LMFDB - Embedded newform 189.4.e.e.163.4

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			163.4
Root			$-1.02968 - 1.78345i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.e.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02968 - 1.78345i) q^{2} +(1.87953 + 3.25543i) q^{4} +(7.25204 - 12.5609i) q^{5} +(-7.76857 - 16.8122i) q^{7} +24.2161 q^{8} +O(q^{10})$	\(q+(1.02968 - 1.78345i) q^{2} +(1.87953 + 3.25543i) q^{4} +(7.25204 - 12.5609i) q^{5} +(-7.76857 - 16.8122i) q^{7} +24.2161 q^{8} +(-14.9345 - 25.8674i) q^{10} +(14.9047 + 25.8157i) q^{11} -13.3320 q^{13} +(-37.9829 - 3.45625i) q^{14} +(9.89856 - 17.1448i) q^{16} +(-32.1415 - 55.6707i) q^{17} +(55.1748 - 95.5655i) q^{19} +54.5216 q^{20} +61.3881 q^{22} +(9.67280 - 16.7538i) q^{23} +(-42.6843 - 73.9314i) q^{25} +(-13.7276 + 23.7769i) q^{26} +(40.1297 - 56.8890i) q^{28} +111.113 q^{29} +(-96.4689 - 167.089i) q^{31} +(76.4797 + 132.467i) q^{32} -132.382 q^{34} +(-267.514 - 24.3424i) q^{35} +(35.7607 - 61.9393i) q^{37} +(-113.625 - 196.803i) q^{38} +(175.616 - 304.176i) q^{40} +277.562 q^{41} -178.522 q^{43} +(-56.0275 + 97.0424i) q^{44} +(-19.9197 - 34.5020i) q^{46} +(-265.937 + 460.617i) q^{47} +(-222.299 + 261.213i) q^{49} -175.804 q^{50} +(-25.0578 - 43.4013i) q^{52} +(-155.416 - 269.188i) q^{53} +432.357 q^{55} +(-188.124 - 407.125i) q^{56} +(114.410 - 198.165i) q^{58} +(361.012 + 625.290i) q^{59} +(-331.535 + 574.235i) q^{61} -397.328 q^{62} +473.375 q^{64} +(-96.6839 + 167.461i) q^{65} +(304.279 + 527.027i) q^{67} +(120.822 - 209.269i) q^{68} +(-318.867 + 452.035i) q^{70} +976.305 q^{71} +(-130.574 - 226.161i) q^{73} +(-73.6440 - 127.555i) q^{74} +414.810 q^{76} +(318.229 - 451.131i) q^{77} +(-618.075 + 1070.54i) q^{79} +(-143.570 - 248.670i) q^{80} +(285.800 - 495.020i) q^{82} +1225.79 q^{83} -932.367 q^{85} +(-183.820 + 318.386i) q^{86} +(360.933 + 625.154i) q^{88} +(395.991 - 685.876i) q^{89} +(103.570 + 224.139i) q^{91} +72.7211 q^{92} +(547.659 + 948.573i) q^{94} +(-800.260 - 1386.09i) q^{95} -935.253 q^{97} +(236.966 + 665.425i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.02968	−	1.78345i	0.364046	−	0.630546i	−0.624576	−	0.780964i	$-0.714728\pi$
$2$	1.02968	−	1.78345i	0.364046	−	0.630546i	0.988623	+	0.150417i	$0.0480617\pi$
$3$		0			0
$3$		0			0
$4$	1.87953	+	3.25543i	0.234941	+	0.406929i
$5$	7.25204	−	12.5609i	0.648643	−	1.12348i	−0.334805	−	0.942288i	$-0.608670\pi$
$5$	7.25204	−	12.5609i	0.648643	−	1.12348i	0.983447	−	0.181194i	$-0.0579963\pi$
$6$		0			0
$7$	−7.76857	−	16.8122i	−0.419463	−	0.907772i
$7$	−7.76857	−	16.8122i	−0.419463	−	0.907772i
$8$	24.2161			1.07021
$9$		0			0
$10$	−14.9345	−	25.8674i	−0.472272	−	0.817999i
$11$	14.9047	+	25.8157i	0.408539	+	0.707610i	0.994726	−	0.102565i	$-0.0327051\pi$
$11$	14.9047	+	25.8157i	0.408539	+	0.707610i	−0.586187	+	0.810176i	$0.699372\pi$
$12$		0			0
$13$	−13.3320			−0.284432			−0.142216	−	0.989836i	$-0.545423\pi$
$13$	−13.3320			−0.284432			−0.142216	+	0.989836i	$0.545423\pi$
$14$	−37.9829	−	3.45625i	−0.725097	−	0.0659800i
$15$		0			0
$16$	9.89856	−	17.1448i	0.154665	−	0.267888i
$17$	−32.1415	−	55.6707i	−0.458557	−	0.794243i	0.540328	−	0.841454i	$-0.318300\pi$
$17$	−32.1415	−	55.6707i	−0.458557	−	0.794243i	−0.998885	+	0.0472110i	$0.984967\pi$
$18$		0			0
$19$	55.1748	−	95.5655i	0.666209	−	1.15391i	−0.312747	−	0.949836i	$-0.601249\pi$
$19$	55.1748	−	95.5655i	0.666209	−	1.15391i	0.978956	−	0.204071i	$-0.0654173\pi$
$20$	54.5216			0.609570
$21$		0			0
$22$	61.3881			0.594908
$23$	9.67280	−	16.7538i	0.0876921	−	0.151887i	−0.818843	−	0.574017i	$-0.805384\pi$
$23$	9.67280	−	16.7538i	0.0876921	−	0.151887i	0.906535	+	0.422130i	$0.138718\pi$
$24$		0			0
$25$	−42.6843	−	73.9314i	−0.341474	−	0.591451i
$26$	−13.7276	+	23.7769i	−0.103546	+	0.179348i
$27$		0			0
$28$	40.1297	−	56.8890i	0.270850	−	0.383965i
$29$	111.113			0.711487			0.355744	−	0.934584i	$-0.384228\pi$
$29$	111.113			0.711487			0.355744	+	0.934584i	$0.384228\pi$
$30$		0			0
$31$	−96.4689	−	167.089i	−0.558914	−	0.968067i	−0.997587	−	0.0694206i	$-0.977885\pi$
$31$	−96.4689	−	167.089i	−0.558914	−	0.968067i	0.438674	−	0.898646i	$-0.355448\pi$
$32$	76.4797	+	132.467i	0.422494	+	0.731782i
$33$		0			0
$34$	−132.382			−0.667743
$35$	−267.514	−	24.3424i	−1.29195	−	0.117561i
$36$		0			0
$37$	35.7607	−	61.9393i	0.158892	−	0.275210i	−0.775577	−	0.631253i	$-0.782541\pi$
$37$	35.7607	−	61.9393i	0.158892	−	0.275210i	0.934470	+	0.356043i	$0.115874\pi$
$38$	−113.625	−	196.803i	−0.485061	−	0.840151i
$39$		0			0
$40$	175.616	−	304.176i	0.694183	−	1.20236i
$41$	277.562			1.05727			0.528634	−	0.848850i	$-0.322704\pi$
$41$	277.562			1.05727			0.528634	+	0.848850i	$0.322704\pi$
$42$		0			0
$43$	−178.522			−0.633124			−0.316562	−	0.948572i	$-0.602528\pi$
$43$	−178.522			−0.633124			−0.316562	+	0.948572i	$0.602528\pi$
$44$	−56.0275	+	97.0424i	−0.191965	+	0.332493i
$45$		0			0
$46$	−19.9197	−	34.5020i	−0.0638479	−	0.110588i
$47$	−265.937	+	460.617i	−0.825338	+	1.42953i	0.0763219	+	0.997083i	$0.475682\pi$
$47$	−265.937	+	460.617i	−0.825338	+	1.42953i	−0.901660	+	0.432445i	$0.857651\pi$
$48$		0			0
$49$	−222.299	+	261.213i	−0.648101	+	0.761554i
$50$	−175.804			−0.497250
$51$		0			0
$52$	−25.0578	−	43.4013i	−0.0668247	−	0.115744i
$53$	−155.416	−	269.188i	−0.402793	−	0.697658i	0.591269	−	0.806475i	$-0.298627\pi$
$53$	−155.416	−	269.188i	−0.402793	−	0.697658i	−0.994062	+	0.108816i	$0.965294\pi$
$54$		0			0
$55$	432.357			1.05998
$56$	−188.124	−	407.125i	−0.448913	−	0.971507i
