LMFDB - Embedded newform 189.4.e.e.109.1

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			109.1
Root			$2.35377 - 4.07684i$ of defining polynomial
Character	$\chi$	$=$	189.109
Dual form			189.4.e.e.163.1

$q$-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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.896304	−	0.443439i	$-0.853758\pi$
$2$	−2.35377	−	4.07684i	−0.832182	−	1.44138i	0.0641227	−	0.997942i	$-0.479575\pi$
$3$		0			0
$3$		0			0
$4$	−7.08042	+	12.2637i	−0.885053	+	1.53296i
$5$	−0.415227	−	0.719194i	−0.0371390	−	0.0643266i	0.846858	−	0.531818i	$-0.178491\pi$
$5$	−0.415227	−	0.719194i	−0.0371390	−	0.0643266i	−0.883997	+	0.467492i	$0.845158\pi$
$6$		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	0.161410	−	0.986887i	$-0.448396\pi$
$11$	34.1251	−	59.1065i	0.935374	−	1.62012i	0.773965	−	0.633229i	$-0.218271\pi$
$12$		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	−0.913617	−	0.406576i	$-0.866723\pi$
$17$	−7.33893	+	12.7114i	−0.104703	+	0.181351i	0.808914	+	0.587927i	$0.200056\pi$
$18$		0			0
$19$	−43.3847	−	75.1445i	−0.523849	−	0.907333i	−0.999615	−	0.0277607i	$-0.991162\pi$
$19$	−43.3847	−	75.1445i	−0.523849	−	0.907333i	0.475766	−	0.879572i	$-0.342171\pi$
$20$	11.7599			0.131480
$21$		0			0
$22$	−321.290			−3.11361
$23$	−29.2043	−	50.5834i	−0.264762	−	0.458581i	0.702739	−	0.711447i	$-0.251960\pi$
$23$	−29.2043	−	50.5834i	−0.264762	−	0.458581i	−0.967501	+	0.252866i	$0.918627\pi$
$24$		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	−0.747626	−	0.664120i	$-0.768806\pi$
$31$	34.7501	−	60.1889i	0.201332	−	0.348718i	0.948958	+	0.315403i	$0.102140\pi$
$32$	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	0.984855	+	0.173379i	$0.0554685\pi$
$37$	144.620	+	250.489i	0.642578	+	1.11298i	−0.342277	+	0.939599i	$0.611198\pi$
$38$	−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	−0.969023	−	0.246970i	$-0.920565\pi$
$47$	−225.034	−	389.769i	−0.698394	−	1.20965i	0.270629	−	0.962684i	$-0.412768\pi$
$48$		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	−0.955865	−	0.293806i	$-0.905078\pi$
$53$	−86.2322	+	149.358i	−0.223489	+	0.387094i	0.732376	+	0.680900i	$0.238411\pi$
$54$		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	−0.508045	−	0.861330i	$-0.669632\pi$
$59$	222.928	−	386.123i	0.491912	−	0.852016i	0.999957	+	0.00931467i	$0.00296499\pi$
$60$		0			0
$61$	−238.157	−	412.500i	−0.499883	−	0.865823i	0.500117	−	0.865958i	$-0.333290\pi$
$61$	−238.157	−	412.500i	−0.499883	−	0.865823i	−1.00000		0.000134725i	$0.999957\pi$
$62$	−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	−0.222153	−	0.975012i	$-0.571308\pi$
$67$	402.160	−	696.562i	0.733309	−	1.27013i	0.955461	−	0.295116i	$-0.0953583\pi$
$68$	−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	−0.365065	−	0.930982i	$-0.618953\pi$
$73$	389.023	−	673.807i	0.623721	−	1.08032i	0.988787	−	0.149335i	$-0.0477133\pi$
$74$	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	0.891234	−	0.453544i	$-0.149841\pi$
$79$	37.0998	+	64.2587i	0.0528361	+	0.0915149i	−0.838398	+	0.545059i	$0.816507\pi$
$80$	−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	−0.824864	−	0.565332i	$-0.808748\pi$
$89$	−757.361	−	1311.79i	−0.902023	−	1.56235i	−0.0771598	−	0.997019i	$-0.524585\pi$
$90$		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	0.399762	+	0.916619i	$0.369093\pi$
$101$	−602.865	+	1044.19i	−0.593934	+	1.02872i	−0.993696	+	0.112105i	$0.964241\pi$
$102$		0			0
