−14185.9			−0.693432
$749$	210.561	−	4775.45i	0.0102720	−	0.232966i
$750$		0			0
$751$	10403.8	−	18020.0i	0.505515	−	0.875577i	−0.494465	−	0.869198i	$-0.664636\pi$
$751$	10403.8	−	18020.0i	0.505515	−	0.875577i	0.999980	−	0.00637972i	$-0.00203074\pi$
$752$	−5230.42	−	9059.36i	−0.253635	−	0.439310i
$753$		0			0
$754$	−5653.11	+	9791.47i	−0.273043	+	0.472924i
$755$	−454.244			−0.0218962
$756$		0			0
$757$	14372.8			0.690078			0.345039	−	0.938588i	$-0.387866\pi$
$757$	14372.8			0.690078			0.345039	+	0.938588i	$0.387866\pi$
$758$	−5490.75	+	9510.26i	−0.263104	+	0.455710i
$759$		0			0
$760$	−1044.93	−	1809.86i	−0.0498729	−	0.0863824i
$761$	−13486.8	+	23359.8i	−0.642439	+	1.11274i	0.342447	+	0.939537i	$0.388744\pi$
$761$	−13486.8	+	23359.8i	−0.642439	+	1.11274i	−0.984887	+	0.173200i	$0.944589\pi$
$762$		0			0
$763$	−9076.47	−	5787.85i	−0.430656	−	0.274619i
$764$	43433.4			2.05676
$765$		0			0
$766$	13301.4	+	23038.7i	0.627413	+	1.08671i
$767$	−7974.61	−	13812.4i	−0.375419	−	0.650245i
$768$		0			0
$769$	−3264.38			−0.153077			−0.0765387	−	0.997067i	$-0.524387\pi$
$769$	−3264.38			−0.153077			−0.0765387	+	0.997067i	$0.524387\pi$
$770$	217.672	−	4936.72i	0.0101875	−	0.231048i
$771$		0			0
$772$	15744.0	−	27269.4i	0.733989	−	1.27131i
$773$	11067.7	+	19169.8i	0.514977	+	0.891966i	0.999849	+	0.0173811i	$0.00553285\pi$
$773$	11067.7	+	19169.8i	0.514977	+	0.891966i	−0.484872	+	0.874585i	$0.661134\pi$
$774$		0			0
$775$	−4319.80	+	7482.11i	−0.200221	+	0.346794i
$776$	47316.1			2.18885
$777$		0			0
$778$	−42560.0			−1.96124
$779$	15520.9	−	26882.9i	0.713854	−	1.23643i
$780$		0			0

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)

\(f(q)\)	\(=\)	\(q+(-2.35377 + 4.07684i) q^{2} +(-7.08042 - 12.2637i) q^{4} +(-0.415227 + 0.719194i) q^{5} +(16.4314 - 8.54463i) q^{7} +29.0024 q^{8} +O(q^{10})\)	\(q+(-2.35377 + 4.07684i) q^{2} +(-7.08042 - 12.2637i) q^{4} +(-0.415227 + 0.719194i) q^{5} +(16.4314 - 8.54463i) q^{7} +29.0024 q^{8} +(-1.95469 - 3.38563i) q^{10} +(34.1251 + 59.1065i) q^{11} -35.7721 q^{13} +(-3.84045 + 87.1001i) q^{14} +(-11.6214 + 20.1289i) q^{16} +(-7.33893 - 12.7114i) q^{17} +(-43.3847 + 75.1445i) q^{19} +11.7599 q^{20} -321.290 q^{22} +(-29.2043 + 50.5834i) q^{23} +(62.1552 + 107.656i) q^{25} +(84.1991 - 145.837i) q^{26} +(-221.129 - 141.009i) q^{28} -67.1398 q^{29} +(34.7501 + 60.1889i) q^{31} +(61.3013 + 106.177i) q^{32} +69.0965 q^{34} +(-0.677492 + 15.3653i) q^{35} +(144.620 - 250.489i) q^{37} +(-204.235 - 353.745i) q^{38} +(-12.0426 + 20.8583i) q^{40} -357.750 q^{41} -235.801 q^{43} +(483.241 - 836.998i) q^{44} +(-137.480 - 238.123i) q^{46} +(-225.034 + 389.769i) q^{47} +(196.979 - 280.800i) q^{49} -585.195 q^{50} +(253.282 + 438.697i) q^{52} +(-86.2322 - 149.358i) q^{53} -56.6787 q^{55} +(476.548 - 247.815i) q^{56} +(158.031 - 273.718i) q^{58} +(222.928 + 386.123i) q^{59} +(-238.157 + 412.500i) q^{61} -327.174 q^{62} -763.099 q^{64} +(14.8535 - 25.7271i) q^{65} +(402.160 + 696.562i) q^{67} +(-103.925 + 180.004i) q^{68} +(-61.0471 - 38.9283i) q^{70} +353.412 q^{71} +(389.023 + 673.807i) q^{73} +(680.803 + 1179.19i) q^{74} +1228.73 q^{76} +(1065.77 + 679.613i) q^{77} +(37.0998 - 64.2587i) q^{79} +(-9.65105 - 16.7161i) q^{80} +(842.059 - 1458.49i) q^{82} -1168.49 q^{83} +12.1893 q^{85} +(555.020 - 961.324i) q^{86} +(989.711 + 1714.23i) q^{88} +(-757.361 + 1311.79i) q^{89} +(-587.784 + 305.659i) q^{91} +827.116 q^{92} +(-1059.35 - 1834.85i) q^{94} +(-36.0289 - 62.4039i) q^{95} +1631.46 q^{97} +(681.134 + 1463.99i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 32 q^{4} - 26 q^{7}+O(q^{10}) \) 12 * q - 32 * q^4 - 26 * q^7	\( 12 q - 32 q^{4} - 26 q^{7} + 20 q^{10} + 104 q^{13} + 148 q^{16} + 62 q^{19} - 712 q^{22} + 46 q^{25} - 348 q^{28} + 82 q^{31} + 840 q^{34} + 1132 q^{37} + 444 q^{40} - 3132 q^{43} + 888 q^{46} + 366 q^{49} + 72 q^{52} + 448 q^{55} - 4 q^{58} - 886 q^{61} - 1848 q^{64} + 2084 q^{67} - 4460 q^{70} + 2398 q^{73} + 6408 q^{76} - 984 q^{79} + 3892 q^{82} - 7200 q^{85} + 5796 q^{88} - 6492 q^{91} - 2772 q^{94} - 1364 q^{97}+O(q^{100}) \) 12 * q - 32 * q^4 - 26 * q^7 + 20 * q^10 + 104 * q^13 + 148 * q^16 + 62 * q^19 - 712 * q^22 + 46 * q^25 - 348 * q^28 + 82 * q^31 + 840 * q^34 + 1132 * q^37 + 444 * q^40 - 3132 * q^43 + 888 * q^46 + 366 * q^49 + 72 * q^52 + 448 * q^55 - 4 * q^58 - 886 * q^61 - 1848 * q^64 + 2084 * q^67 - 4460 * q^70 + 2398 * q^73 + 6408 * q^76 - 984 * q^79 + 3892 * q^82 - 7200 * q^85 + 5796 * q^88 - 6492 * q^91 - 2772 * q^94 - 1364 * q^97

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