$57$		0			0
$58$	114.410	−	198.165i	0.259014	−	0.448626i
$59$	361.012	+	625.290i	0.796605	+	1.37976i	0.921815	+	0.387630i	$0.126706\pi$
$59$	361.012	+	625.290i	0.796605	+	1.37976i	−0.125210	+	0.992130i	$0.539960\pi$
$60$		0			0
$61$	−331.535	+	574.235i	−0.695880	+	1.20530i	0.274003	+	0.961729i	$0.411652\pi$
$61$	−331.535	+	574.235i	−0.695880	+	1.20530i	−0.969883	+	0.243571i	$0.921681\pi$
$62$	−397.328			−0.813882
$63$		0			0
$64$	473.375			0.924560
$65$	−96.6839	+	167.461i	−0.184495	+	0.319554i
$66$		0			0
$67$	304.279	+	527.027i	0.554830	+	0.960994i	0.997917	+	0.0645154i	$0.0205502\pi$
$67$	304.279	+	527.027i	0.554830	+	0.960994i	−0.443086	+	0.896479i	$0.646116\pi$
$68$	120.822	−	209.269i	0.215467	−	0.373200i
$69$		0			0
$70$	−318.867	+	452.035i	−0.544456	+	0.771836i
$71$	976.305			1.63192			0.815958	−	0.578111i	$-0.196210\pi$
$71$	976.305			1.63192			0.815958	+	0.578111i	$0.196210\pi$
$72$		0			0
$73$	−130.574	−	226.161i	−0.209350	−	0.362605i	0.742160	−	0.670223i	$-0.233801\pi$
$73$	−130.574	−	226.161i	−0.209350	−	0.362605i	−0.951510	+	0.307618i	$0.900468\pi$
$74$	−73.6440	−	127.555i	−0.115688	−	0.200378i
$75$		0			0
$76$	414.810			0.626078
$77$	318.229	−	451.131i	0.470982	−	0.667677i
$78$		0			0
$79$	−618.075	+	1070.54i	−0.880239	+	1.52462i	−0.0291637	+	0.999575i	$0.509284\pi$
$79$	−618.075	+	1070.54i	−0.880239	+	1.52462i	−0.851075	+	0.525044i	$0.824049\pi$
$80$	−143.570	−	248.670i	−0.200645	−	0.347527i
$81$		0			0
$82$	285.800	−	495.020i	0.384894	−	0.666656i
$83$	1225.79			1.62106			0.810529	−	0.585699i	$-0.199180\pi$
$83$	1225.79			1.62106			0.810529	+	0.585699i	$0.199180\pi$
$84$		0			0
$85$	−932.367			−1.18976
$86$	−183.820	+	318.386i	−0.230486	+	0.399214i
$87$		0			0
$88$	360.933	+	625.154i	0.437222	+	0.757291i
$89$	395.991	−	685.876i	0.471629	−	0.816885i	−0.527845	−	0.849341i	$-0.677000\pi$
$89$	395.991	−	685.876i	0.471629	−	0.816885i	0.999473	+	0.0324564i	$0.0103330\pi$
$90$		0			0
$91$	103.570	+	224.139i	0.119309	+	0.258200i
$92$	72.7211			0.0824098
$93$		0			0
$94$	547.659	+	948.573i	0.600923	+	1.04083i
$95$	−800.260	−	1386.09i	−0.864263	−	1.49695i
$96$		0			0
$97$	−935.253			−0.978975			−0.489488	−	0.872010i	$-0.662816\pi$
$97$	−935.253			−0.978975			−0.489488	+	0.872010i	$0.662816\pi$
$98$	236.966	+	665.425i	0.244256	+	0.685899i
$99$		0			0
$100$	160.453	−	277.912i	0.160453	−	0.277912i
$101$	221.485	+	383.623i	0.218203	+	0.377940i	0.954259	−	0.298982i	$-0.0966470\pi$
$101$	221.485	+	383.623i	0.218203	+	0.377940i	−0.736055	+	0.676921i	$0.763314\pi$
$102$		0			0
$103$	349.700	−	605.699i	0.334534	−	0.579430i	−0.648861	−	0.760907i	$-0.724754\pi$
$103$	349.700	−	605.699i	0.334534	−	0.579430i	0.983395	+	0.181477i	$0.0580878\pi$
$104$	−322.848			−0.304402
$105$		0			0
$106$	−640.114			−0.586541
$107$	−955.591	+	1655.13i	−0.863369	+	1.49540i	0.00528834	+	0.999986i	$0.498317\pi$
$107$	−955.591	+	1655.13i	−0.863369	+	1.49540i	−0.868657	+	0.495413i	$0.835017\pi$
$108$		0			0
$109$	1035.71	+	1793.90i	0.910118	+	1.57637i	0.813896	+	0.581011i	$0.197343\pi$
$109$	1035.71	+	1793.90i	0.910118	+	1.57637i	0.0962224	+	0.995360i	$0.469324\pi$
$110$	445.189	−	771.090i	0.385883	−	0.668369i
$111$		0			0
$112$	−365.139	−	33.2258i	−0.308057	−	0.0280316i
$113$	−2313.34			−1.92585			−0.962926	−	0.269767i	$-0.913053\pi$
$113$	−2313.34			−1.92585			−0.962926	+	0.269767i	$0.913053\pi$
$114$		0			0
$115$	−140.295	−	242.998i	−0.113762	−	0.197041i
$116$	208.839	+	361.721i	0.167157	+	0.289525i
$117$		0			0
$118$	1486.90			1.16000
$119$	−686.253	+	972.851i	−0.528644	+	0.749421i
$120$		0			0
$121$	221.201	−	383.132i	0.166192	−	0.287853i
$122$	682.748	+	1182.55i	0.506665	+	0.877570i
$123$		0			0
$124$	362.632	−	628.096i	0.262623	−	0.454877i
$125$	574.817			0.411306
$126$		0			0
$127$	−1317.50			−0.920542			−0.460271	−	0.887778i	$-0.652248\pi$
$127$	−1317.50			−0.920542			−0.460271	+	0.887778i	$0.652248\pi$
$128$	−124.414	+	215.491i	−0.0859119	+	0.148804i
$129$		0			0
$130$	199.107	+	344.863i	0.134329	+	0.232665i
$131$	229.421	−	397.368i	0.153012	−	0.265024i	−0.779321	−	0.626624i	$-0.784436\pi$
$131$	229.421	−	397.368i	0.153012	−	0.265024i	0.932333	+	0.361600i	$0.117769\pi$
$132$		0			0
$133$	−2035.29	−	185.201i	−1.32694	−	0.120744i
$134$	1253.24			0.807935
$135$		0			0
$136$	−778.341	−	1348.13i	−0.490752	−	0.850007i
$137$	−666.378	−	1154.20i	−0.415566	−	0.719781i	0.579922	−	0.814672i	$-0.303083\pi$
$137$	−666.378	−	1154.20i	−0.415566	−	0.719781i	−0.995488	+	0.0948911i	$0.969750\pi$
$138$		0			0
$139$	−406.835			−0.248254			−0.124127	−	0.992266i	$-0.539613\pi$
$139$	−406.835			−0.248254			−0.124127	+	0.992266i	$0.539613\pi$
$140$	−423.555	−	916.627i	−0.255692	−	0.553351i
$141$		0			0
$142$	1005.28	−	1741.20i	0.594093	−	1.02900i
$143$	−198.708	−	344.173i	−0.116202	−	0.201267i
$144$		0			0
$145$	805.795	−	1395.68i	0.461501	−	0.799343i
$146$	−537.797			−0.304852
$147$		0			0
$148$	268.853			0.149321
$149$	217.761	−	377.174i	0.119730	−	0.207378i	−0.799931	−	0.600092i	$-0.795131\pi$
$149$	217.761	−	377.174i	0.119730	−	0.207378i	0.919660	+	0.392714i	$0.128464\pi$
$150$		0			0
$151$	982.668	+	1702.03i	0.529592	+	0.917280i	0.999404	+	0.0345136i	$0.0109882\pi$
$151$	982.668	+	1702.03i	0.529592	+	0.917280i	−0.469812	+	0.882766i	$0.655678\pi$
$152$	1336.12	−	2314.22i	0.712983	−	1.23492i
$153$		0			0
$154$	−476.897	−	1032.07i	−0.249542	−	0.540041i
$155$	−2798.39			−1.45014
$156$		0			0
$157$	−415.741	−	720.085i	−0.211336	−	0.366045i	0.740797	−	0.671729i	$-0.234448\pi$