$103$	242.681	+	420.336i	0.232156	+	0.402106i	0.958442	−	0.285286i	$-0.0920886\pi$
$103$	242.681	+	420.336i	0.232156	+	0.402106i	−0.726286	+	0.687392i	$0.758755\pi$
$104$	−1037.48			−0.978201
$105$		0			0
$106$	811.881			0.743933
$107$	129.050	+	223.522i	0.116596	+	0.201950i	0.918417	−	0.395615i	$-0.129468\pi$
$107$	129.050	+	223.522i	0.116596	+	0.201950i	−0.801821	+	0.597565i	$0.796135\pi$
$108$		0			0
$109$	−290.623	+	503.374i	−0.255382	+	0.442335i	−0.964999	−	0.262253i	$-0.915535\pi$
$109$	−290.623	+	503.374i	−0.255382	+	0.442335i	0.709617	+	0.704587i	$0.248868\pi$
$110$	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	0.918113	+	0.396320i	$0.129713\pi$
$131$	1202.91	+	2083.50i	0.802279	+	1.38959i	−0.115834	+	0.993269i	$0.536954\pi$
$132$		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	−0.619320	−	0.785138i	$-0.712592\pi$
$137$	593.775	−	1028.45i	0.370289	−	0.641360i	0.989610	+	0.143778i	$0.0459252\pi$
$138$		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	0.991677	+	0.128753i	$0.0410975\pi$
$149$	1104.62	+	1913.26i	0.607342	+	1.05195i	−0.384335	+	0.923194i	$0.625569\pi$
$150$		0			0
$151$	273.491	−	473.701i	0.147394	−	0.255293i	−0.782870	−	0.622185i	$-0.786245\pi$
$151$	273.491	−	473.701i	0.147394	−	0.255293i	0.930263	+	0.366892i	$0.119578\pi$
$152$	−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	−0.999601	−	0.0282414i	$-0.991009\pi$
$157$	−935.096	+	1619.63i	−0.475343	+	0.823318i	0.524258	+	0.851559i	$0.324343\pi$
$158$	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	0.956977	+	0.290163i	$0.0937096\pi$
$163$	1518.70	+	2630.46i	0.729777	+	1.26401i	−0.227200	+	0.973848i	$0.572957\pi$
$164$	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	0.881496	+	0.472191i	$0.156537\pi$
$173$	1933.41	+	3348.76i	0.849677	+	1.47168i	−0.0318190	+	0.999494i	$0.510130\pi$
$174$		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	−0.898850	−	0.438256i	$-0.855596\pi$
$179$	−167.363	+	289.881i	−0.0698844	+	0.121043i	0.828966	+	0.559299i	$0.188930\pi$
$180$		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	−0.995365	−	0.0961730i	$-0.969340\pi$
$191$	−1533.57	−	2656.22i	−0.580971	−	1.00627i	0.414394	−	0.910098i	$-0.363994\pi$
$192$		0			0
$193$	1111.80	−	1925.69i	0.414658	−	0.718209i	−0.580734	−	0.814093i	$-0.697235\pi$
$193$	1111.80	−	1925.69i	0.414658	−	0.718209i	0.995392	+	0.0958843i	$0.0305679\pi$
$194$	−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	−0.763870	−	0.645370i	$-0.776703\pi$
$199$	496.801	−	860.485i	0.176971	−	0.306523i	0.940842	+	0.338846i	$0.110037\pi$
$200$	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	−0.828287	−	0.560304i	$-0.810684\pi$
$227$	243.149	−	421.146i	0.0710940	−	0.123138i	0.899381	+	0.437166i	$0.144018\pi$
$228$		0			0
$229$	−2107.34	−	3650.02i	−0.608109	−	1.05328i	−0.991552	−	0.129712i	$-0.958595\pi$
$229$	−2107.34	−	3650.02i	−0.608109	−	1.05328i	0.383442	−	0.923565i	$-0.374738\pi$
$230$	228.342			0.0654627
$231$		0			0
$232$	−1947.21			−0.551038
$233$	549.671	+	952.058i	0.154550	+	0.267688i	0.932895	−	0.360148i	$-0.117274\pi$
$233$	549.671	+	952.058i	0.154550	+	0.267688i	−0.778345	+	0.627837i	$0.783941\pi$
$234$		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	−0.784002	−	0.620758i	$-0.786825\pi$
$241$	544.702	−	943.452i	0.145591	−	0.252171i	0.929593	+	0.368587i	$0.120158\pi$
$242$	−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	0.923311	−	0.384052i	$-0.125472\pi$