$157$	−415.741	−	720.085i	−0.211336	−	0.366045i	−0.952133	+	0.305684i	$0.901115\pi$
$158$	1272.84	+	2204.62i	0.640895	+	1.11006i
$159$		0			0
$160$	2218.54			1.09619
$161$	−356.811	−	32.4680i	−0.174663	−	0.0158934i
$162$		0			0
$163$	588.061	−	1018.55i	0.282579	−	0.489442i	−0.689440	−	0.724343i	$-0.742143\pi$
$163$	588.061	−	1018.55i	0.282579	−	0.489442i	0.972019	+	0.234901i	$0.0754766\pi$
$164$	521.686	+	903.587i	0.248395	+	0.430233i
$165$		0			0
$166$	1262.17	−	2186.14i	0.590140	−	1.02215i
$167$	1674.29			0.775809			0.387905	−	0.921700i	$-0.373199\pi$
$167$	1674.29			0.775809			0.387905	+	0.921700i	$0.373199\pi$
$168$		0			0
$169$	−2019.26			−0.919098
$170$	−960.038	+	1662.83i	−0.433127	+	0.750197i
$171$		0			0
$172$	−335.536	−	581.166i	−0.148747	−	0.257637i
$173$	−716.460	+	1240.95i	−0.314864	+	0.545360i	−0.979409	−	0.201888i	$-0.935292\pi$
$173$	−716.460	+	1240.95i	−0.314864	+	0.545360i	0.664545	+	0.747249i	$0.268626\pi$
$174$		0			0
$175$	−911.352	+	1291.96i	−0.393667	+	0.558073i
$176$	590.139			0.252747
$177$		0			0
$178$	−815.486	−	1412.46i	−0.343389	−	0.594767i
$179$	597.265	+	1034.49i	0.249395	+	0.431965i	0.963358	−	0.268219i	$-0.0864349\pi$
$179$	597.265	+	1034.49i	0.249395	+	0.431965i	−0.713963	+	0.700183i	$0.753102\pi$
$180$		0			0
$181$	741.424			0.304473			0.152236	−	0.988344i	$-0.451352\pi$
$181$	741.424			0.304473			0.152236	+	0.988344i	$0.451352\pi$
$182$	506.386	+	46.0785i	0.206241	+	0.0187668i
$183$		0			0
$184$	234.237	−	405.711i	0.0938489	−	0.162551i
$185$	−518.676	−	898.373i	−0.206129	−	0.357026i
$186$		0			0
$187$	958.118	−	1659.51i	0.374676	−	0.648959i
$188$	−1999.34			−0.775623
$189$		0			0
$190$	−3296.04			−1.25853
$191$	1951.99	−	3380.95i	0.739483	−	1.28082i	−0.213246	−	0.976999i	$-0.568403\pi$
$191$	1951.99	−	3380.95i	0.739483	−	1.28082i	0.952728	−	0.303823i	$-0.0982632\pi$
$192$		0			0
$193$	−885.627	−	1533.95i	−0.330305	−	0.572104i	0.652267	−	0.757989i	$-0.273818\pi$
$193$	−885.627	−	1533.95i	−0.330305	−	0.572104i	−0.982572	+	0.185885i	$0.940485\pi$
$194$	−963.010	+	1667.98i	−0.356392	+	0.617289i
$195$		0			0
$196$	−1268.18	−	232.722i	−0.462164	−	0.0848113i
$197$	830.366			0.300310			0.150155	−	0.988662i	$-0.452023\pi$
$197$	830.366			0.300310			0.150155	+	0.988662i	$0.452023\pi$
$198$		0			0
$199$	−531.253	−	920.156i	−0.189244	−	0.327780i	0.755755	−	0.654855i	$-0.227270\pi$
$199$	−531.253	−	920.156i	−0.189244	−	0.327780i	−0.944998	+	0.327075i	$0.893937\pi$
$200$	−1033.65	−	1790.33i	−0.365449	−	0.632977i
$201$		0			0
$202$	912.232			0.317745
$203$	−863.187	−	1868.05i	−0.298443	−	0.645869i
$204$		0			0
$205$	2012.90	−	3486.44i	0.685789	−	1.18782i
$206$	−720.158	−	1247.35i	−0.243572	−	0.421878i
$207$		0			0
$208$	−131.967	+	228.574i	−0.0439917	+	0.0761958i
$209$	3289.45			1.08869
$210$		0			0
$211$	−3848.67			−1.25570			−0.627851	−	0.778333i	$-0.716065\pi$
$211$	−3848.67			−1.25570			−0.627851	+	0.778333i	$0.716065\pi$
$212$	584.217	−	1011.89i	0.189265	−	0.327817i
$213$		0			0
$214$	1967.90	+	3408.51i	0.628612	+	1.08879i
$215$	−1294.65	+	2242.40i	−0.410671	+	0.711303i
$216$		0			0
$217$	−2059.71	+	2919.89i	−0.644341	+	0.913435i
$218$	4265.79			1.32530
$219$		0			0
$220$	812.627	+	1407.51i	0.249033	+	0.431338i
$221$	428.509	+	742.200i	0.130428	+	0.225908i
$222$		0			0
$223$	5482.75			1.64642			0.823211	−	0.567736i	$-0.192181\pi$
$223$	5482.75			1.64642			0.823211	+	0.567736i	$0.192181\pi$
$224$	1632.92	−	2314.87i	0.487070	−	0.690484i
$225$		0			0
$226$	−2382.00	+	4125.75i	−0.701099	+	1.21434i
$227$	−197.418	−	341.939i	−0.0577230	−	0.0999791i	0.835720	−	0.549156i	$-0.185051\pi$
$227$	−197.418	−	341.939i	−0.0577230	−	0.0999791i	−0.893443	+	0.449177i	$0.851717\pi$
$228$		0			0
$229$	1911.78	−	3311.30i	0.551678	−	0.955534i	−0.446476	−	0.894796i	$-0.647321\pi$
$229$	1911.78	−	3311.30i	0.551678	−	0.955534i	0.998154	−	0.0607380i	$-0.0193454\pi$
$230$	−577.835			−0.165658
$231$		0			0
$232$	2690.72			0.761441
$233$	1268.77	−	2197.57i	0.356738	−	0.617888i	−0.630676	−	0.776046i	$-0.717222\pi$
$233$	1268.77	−	2197.57i	0.356738	−	0.617888i	0.987414	+	0.158159i	$0.0505557\pi$
$234$		0			0
$235$	3857.17	+	6680.82i	1.07070	+	1.85451i
$236$	−1357.06	+	2350.50i	−0.374310	+	0.648324i
$237$		0			0
$238$	1028.42	+	2225.62i	0.280094	+	0.606159i
$239$	5368.81			1.45305			0.726526	−	0.687139i	$-0.241134\pi$
$239$	5368.81			1.45305			0.726526	+	0.687139i	$0.241134\pi$
$240$		0			0
$241$	−1054.01	−	1825.60i	−0.281721	−	0.487955i	0.690088	−	0.723726i	$-0.257572\pi$
$241$	−1054.01	−	1825.60i	−0.281721	−	0.487955i	−0.971809	+	0.235771i	$0.924239\pi$
$242$	−455.532	−	789.005i	−0.121003	−	0.209583i
$243$		0			0
$244$	−2492.51			−0.653962
$245$	1668.95	+	4686.60i	0.435206	+	1.22211i
$246$		0			0
$247$	−735.588	+	1274.08i	−0.189491	+	0.328208i
$248$	−2336.10	−	4046.24i	−0.598155	−	1.03603i
$249$		0			0
$250$	591.877	−	1025.16i	0.149734	−	0.259347i
$251$	−5717.94			−1.43790			−0.718951	−	0.695061i	$-0.755377\pi$
$251$	−5717.94			−1.43790			−0.718951	+	0.695061i	$0.755377\pi$
$252$		0			0
$253$	576.680			0.143303
$254$	−1356.60	+	2349.69i	−0.335120	+	0.580445i
$255$		0			0
$256$	2149.71	+	3723.41i	0.524832	+	0.909035i
$257$	−2493.73	+	4319.28i	−0.605272	+	1.04836i	0.386736	+	0.922190i	$0.373602\pi$
$257$	−2493.73	+	4319.28i	−0.605272	+	1.04836i	−0.992008	+	0.126172i	$0.959731\pi$
$258$		0			0
$259$	−1319.14	−	120.035i	−0.316477	−	0.0287978i
$260$	−726.880			−0.173381
$261$		0			0
$262$	−472.459	−	818.322i	−0.111407	−	0.192962i
$263$	−307.637	−	532.842i	−0.0721281	−	0.124930i	0.827706	−	0.561162i	$-0.189646\pi$
$263$	−307.637	−	532.842i	−0.0721281	−	0.124930i	−0.899834	+	0.436233i	$0.856312\pi$
$264$		0			0
$265$	−4508.34			−1.04508
$266$	−2426.00	+	3439.16i	−0.559200	+	0.792738i
$267$		0			0
$268$	−1143.80	+	1981.12i	−0.260705	+	0.451553i
$269$	396.981	+	687.591i	0.0899790	+	0.155848i	0.907502	−	0.420048i	$-0.137987\pi$
$269$	396.981	+	687.591i	0.0899790	+	0.155848i	−0.817523	+	0.575896i	$0.804653\pi$
$270$		0			0
$271$	−1882.47	+	3260.54i	−0.421964	+	0.730862i	−0.996131	−	0.0878752i	$-0.971992\pi$
$271$	−1882.47	+	3260.54i	−0.421964	+	0.730862i	0.574168	+	0.818738i	$0.305326\pi$
$272$	−1272.62			−0.283690
$273$		0			0
$274$	−2744.62			−0.605141
$275$	1272.39	−	2203.85i	0.279011	−	0.483262i
$276$		0			0
$277$	1598.27	+	2768.29i	0.346682	+	0.600471i	0.985658	−	0.168756i	$-0.0539750\pi$
$277$	1598.27	+	2768.29i	0.346682	+	0.600471i	−0.638976	+	0.769227i	$0.720642\pi$
$278$	−418.909	+	725.571i	−0.0903758	+	0.156535i
$279$		0			0
$280$	−6478.15	−	589.478i	−1.38265	−	0.125814i
$281$	−6225.15			−1.32157			−0.660785	−	0.750575i	$-0.729777\pi$
$281$	−6225.15			−1.32157			−0.660785	+	0.750575i	$0.729777\pi$
$282$		0			0
$283$	1858.75	+	3219.45i	0.390429	+	0.676242i	0.992506	−	0.122195i	$-0.0389935\pi$
$283$	1858.75	+	3219.45i	0.390429	+	0.676242i	−0.602077	+	0.798438i	$0.705660\pi$
$284$	1834.99	+	3178.30i	0.383404	+	0.664075i
$285$		0			0
$286$	−818.423			−0.169211
$287$	−2156.26	−	4666.43i	−0.443485	−	0.959758i
$288$		0			0
$289$	390.347	−	676.100i	0.0794518	−	0.137615i
$290$	−1659.42	−	2874.20i	−0.336015	−	0.581996i
$291$		0			0
$292$	490.835	−	850.151i	0.0983696	−	0.170381i
$293$	−6392.56			−1.27460			−0.637299	−	0.770616i	$-0.719948\pi$
$293$	−6392.56			−1.27460			−0.637299	+	0.770616i	$0.719948\pi$
$294$		0			0
$295$	10472.3			2.06685
$296$	865.983	−	1499.93i	0.170048	−	0.294532i
$297$		0			0
$298$	−448.448	−	776.735i	−0.0871742	−	0.150990i
$299$	−128.957	+	223.361i	−0.0249425	+	0.0432016i
$300$		0			0
$301$	1386.86	+	3001.34i	0.265572	+	0.574732i
$302$	4047.33			0.771183
$303$		0			0
$304$	−1092.30	−	1891.92i	−0.206078	−	0.356938i
$305$	4808.61	+	8328.76i	0.902755	+	1.56362i
$306$		0			0
$307$	939.255			0.174613			0.0873063	−	0.996182i	$-0.472174\pi$
$307$	939.255			0.174613			0.0873063	+	0.996182i	$0.472174\pi$
$308$	2066.75	+	188.063i	0.382350	+	0.0347919i
$309$		0			0
$310$	−2881.44	+	4990.80i	−0.527918	+	0.914381i
$311$	1375.81	+	2382.97i	0.250851	+	0.434487i	0.963760	−	0.266769i	$-0.0859561\pi$
$311$	1375.81	+	2382.97i	0.250851	+	0.434487i	−0.712909	+	0.701257i	$0.752623\pi$
$312$		0			0
$313$	318.550	−	551.744i	0.0575255	−	0.0996372i	−0.835829	−	0.548991i	$-0.815012\pi$
$313$	318.550	−	551.744i	0.0575255	−	0.0996372i	0.893354	+	0.449353i	$0.148346\pi$
$314$	−1712.32			−0.307744
$315$		0			0
$316$	−4646.75			−0.827216
$317$	1436.10	−	2487.39i	0.254445	−	0.440712i	−0.710299	−	0.703900i	$-0.751440\pi$
$317$	1436.10	−	2487.39i	0.254445	−	0.440712i	0.964745	+	0.263187i	$0.0847738\pi$
$318$		0			0
$319$	1656.10	+	2868.45i	0.290670	+	0.503456i
$320$	3432.93	−	5946.02i	0.599709	−	1.03873i
$321$		0			0
$322$	−425.306	+	602.925i	−0.0736068	+	0.104347i
$323$	−7093.60			−1.22198
$324$		0			0
$325$	569.065	+	985.650i	0.0971263	+	0.168228i
$326$	−1211.03	−	2097.56i	−0.205744	−	0.356359i
$327$		0			0
$328$	6721.47			1.13150
$329$	9809.92	+	892.651i	1.64389	+	0.149585i
$330$		0			0
$331$	3196.80	−	5537.02i	0.530852	−	0.919463i	−0.468499	−	0.883464i	$-0.655205\pi$
$331$	3196.80	−	5537.02i	0.530852	−	0.919463i	0.999352	−	0.0359995i	$-0.0114615\pi$
$332$	2303.90	+	3990.47i	0.380852	+	0.659656i
$333$		0			0
$334$	1723.98	−	2986.01i	0.282430	−	0.489184i
$335$	8826.59			1.43955
$336$		0			0
$337$	−12107.6			−1.95710			−0.978549	−	0.206016i	$-0.933950\pi$
$337$	−12107.6			−1.95710			−0.978549	+	0.206016i	$0.933950\pi$
$338$	−2079.19	+	3601.26i	−0.334594	+	0.579534i
$339$		0			0
$340$	−1752.41	−	3035.26i	−0.279522	−	0.484147i
$341$	2875.68	−	4980.82i	0.456676	−	0.790986i
$342$		0			0
$343$	6118.50	+	1708.08i	0.963172	+	0.268884i
$344$	−4323.10			−0.677575
$345$		0			0
$346$	1475.45	+	2555.55i	0.229250	+	0.397073i
$347$	−1355.07	−	2347.05i	−0.209636	−	0.363101i	0.741964	−	0.670440i	$-0.233895\pi$
$347$	−1355.07	−	2347.05i	−0.209636	−	0.363101i	−0.951600	+	0.307339i	$0.900561\pi$
$348$		0			0
$349$	−1175.22			−0.180252			−0.0901261	−	0.995930i	$-0.528727\pi$
$349$	−1175.22			−0.180252			−0.0901261	+	0.995930i	$0.528727\pi$
$350$	1365.75	+	2955.65i	0.208578	+	0.451390i
$351$		0			0
$352$	−2279.81	+	3948.74i	−0.345211	+	0.597923i
$353$	−2638.20	−	4569.50i	−0.397783	−	0.688980i	0.595669	−	0.803230i	$-0.296887\pi$
$353$	−2638.20	−	4569.50i	−0.397783	−	0.688980i	−0.993452	+	0.114250i	$0.963554\pi$
$354$		0			0
$355$	7080.21	−	12263.3i	1.05853	−	1.83343i
$356$	2977.10			0.443219
$357$		0			0
$358$	2459.96			0.363165
$359$	5643.27	−	9774.43i	0.829639	−	1.43698i	−0.0686829	−	0.997639i	$-0.521880\pi$
$359$	5643.27	−	9774.43i	0.829639	−	1.43698i	0.898322	−	0.439338i	$-0.144787\pi$
$360$		0			0
$361$	−2659.01	−	4605.55i	−0.387668	−	0.671460i
$362$	763.428	−	1322.30i	0.110842	−	0.191984i
$363$		0			0
$364$	−535.008	+	758.441i	−0.0770385	+	0.109212i
$365$	−3787.72			−0.543173
$366$		0			0
$367$	−3783.80	−	6553.73i	−0.538181	−	0.932158i	−0.999002	−	0.0446643i	$-0.985778\pi$
$367$	−3783.80	−	6553.73i	−0.538181	−	0.932158i	0.460821	−	0.887493i	$-0.347555\pi$