$257$	531.716	+	920.959i	0.129056	+	0.223532i	−0.794255	+	0.607585i	$0.792138\pi$
$258$		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	−0.996940	−	0.0781735i	$-0.975091\pi$
$263$	−1837.29	+	3182.29i	−0.430770	+	0.746115i	0.566170	+	0.824288i	$0.308425\pi$
$264$		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	0.137961	+	0.990438i	$0.455945\pi$
$269$	−3479.97	+	6027.48i	−0.788764	+	1.36618i	−0.926725	+	0.375741i	$0.877388\pi$
$270$		0			0
$271$	3297.89	+	5712.11i	0.739235	+	1.28039i	0.952840	+	0.303472i	$0.0981459\pi$
$271$	3297.89	+	5712.11i	0.739235	+	1.28039i	−0.213606	+	0.976920i	$0.568521\pi$
$272$	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	−0.645655	−	0.763629i	$-0.723416\pi$
$277$	1560.53	−	2702.92i	0.338495	−	0.586290i	0.984150	+	0.177339i	$0.0567489\pi$
$278$	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	−0.888846	−	0.458206i	$-0.848492\pi$
$283$	−226.639	+	392.551i	−0.0476053	+	0.0824548i	0.841241	+	0.540661i	$0.181826\pi$
$284$	−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	−0.847229	−	0.531228i	$-0.821731\pi$
$311$	199.870	−	346.185i	0.0364424	−	0.0631201i	0.883671	+	0.468108i	$0.155064\pi$
$312$		0			0
$313$	−1865.24	−	3230.69i	−0.336836	−	0.583417i	0.647000	−	0.762490i	$-0.276023\pi$
$313$	−1865.24	−	3230.69i	−0.336836	−	0.583417i	−0.983836	+	0.179073i	$0.942690\pi$
$314$	8803.99			1.58229
$315$		0			0
$316$	−1050.73			−0.187051
$317$	−4186.74	−	7251.64i	−0.741800	−	1.28483i	−0.951675	−	0.307107i	$-0.900639\pi$
$317$	−4186.74	−	7251.64i	−0.741800	−	1.28483i	0.209875	−	0.977728i	$-0.432694\pi$
$318$		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	0.916603	−	0.399799i	$-0.130920\pi$
$331$	674.858	+	1168.89i	0.112065	+	0.194102i	−0.804538	+	0.593902i	$0.797587\pi$
$332$	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	−0.991507	−	0.130054i	$-0.958485\pi$
$347$	−2476.47	+	4289.37i	−0.383123	+	0.663589i	0.608384	+	0.793643i	$0.291818\pi$
$348$		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	−0.798781	−	0.601622i	$-0.794521\pi$
$353$	806.677	−	1397.21i	0.121629	−	0.210668i	0.920410	+	0.390954i	$0.127855\pi$
$354$		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	−0.697507	−	0.716578i	$-0.745708\pi$
$359$	−6593.45	−	11420.2i	−0.969328	−	1.67893i	−0.271821	−	0.962348i	$-0.587626\pi$
$360$		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	−0.988443	−	0.151596i	$-0.951559\pi$
$367$	−2551.69	+	4419.66i	−0.362936	+	0.628623i	0.625507	+	0.780219i	$0.284892\pi$
$368$	−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	0.912212	−	0.409719i	$-0.134373\pi$
$373$	729.593	+	1263.69i	0.101279	+	0.175420i	−0.810933	+	0.585139i	$0.801040\pi$
$374$	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	0.990620	−	0.136648i	$-0.0436330\pi$
$383$	2825.55	+	4894.00i	0.376969	+	0.652929i	−0.613651	+	0.789578i	$0.710300\pi$
$384$		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	−0.405152	−	0.914250i	$-0.632781\pi$
$389$	4520.41	−	7829.58i	0.589188	−	1.02050i	0.994339	−	0.106253i	$-0.0338854\pi$
$390$		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	0.732876	−	0.680363i	$-0.238178\pi$
$397$	−1762.18	−	3052.18i	−0.222774	−	0.385855i	−0.955649	+	0.294507i	$0.904844\pi$
$398$	−4677.41			−0.589089
$399$		0			0
$400$	−2889.33			−0.361166
$401$	2234.91	+	3870.97i	0.278319	+	0.482062i	0.970967	−	0.239213i	$-0.0768895\pi$
$401$	2234.91	+	3870.97i	0.278319	+	0.482062i	−0.692648	+	0.721276i	$0.743556\pi$