$368$	−191.493	−	331.676i	−0.0271258	−	0.0469832i
$369$		0			0
$370$	−2136.28			−0.300162
$371$	−3318.29	+	4704.09i	−0.464358	+	0.658286i
$372$		0			0
$373$	3251.99	−	5632.61i	0.451425	−	0.781891i	−0.547050	−	0.837100i	$-0.684249\pi$
$373$	3251.99	−	5632.61i	0.451425	−	0.781891i	0.998475	+	0.0552092i	$0.0175826\pi$
$374$	−1973.11	−	3417.52i	−0.272799	−	0.472502i
$375$		0			0
$376$	−6439.95	+	11154.3i	−0.883285	+	1.52989i
$377$	−1481.35			−0.202370
$378$		0			0
$379$	10773.8			1.46019			0.730097	−	0.683344i	$-0.239475\pi$
$379$	10773.8			1.46019			0.730097	+	0.683344i	$0.239475\pi$
$380$	3008.22	−	5210.39i	0.406101	−	0.703388i
$381$		0			0
$382$	−4019.85	−	6962.58i	−0.538412	−	0.932557i
$383$	3183.06	−	5513.23i	0.424666	−	0.735542i	−0.571724	−	0.820446i	$-0.693725\pi$
$383$	3183.06	−	5513.23i	0.424666	−	0.735542i	0.996389	+	0.0849039i	$0.0270583\pi$
$384$		0			0
$385$	−3358.80	−	7268.87i	−0.444624	−	0.962223i
$386$	−3647.64			−0.480985
$387$		0			0
$388$	−1757.83	−	3044.66i	−0.230001	−	0.398374i
$389$	2951.72	+	5112.53i	0.384725	+	0.666363i	0.991731	−	0.128334i	$-0.0409629\pi$
$389$	2951.72	+	5112.53i	0.384725	+	0.666363i	−0.607006	+	0.794697i	$0.707630\pi$
$390$		0			0
$391$	−1243.59			−0.160847
$392$	−5383.20	+	6325.56i	−0.693604	+	0.815022i
$393$		0			0
$394$	855.010	−	1480.92i	0.109327	−	0.189360i
$395$	8964.62	+	15527.2i	1.14192	+	1.97786i
$396$		0			0
$397$	−1883.39	+	3262.13i	−0.238097	+	0.412397i	−0.960168	−	0.279422i	$-0.909857\pi$
$397$	−1883.39	+	3262.13i	−0.238097	+	0.412397i	0.722071	+	0.691819i	$0.243190\pi$
$398$	−2188.08			−0.275574
$399$		0			0
$400$	−1690.05			−0.211256
$401$	−3626.00	+	6280.42i	−0.451556	+	0.782118i	−0.998483	−	0.0550625i	$-0.982464\pi$
$401$	−3626.00	+	6280.42i	−0.451556	+	0.782118i	0.546927	+	0.837180i	$0.315798\pi$
$402$		0			0
$403$	1286.12	+	2227.62i	0.158973	+	0.275349i
$404$	−832.573	+	1442.06i	−0.102530	+	0.177587i
$405$		0			0
$406$	−4220.39	−	384.033i	−0.515897	−	0.0469440i
$407$	2132.01			0.259655
$408$		0			0
$409$	−6273.70	−	10866.4i	−0.758471	−	1.31371i	−0.943630	−	0.331002i	$-0.892613\pi$
$409$	−6273.70	−	10866.4i	−0.758471	−	1.31371i	0.185159	−	0.982709i	$-0.440720\pi$
$410$	−4145.27	−	7179.82i	−0.499318	−	0.864844i
$411$		0			0
$412$	2629.08			0.314383
$413$	7707.95	−	10927.0i	0.918362	−	1.30190i
$414$		0			0
$415$	8889.47	−	15397.0i	1.05149	−	1.82123i
$416$	−1019.62	−	1766.04i	−0.120171	−	0.208142i
$417$		0			0
$418$	3387.07	−	5866.58i	0.396333	−	0.686469i
$419$	−12631.5			−1.47276			−0.736381	−	0.676567i	$-0.763467\pi$
$419$	−12631.5			−1.47276			−0.736381	+	0.676567i	$0.763467\pi$
$420$		0			0
$421$	−3495.94			−0.404707			−0.202354	−	0.979312i	$-0.564859\pi$
$421$	−3495.94			−0.404707			−0.202354	+	0.979312i	$0.564859\pi$
$422$	−3962.89	+	6863.92i	−0.457134	+	0.791779i
$423$		0			0
$424$	−3763.57	−	6518.69i	−0.431073	−	0.746640i
$425$	−2743.88	+	4752.53i	−0.313171	+	0.542427i
$426$		0			0
$427$	12229.7	+	1112.84i	1.38603	+	0.126122i
$428$	−7184.23			−0.811362
$429$		0			0
$430$	2666.14	+	4617.89i	0.299006	+	0.517894i
$431$	1172.59	+	2030.99i	0.131048	+	0.226982i	0.924081	−	0.382197i	$-0.124832\pi$
$431$	1172.59	+	2030.99i	0.131048	+	0.226982i	−0.793033	+	0.609179i	$0.791499\pi$
$432$		0			0
$433$	3250.63			0.360774			0.180387	−	0.983596i	$-0.442265\pi$
$433$	3250.63			0.360774			0.180387	+	0.983596i	$0.442265\pi$
$434$	3086.67	+	6679.94i	0.341393	+	0.738819i
$435$		0			0
$436$	−3893.28	+	6743.36i	−0.427648	+	0.740708i
$437$	−1067.39	−	1848.77i	−0.116842	−	0.202377i
$438$		0			0
$439$	−8120.24	+	14064.7i	−0.882820	+	1.52909i	−0.0346287	+	0.999400i	$0.511025\pi$
$439$	−8120.24	+	14064.7i	−0.882820	+	1.52909i	−0.848192	+	0.529689i	$0.822308\pi$
$440$	10470.0			1.13440
$441$		0			0
$442$	1764.91			0.189928
$443$	−2424.52	+	4199.39i	−0.260028	+	0.450382i	−0.966249	−	0.257610i	$-0.917065\pi$
$443$	−2424.52	+	4199.39i	−0.260028	+	0.450382i	0.706221	+	0.707991i	$0.250398\pi$
$444$		0			0
$445$	−5743.49	−	9948.01i	−0.611837	−	1.05973i
$446$	5645.47	−	9778.23i	0.599373	−	1.03815i
$447$		0			0
$448$	−3677.44	−	7958.46i	−0.387819	−	0.839290i
$449$	4139.93			0.435134			0.217567	−	0.976045i	$-0.430188\pi$
$449$	4139.93			0.435134			0.217567	+	0.976045i	$0.430188\pi$
$450$		0			0
$451$	4136.98	+	7165.46i	0.431935	+	0.748134i
$452$	−4347.99	−	7530.94i	−0.452461	−	0.783685i
$453$		0			0
$454$	−813.110			−0.0840553
$455$	3566.49	+	324.532i	0.367471	+	0.0334380i
$456$		0			0
$457$	−4616.24	+	7995.56i	−0.472513	+	0.818417i	−0.999505	−	0.0314531i	$-0.989987\pi$
$457$	−4616.24	+	7995.56i	−0.472513	+	0.818417i	0.526992	+	0.849870i	$0.323320\pi$
$458$	−3937.04	−	6819.16i	−0.401672	−	0.695717i
$459$		0			0
$460$	527.377	−	913.443i	0.0534545	−	0.0925859i
$461$	−1274.90			−0.128803			−0.0644013	−	0.997924i	$-0.520514\pi$
$461$	−1274.90			−0.128803			−0.0644013	+	0.997924i	$0.520514\pi$
$462$		0			0
$463$	2061.80			0.206955			0.103477	−	0.994632i	$-0.467003\pi$
$463$	2061.80			0.206955			0.103477	+	0.994632i	$0.467003\pi$
$464$	1099.86	−	1905.01i	0.110042	−	0.190599i
$465$		0			0
$466$	−2612.85	−	4525.59i	−0.259738	−	0.449879i
$467$	−484.021	+	838.348i	−0.0479610	+	0.0830710i	−0.889009	−	0.457889i	$-0.848606\pi$
$467$	−484.021	+	838.348i	−0.0479610	+	0.0830710i	0.841048	+	0.540960i	$0.181939\pi$
$468$		0			0
$469$	6496.66	−	9209.84i	0.639633	−	0.906761i
$470$	15886.6			1.55914
$471$		0			0
$472$	8742.29	+	15142.1i	0.852535	+	1.47663i
$473$	−2660.81	−	4608.66i	−0.258656	−	0.448005i
$474$		0			0
$475$	−9420.39			−0.909973