$402$		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	−0.543387	−	0.839482i	$-0.682858\pi$
$409$	3766.18	−	6523.22i	0.455320	−	0.788637i	0.998707	+	0.0508458i	$0.0161917\pi$
$410$	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	0.416900	+	0.908952i	$0.363116\pi$
$431$	−5178.32	+	8969.11i	−0.578726	+	1.00238i	−0.995626	+	0.0934300i	$0.970217\pi$
$432$		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	0.944417	−	0.328750i	$-0.106627\pi$
$439$	1724.66	+	2987.20i	0.187502	+	0.324763i	−0.756915	+	0.653514i	$0.773294\pi$
$440$	−1643.82			−0.178104
$441$		0			0
$442$	−2471.73			−0.265991
$443$	1122.33	+	1943.93i	0.120369	+	0.208485i	0.919913	−	0.392122i	$-0.128259\pi$
$443$	1122.33	+	1943.93i	0.120369	+	0.208485i	−0.799544	+	0.600607i	$0.794926\pi$
$444$		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	0.851854	−	0.523779i	$-0.175478\pi$
$457$	−270.412	−	468.367i	−0.0276790	−	0.0479415i	−0.879533	+	0.475838i	$0.842145\pi$
$458$	−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	0.797635	−	0.603141i	$-0.206084\pi$
$467$	−1246.53	−	2159.06i	−0.123518	−	0.213939i	−0.921153	+	0.389202i	$0.872751\pi$
$468$		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	−0.993446	−	0.114301i	$-0.963537\pi$
$479$	−4169.63	+	7222.02i	−0.397736	+	0.688899i	0.595710	+	0.803199i	$0.296871\pi$
$480$		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	−0.784718	−	0.619853i	$-0.787192\pi$
$487$	1552.42	−	2688.88i	0.144450	−	0.250194i	0.929167	+	0.369659i	$0.120525\pi$
$488$	−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	0.993617	+	0.112805i	$0.0359836\pi$
$499$	6626.79	+	11477.9i	0.594501	+	1.02971i	−0.399116	+	0.916900i	$0.630683\pi$
$500$	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	0.669613	−	0.742710i	$-0.266460\pi$
$509$	−3541.52	−	6134.10i	−0.308399	−	0.534163i	−0.978012	+	0.208547i	$0.933127\pi$
$510$		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	0.273188	+	0.961961i	$0.411922\pi$
$521$	−8282.67	+	14346.0i	−0.696489	+	1.20635i	−0.969676	+	0.244393i	$0.921411\pi$
$522$		0			0
$523$	3236.34	+	5605.51i	0.270584	+	0.468665i	0.969011	−	0.247016i	$-0.0794499\pi$
$523$	3236.34	+	5605.51i	0.270584	+	0.468665i	−0.698428	+	0.715681i	$0.746117\pi$
$524$	−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	0.925467	−	0.378828i	$-0.123673\pi$
$541$	1694.46	+	2934.89i	0.134659	+	0.233236i	−0.790808	+	0.612064i	$0.790339\pi$
$542$	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	−0.738801	−	0.673924i	$-0.764608\pi$
$557$	2816.25	−	4877.90i	0.214234	−	0.371065i	0.953035	+	0.302859i	$0.0979410\pi$
$558$		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	−0.891892	−	0.452248i	$-0.850622\pi$
$563$	−725.207	+	1256.10i	−0.0542874	+	0.0940286i	0.837605	+	0.546277i	$0.183955\pi$
$564$		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	0.994160	+	0.107913i	$0.0344168\pi$
$569$	8015.20	+	13882.7i	0.590536	+	1.02284i	−0.403625	+	0.914925i	$0.632250\pi$
$570$		0			0
$571$	8270.39	−	14324.7i	0.606139	−	1.04986i	−0.385732	−	0.922611i	$-0.626051\pi$
$571$	8270.39	−	14324.7i	0.606139	−	1.04986i	0.991870	−	0.127252i	$-0.0406157\pi$
$572$	−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	−0.826895	−	0.562356i	$-0.809895\pi$
$577$	1019.63	−	1766.06i	0.0735666	−	0.127421i	0.900462	+	0.434935i	$0.143229\pi$
$578$	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	0.967830	+	0.251604i	$0.0809579\pi$
$593$	10134.5	+	17553.4i	0.701810	+	1.21557i	−0.266020	+	0.963967i	$0.585709\pi$
$594$		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	−0.181079	−	0.983468i	$-0.557959\pi$
$599$	11158.9	−	19327.8i	0.761169	−	1.31838i	0.942248	−	0.334915i	$-0.108708\pi$
$600$		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	0.998476	+	0.0551891i	$0.0175762\pi$
$607$	8180.82	+	14169.6i	0.547033	+	0.947489i	−0.451443	+	0.892300i	$0.649090\pi$
$608$	−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	−0.475074	−	0.879946i	$-0.657579\pi$
$613$	7960.70	−	13788.3i	0.524518	−	0.908492i	0.999592	−	0.0285467i	$-0.00908792\pi$
$614$	−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	−0.856054	−	0.516887i	$-0.827091\pi$
$619$	302.006	−	523.089i	0.0196101	−	0.0339657i	0.875664	+	0.482921i	$0.160424\pi$
$620$	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	−0.789342	−	0.613954i	$-0.789578\pi$
$641$	2223.81	−	3851.76i	0.137029	−	0.237340i	0.926371	+	0.376613i	$0.122911\pi$
$642$		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	0.419318	+	0.907840i	$0.362269\pi$
$647$	−9488.46	+	16434.5i	−0.576553	+	0.998620i	−0.995871	+	0.0907801i	$0.971064\pi$
$648$		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	0.967192	−	0.254046i	$-0.0817616\pi$
$653$	4398.36	+	7618.19i	0.263585	+	0.456543i	−0.703607	+	0.710590i	$0.748428\pi$
$654$		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	−0.191520	−	0.981489i	$-0.561342\pi$
$661$	12817.7	−	22200.8i	0.754234	−	1.30637i	0.945754	−	0.324883i	$-0.105325\pi$
$662$	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	0.999922	+	0.0124573i	$0.00396539\pi$
$677$	8996.86	+	15583.0i	0.510750	+	0.884644i	−0.489173	+	0.872187i	$0.662701\pi$
$678$		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	−0.497721	−	0.867337i	$-0.665830\pi$
$683$	8965.46	−	15528.6i	0.502275	−	0.869966i	0.999997	−	0.00262913i	$-0.000836880\pi$
$684$		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	−0.964601	−	0.263714i	$-0.915053\pi$
$691$	−12909.0	−	22359.1i	−0.710683	−	1.23094i	0.253918	−	0.967226i	$-0.418281\pi$
$692$	−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	0.942738	−	0.333535i	$-0.108241\pi$
$709$	3445.71	+	5968.14i	0.182519	+	0.316133i	−0.760218	+	0.649667i	$0.774908\pi$
$710$	−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	0.968832	−	0.247721i	$-0.0796815\pi$
$719$	5203.19	+	9012.19i	0.269884	+	0.467452i	−0.698948	+	0.715172i	$0.746348\pi$
$720$		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	0.955128	−	0.296193i	$-0.0957172\pi$
$733$	4386.85	+	7598.24i	0.221053	+	0.382875i	−0.734075	+	0.679069i	$0.762384\pi$
$734$	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	0.292891	+	0.956146i	$0.405383\pi$
$739$	−13692.9	+	23716.9i	−0.681601	+	1.18057i	−0.974492	+	0.224422i	$0.927951\pi$
$740$	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	0.999980	+	0.00637972i	$0.00203074\pi$
$751$	10403.8	+	18020.0i	0.505515	+	0.875577i	−0.494465	+	0.869198i	$0.664636\pi$
$752$	−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	−0.984887	−	0.173200i	$-0.944589\pi$
$761$	−13486.8	−	23359.8i	−0.642439	−	1.11274i	0.342447	−	0.939537i	$-0.388744\pi$
$762$		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	−0.484872	−	0.874585i	$-0.661134\pi$
$773$	11067.7	−	19169.8i	0.514977	−	0.891966i	0.999849	−	0.0173811i	$-0.00553285\pi$
$774$		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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