$476$	−4456.88	−	405.553i	−0.429161	−	0.0390515i
$477$		0			0
$478$	5528.15	−	9575.03i	0.528978	−	0.916217i
$479$	3100.02	+	5369.40i	0.295707	+	0.512180i	0.975149	−	0.221549i	$-0.0711114\pi$
$479$	3100.02	+	5369.40i	0.295707	+	0.512180i	−0.679442	+	0.733729i	$0.737778\pi$
$480$		0			0
$481$	−476.760	+	825.772i	−0.0451941	+	0.0782785i
$482$	−4341.17			−0.410238
$483$		0			0
$484$	1663.01			0.156181
$485$	−6782.50	+	11747.6i	−0.635005	+	1.09986i
$486$		0			0
$487$	4914.83	+	8512.74i	0.457315	+	0.792092i	0.998818	−	0.0486063i	$-0.0154780\pi$
$487$	4914.83	+	8512.74i	0.457315	+	0.792092i	−0.541503	+	0.840699i	$0.682145\pi$
$488$	−8028.47	+	13905.7i	−0.744738	+	1.28992i
$489$		0			0
$490$	10076.8	+	1849.19i	0.929030	+	0.170485i
$491$	5053.57			0.464489			0.232245	−	0.972657i	$-0.425393\pi$
$491$	5053.57			0.464489			0.232245	+	0.972657i	$0.425393\pi$
$492$		0			0
$493$	−3571.33	−	6185.73i	−0.326257	−	0.565094i
$494$	1514.84	+	2623.77i	0.137967	+	0.238966i
$495$		0			0
$496$	−3819.61			−0.345777
$497$	−7584.49	−	16413.8i	−0.684529	−	1.48141i
$498$		0			0
$499$	−7030.82	+	12177.7i	−0.630747	+	1.09249i	0.356652	+	0.934237i	$0.383918\pi$
$499$	−7030.82	+	12177.7i	−0.630747	+	1.09249i	−0.987399	+	0.158249i	$0.949415\pi$
$500$	1080.38	+	1871.28i	0.0966325	+	0.167372i
$501$		0			0
$502$	−5887.64	+	10197.7i	−0.523463	+	0.906664i
$503$	−8001.67			−0.709298			−0.354649	−	0.934999i	$-0.615400\pi$
$503$	−8001.67			−0.709298			−0.354649	+	0.934999i	$0.615400\pi$
$504$		0			0
$505$	6424.87			0.566144
$506$	593.794	−	1028.48i	0.0521687	−	0.0903589i
$507$		0			0
$508$	−2476.27	−	4289.02i	−0.216273	−	0.374596i
$509$	−5456.91	+	9451.65i	−0.475193	+	0.823059i	−0.999596	−	0.0284114i	$-0.990955\pi$
$509$	−5456.91	+	9451.65i	−0.475193	+	0.823059i	0.524403	+	0.851470i	$0.324288\pi$
$510$		0			0
$511$	−2787.88	+	3952.18i	−0.241348	+	0.342141i
$512$	6863.42			0.592428
$513$		0			0
$514$	5135.49	+	8894.93i	0.440694	+	0.763304i
$515$	−5072.08	−	8785.11i	−0.433986	−	0.751686i
$516$		0			0
$517$	−15854.8			−1.34873
$518$	−1572.37	+	2229.04i	−0.133371	+	0.189070i
$519$		0			0
$520$	−2341.31	+	4055.26i	−0.197448	+	0.341990i
$521$	−7901.70	−	13686.1i	−0.664452	−	1.15087i	−0.979433	−	0.201767i	$-0.935332\pi$
$521$	−7901.70	−	13686.1i	−0.664452	−	1.15087i	0.314981	−	0.949098i	$-0.398002\pi$
$522$		0			0
$523$	323.047	−	559.534i	0.0270093	−	0.0467815i	−0.852205	−	0.523208i	$-0.824735\pi$
$523$	323.047	−	559.534i	0.0270093	−	0.0467815i	0.879214	+	0.476427i	$0.158068\pi$
$524$	1724.81			0.143795
$525$		0			0
$526$	−1267.07			−0.105032
$527$	−6201.31	+	10741.0i	−0.512587	+	0.887827i
$528$		0			0
$529$	5896.37	+	10212.8i	0.484620	+	0.839387i
$530$	−4642.14	+	8040.41i	−0.380456	+	0.658968i
$531$		0			0
$532$	−3222.48	−	6973.86i	−0.262617	−	0.568337i
$533$	−3700.45			−0.300721
$534$		0			0
$535$	13860.0	+	24006.2i	1.12004	+	1.93996i
$536$	7368.45	+	12762.5i	0.593785	+	1.02847i
$537$		0			0
$538$	1635.05			0.131026
$539$	−10056.7	−	1845.49i	−0.803658	−	0.147479i
$540$		0			0
$541$	−5123.33	+	8873.86i	−0.407152	+	0.705207i	−0.994569	−	0.104077i	$-0.966811\pi$
$541$	−5123.33	+	8873.86i	−0.407152	+	0.705207i	0.587418	+	0.809284i	$0.300145\pi$
$542$	3876.68	+	6714.61i	0.307228	+	0.532135i
$543$		0			0
$544$	4916.34	−	8515.36i	0.387475	−	0.671127i
$545$	30044.0			2.36137
$546$		0			0
$547$	4368.98			0.341506			0.170753	−	0.985314i	$-0.445380\pi$
$547$	4368.98			0.341506			0.170753	+	0.985314i	$0.445380\pi$
$548$	2504.95	−	4338.70i	0.195267	−	0.338212i
$549$		0			0
$550$	−2620.31	−	4538.50i	−0.203146	−	0.351859i
$551$	6130.63	−	10618.6i	0.473999	−	0.820990i
$552$		0			0
$553$	22799.6	+	2074.65i	1.75323	+	0.159535i
$554$	6582.82			0.504833
$555$		0			0
$556$	−764.656	−	1324.42i	−0.0583249	−	0.101022i
$557$	−4198.21	−	7271.52i	−0.319361	−	0.553149i	0.660994	−	0.750391i	$-0.270135\pi$
$557$	−4198.21	−	7271.52i	−0.319361	−	0.553149i	−0.980355	+	0.197242i	$0.936802\pi$
$558$		0			0
$559$	2380.04			0.180081
$560$	−3065.35	+	4345.52i	−0.231312	+	0.327914i
$561$		0			0
$562$	−6409.90	+	11102.3i	−0.481113	+	0.833312i
$563$	6071.13	+	10515.5i	0.454472	+	0.787169i	0.998658	−	0.0517962i	$-0.0164946\pi$
$563$	6071.13	+	10515.5i	0.454472	+	0.787169i	−0.544186	+	0.838965i	$0.683161\pi$
$564$		0			0
$565$	−16776.5	+	29057.7i	−1.24919	+	2.16366i
$566$	7655.66			0.568536
$567$		0			0
$568$	23642.3			1.74649
$569$	5598.06	−	9696.12i	0.412448	−	0.714381i	−0.582709	−	0.812681i	$-0.698007\pi$
$569$	5598.06	−	9696.12i	0.412448	−	0.714381i	0.995157	+	0.0983003i	$0.0313406\pi$
$570$		0			0
$571$	−9829.79	−	17025.7i	−0.720427	−	1.24782i	−0.960829	−	0.277143i	$-0.910612\pi$
$571$	−9829.79	−	17025.7i	−0.720427	−	1.24782i	0.240402	−	0.970674i	$-0.422721\pi$
$572$	746.955	−	1293.76i	0.0546010	−	0.0945717i
$573$		0			0
$574$	−10542.6	−	959.324i	−0.766621	−	0.0697586i
$575$	−1651.51			−0.119778
$576$		0			0
$577$	−4258.23	−	7375.46i	−0.307231	−	0.532140i	0.670525	−	0.741887i	$-0.266069\pi$
$577$	−4258.23	−	7375.46i	−0.307231	−	0.532140i	−0.977756	+	0.209748i	$0.932736\pi$
$578$	−803.863	−	1392.33i	−0.0578482	−	0.100196i
$579$		0			0
$580$	6058.05			0.433702
$581$	−9522.62	−	20608.2i	−0.679974	−	1.47155i
$582$		0			0
$583$	4632.85	−	8024.33i	0.329113	−	0.570041i
$584$	−3161.99	−	5476.73i	−0.224048	−	0.388063i
$585$		0			0
$586$	−6582.28	+	11400.8i	−0.464013	+	0.803694i
$587$	7115.53			0.500323			0.250161	−	0.968204i	$-0.419516\pi$
$587$	7115.53			0.500323			0.250161	+	0.968204i	$0.419516\pi$
$588$		0			0
$589$	−21290.6			−1.48941
$590$	10783.1	−	18676.9i	0.752428	−	1.30324i
$591$		0			0
$592$	−707.958	−	1226.22i	−0.0491502	−	0.0851306i
$593$	3072.24	−	5321.28i	0.212752	−	0.368497i	−0.739823	−	0.672802i	$-0.765091\pi$
$593$	3072.24	−	5321.28i	0.212752	−	0.368497i	0.952575	+	0.304305i	$0.0984241\pi$
$594$		0			0
$595$	7243.15	+	15675.1i	0.499059	+	1.08003i
$596$	1637.15			0.112517
$597$		0			0
$598$	265.569	+	459.979i	0.0181604	+	0.0314547i
$599$	4789.20	+	8295.13i	0.326680	+	0.565826i	0.981851	−	0.189654i	$-0.0607368\pi$
$599$	4789.20	+	8295.13i	0.326680	+	0.565826i	−0.655171	+	0.755481i	$0.727403\pi$
$600$		0			0
$601$	−19113.8			−1.29728			−0.648642	−	0.761094i	$-0.724663\pi$
$601$	−19113.8			−1.29728			−0.648642	+	0.761094i	$0.724663\pi$
$602$	6780.77	+	617.015i	0.459076	+	0.0417735i
$603$		0			0
$604$	−3693.90	+	6398.02i	−0.248845	+	0.431013i
$605$	−3208.32	−	5556.98i	−0.215598	−	0.373427i
$606$		0			0
$607$	−10221.3	+	17703.9i	−0.683477	+	1.18382i	0.290435	+	0.956895i	$0.406200\pi$
$607$	−10221.3	+	17703.9i	−0.683477	+	1.18382i	−0.973913	+	0.226923i	$0.927134\pi$
$608$	16879.0			1.12588
$609$		0			0
$610$	19805.3			1.31458
$611$	3545.46	−	6140.92i	0.234753	−	0.406604i
$612$		0			0
$613$	−8711.37	−	15088.5i	−0.573978	−	0.994160i	−0.996152	−	0.0876447i	$-0.972066\pi$
$613$	−8711.37	−	15088.5i	−0.573978	−	0.994160i	0.422173	−	0.906515i	$-0.361267\pi$
$614$	967.130	−	1675.12i	0.0635671	−	0.110101i
$615$		0			0
$616$	7706.27	−	10924.6i	0.504049	−	0.714554i
$617$	1805.17			0.117785			0.0588926	−	0.998264i	$-0.481243\pi$
$617$	1805.17			0.117785			0.0588926	+	0.998264i	$0.481243\pi$
$618$		0			0
$619$	−4071.12	−	7051.38i	−0.264349	−	0.457866i	0.703044	−	0.711146i	$-0.251824\pi$
$619$	−4071.12	−	7051.38i	−0.264349	−	0.457866i	−0.967393	+	0.253281i	$0.918490\pi$
$620$	−5259.64	−	9109.97i	−0.340697	−	0.590105i
$621$		0			0
$622$	5666.55			0.365286
$623$	−14607.4	−	1329.19i	−0.939376	−	0.0854783i
$624$		0			0
$625$	9504.14	−	16461.7i	0.608265	−	1.05355i
$626$	−656.007	−	1136.24i	−0.0418839	−	0.0725451i
$627$		0			0
$628$	1562.79	−	2706.84i	0.0993029	−	0.171998i
$629$	−4597.61			−0.291445
$630$		0			0
$631$	3630.07			0.229019			0.114509	−	0.993422i	$-0.463470\pi$
$631$	3630.07			0.229019			0.114509	+	0.993422i	$0.463470\pi$
$632$	−14967.4	+	25924.2i	−0.942040	+	1.63166i
$633$		0			0
$634$	−2957.43	−	5122.42i	−0.185260	−	0.320879i
$635$	−9554.54	+	16548.9i	−0.597103	+	1.03421i
$636$		0			0
$637$	2963.68	−	3482.48i	0.184341	−	0.216611i
$638$	6821.00			0.423270
$639$		0			0
$640$	1804.51	+	3125.50i	0.111452	+	0.193041i
$641$	11111.8	+	19246.2i	0.684696	+	1.18593i	0.973532	+	0.228550i	$0.0733984\pi$
$641$	11111.8	+	19246.2i	0.684696	+	1.18593i	−0.288836	+	0.957379i	$0.593268\pi$
$642$		0			0
$643$	−5013.00			−0.307455			−0.153727	−	0.988113i	$-0.549128\pi$
$643$	−5013.00			−0.307455			−0.153727	+	0.988113i	$0.549128\pi$
$644$	−564.939	−	1222.60i	−0.0345679	−	0.0748093i
$645$		0			0
$646$	−7304.13	+	12651.1i	−0.444856	+	0.770514i
$647$	3858.08	+	6682.39i	0.234431	+	0.406046i	0.959107	−	0.283043i	$-0.0913440\pi$
$647$	3858.08	+	6682.39i	0.234431	+	0.406046i	−0.724676	+	0.689090i	$0.758011\pi$
$648$		0			0
$649$	−10761.5	+	18639.5i	−0.650889	+	1.12737i
$650$	2343.82			0.141434
$651$		0			0
$652$	4421.10			0.265558
$653$	−2822.20	+	4888.20i	−0.169129	+	0.292940i	−0.938114	−	0.346327i	$-0.887429\pi$
$653$	−2822.20	+	4888.20i	−0.169129	+	0.292940i	0.768985	+	0.639267i	$0.220762\pi$
$654$		0			0
$655$	−3327.54	−	5763.46i	−0.198500	−	0.343812i
$656$	2747.47	−	4758.75i	0.163522	−	0.283229i
$657$		0			0
$658$	11693.1	−	16576.4i	0.692770	−	0.982090i
$659$	−8812.27			−0.520906			−0.260453	−	0.965487i	$-0.583872\pi$
$659$	−8812.27			−0.520906			−0.260453	+	0.965487i	$0.583872\pi$
$660$		0			0
$661$	3095.51	+	5361.58i	0.182150	+	0.315493i	0.942613	−	0.333889i	$-0.108361\pi$
$661$	3095.51	+	5361.58i	0.182150	+	0.315493i	−0.760462	+	0.649382i	$0.775028\pi$
$662$	−6583.35	−	11402.7i	−0.386510	−	0.669454i
$663$		0			0
$664$	29683.8			1.73487
$665$	−17086.3	+	24222.1i	−0.996360	+	1.41247i
$666$		0			0
$667$	1074.77	−	1861.56i	0.0623918	−	0.108066i
$668$	3146.86	+	5450.53i	0.182269	+	0.315699i
$669$		0			0
$670$	9088.54	−	15741.8i	0.524061	−	0.907701i
$671$	−19765.7			−1.13718
$672$		0			0
$673$	29580.7			1.69428			0.847141	−	0.531368i	$-0.178322\pi$
$673$	29580.7			1.69428			0.847141	+	0.531368i	$0.178322\pi$
$674$	−12466.9	+	21593.3i	−0.712474	+	1.23404i
$675$		0			0
$676$	−3795.25	−	6573.57i	−0.215934	−	0.374008i
$677$	13145.0	−	22767.8i	0.746239	−	1.29252i	−0.203374	−	0.979101i	$-0.565191\pi$
$677$	13145.0	−	22767.8i	0.746239	−	1.29252i	0.949613	−	0.313423i	$-0.101476\pi$
$678$		0			0
$679$	7265.58	+	15723.6i	0.410644	+	0.888686i
$680$	−22578.3			−1.27329
$681$		0			0
$682$	−5922.04	−	10257.3i	−0.332502	−	0.575911i
$683$	−405.342	−	702.073i	−0.0227086	−	0.0393325i	0.854448	−	0.519537i	$-0.173896\pi$
$683$	−405.342	−	702.073i	−0.0227086	−	0.0393325i	−0.877156	+	0.480205i	$0.840562\pi$
$684$		0			0
$685$	−19330.4			−1.07821
$686$	9346.36	−	9153.31i	0.520183	−	0.509439i
$687$		0			0
$688$	−1767.11	+	3060.72i	−0.0979220	+	0.169606i
$689$	2072.00	+	3588.81i	0.114567	+	0.198436i
$690$		0			0
$691$	−585.690	+	1014.45i	−0.0322442	+	0.0558485i	−0.881697	−	0.471816i	$-0.843599\pi$
$691$	−585.690	+	1014.45i	−0.0322442	+	0.0558485i	0.849453	+	0.527664i	$0.176932\pi$
$692$	−5386.42			−0.295897
$693$		0			0
$694$	−5581.14			−0.305269
$695$	−2950.38	+	5110.21i	−0.161028	+	0.278908i
$696$		0			0
$697$	−8921.28	−	15452.1i	−0.484817	−	0.839728i
$698$	−1210.10	+	2095.95i	−0.0656201	+	0.113657i
$699$		0			0
$700$	−5918.79	−	538.579i	−0.319585	−	0.0290805i
$701$	1057.70			0.0569885			0.0284943	−	0.999594i	$-0.490929\pi$
$701$	1057.70			0.0569885			0.0284943	+	0.999594i	$0.490929\pi$
$702$		0			0
$703$	−3946.18	−	6834.98i	−0.211711	−	0.366694i
$704$	7055.49	+	12220.5i	0.377719	+	0.654228i
$705$		0			0
$706$	−10866.0			−0.579245
$707$	4728.92	−	6703.84i	0.251555	−	0.356611i
$708$		0			0
$709$	14621.9	−	25325.8i	0.774521	−	1.34151i	−0.160542	−	0.987029i	$-0.551324\pi$
$709$	14621.9	−	25325.8i	0.774521	−	1.34151i	0.935063	−	0.354481i	$-0.115343\pi$
$710$	−14580.7	−	25254.5i	−0.770708	−	1.33491i
$711$		0			0
$712$	9589.34	−	16609.2i	0.504741	−	0.874238i
$713$	−3732.50			−0.196049
$714$		0			0
$715$	−5764.17			−0.301493
$716$	−2245.15	+	3888.72i	−0.117186	+	0.202972i
$717$		0			0
$718$	−11621.5	−	20129.0i	−0.604054	−	1.04625i
$719$	12278.9	−	21267.6i	0.636890	−	1.10313i	−0.349221	−	0.937040i	$-0.613554\pi$
$719$	12278.9	−	21267.6i	0.636890	−	1.10313i	0.986111	−	0.166086i	$-0.0531128\pi$
$720$		0			0
$721$	−12899.8	−	1173.81i	−0.666315	−	0.0606312i
$722$	−10951.7			−0.564516
$723$		0			0
$724$	1393.53	+	2413.66i	0.0715331	+	0.123899i
$725$	−4742.77	−	8214.72i	−0.242955	−	0.420810i
$726$		0			0
$727$	−23444.2			−1.19601			−0.598003	−	0.801494i	$-0.704039\pi$
$727$	−23444.2			−1.19601			−0.598003	+	0.801494i	$0.704039\pi$
$728$	2508.06	+	5427.77i	0.127685	+	0.276328i
$729$		0			0
$730$	−3900.13	+	6755.22i	−0.197740	+	0.342496i
$731$	5737.96	+	9938.44i	0.290323	+	0.502854i
$732$		0			0
$733$	17985.6	−	31152.0i	0.906296	−	1.56975i	0.0871278	−	0.996197i	$-0.472231\pi$
$733$	17985.6	−	31152.0i	0.906296	−	1.56975i	0.819168	−	0.573553i	$-0.194436\pi$
$734$	−15584.4			−0.783692
$735$		0			0
$736$	2959.09			0.148198
$737$	−9070.37	+	15710.3i	−0.453340	+	0.785207i
$738$		0			0
$739$	−6034.31	−	10451.7i	−0.300373	−	0.520261i	0.675848	−	0.737041i	$-0.263778\pi$
$739$	−6034.31	−	10451.7i	−0.300373	−	0.520261i	−0.976220	+	0.216780i	$0.930444\pi$
$740$	1949.73	−	3377.03i	0.0968561	−	0.167760i
$741$		0			0
$742$	4972.77	+	10761.7i	0.246032	+	0.532446i
$743$	5475.09			0.270339			0.135169	−	0.990823i	$-0.456842\pi$
$743$	5475.09			0.270339			0.135169	+	0.990823i	$0.456842\pi$
$744$		0			0
$745$	−3158.43	−	5470.56i	−0.155323	−	0.269028i
$746$	−6697.00	−	11599.5i	−0.328679	−	0.569289i
$747$		0			0
$748$	7203.23			0.352107
$749$	35250.0	+	3207.56i	1.71963	+	0.156478i
$750$		0			0
$751$	−12637.3	+	21888.4i	−0.614036	+	1.06354i	0.376517	+	0.926410i	$0.377122\pi$
$751$	−12637.3	+	21888.4i	−0.614036	+	1.06354i	−0.990553	+	0.137132i	$0.956212\pi$
$752$	5264.79	+	9118.88i	0.255302	+	0.442196i
$753$		0			0
$754$	−1525.31	+	2641.92i	−0.0736720	+	0.127604i
$755$	28505.4			1.37406
$756$		0			0
$757$	−23583.7			−1.13232			−0.566159	−	0.824296i	$-0.691571\pi$
$757$	−23583.7			−1.13232			−0.566159	+	0.824296i	$0.691571\pi$
$758$	11093.6	−	19214.6i	0.531578	−	0.920720i
$759$		0			0
$760$	−19379.2	−	33565.7i	−0.924942	−	1.60205i
$761$	−8101.35	+	14032.0i	−0.385905	+	0.668407i	−0.991894	−	0.127066i	$-0.959444\pi$
$761$	−8101.35	+	14032.0i	−0.385905	+	0.668407i	0.605989	+	0.795473i	$0.292777\pi$
$762$		0			0
$763$	22113.4	−	31348.5i	1.04922	−	1.48741i
$764$	14675.3			0.694939
$765$		0			0
$766$	−6555.06	−	11353.7i	−0.309196	−	0.535543i
$767$	−4812.99	−	8336.34i	−0.226580	−	0.392448i
$768$		0			0
$769$	−18603.1			−0.872362			−0.436181	−	0.899859i	$-0.643669\pi$
$769$	−18603.1			−0.872362			−0.436181	+	0.899859i	$0.643669\pi$
$770$	−16422.2	−	1494.33i	−0.768590	−	0.0699377i
$771$		0			0
$772$	3329.12	−	5766.20i	0.155204	−	0.268821i
$773$	13640.7	+	23626.3i	0.634697	+	1.09933i	0.986579	+	0.163283i	$0.0522083\pi$
$773$	13640.7	+	23626.3i	0.634697	+	1.09933i	−0.351883	+	0.936044i	$0.614458\pi$
$774$		0			0
$775$	−8235.42	+	14264.2i	−0.381709	+	0.661140i
$776$	−22648.2			−1.04771
$777$		0			0
$778$	12157.3			0.560231
$779$	15314.5	−	26525.4i	0.704361	−	1.21999i

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)

\(f(q)\)	\(=\)	\(q+(1.02968 - 1.78345i) q^{2} +(1.87953 + 3.25543i) q^{4} +(7.25204 - 12.5609i) q^{5} +(-7.76857 - 16.8122i) q^{7} +24.2161 q^{8} +O(q^{10})\)	\(q+(1.02968 - 1.78345i) q^{2} +(1.87953 + 3.25543i) q^{4} +(7.25204 - 12.5609i) q^{5} +(-7.76857 - 16.8122i) q^{7} +24.2161 q^{8} +(-14.9345 - 25.8674i) q^{10} +(14.9047 + 25.8157i) q^{11} -13.3320 q^{13} +(-37.9829 - 3.45625i) q^{14} +(9.89856 - 17.1448i) q^{16} +(-32.1415 - 55.6707i) q^{17} +(55.1748 - 95.5655i) q^{19} +54.5216 q^{20} +61.3881 q^{22} +(9.67280 - 16.7538i) q^{23} +(-42.6843 - 73.9314i) q^{25} +(-13.7276 + 23.7769i) q^{26} +(40.1297 - 56.8890i) q^{28} +111.113 q^{29} +(-96.4689 - 167.089i) q^{31} +(76.4797 + 132.467i) q^{32} -132.382 q^{34} +(-267.514 - 24.3424i) q^{35} +(35.7607 - 61.9393i) q^{37} +(-113.625 - 196.803i) q^{38} +(175.616 - 304.176i) q^{40} +277.562 q^{41} -178.522 q^{43} +(-56.0275 + 97.0424i) q^{44} +(-19.9197 - 34.5020i) q^{46} +(-265.937 + 460.617i) q^{47} +(-222.299 + 261.213i) q^{49} -175.804 q^{50} +(-25.0578 - 43.4013i) q^{52} +(-155.416 - 269.188i) q^{53} +432.357 q^{55} +(-188.124 - 407.125i) q^{56} +(114.410 - 198.165i) q^{58} +(361.012 + 625.290i) q^{59} +(-331.535 + 574.235i) q^{61} -397.328 q^{62} +473.375 q^{64} +(-96.6839 + 167.461i) q^{65} +(304.279 + 527.027i) q^{67} +(120.822 - 209.269i) q^{68} +(-318.867 + 452.035i) q^{70} +976.305 q^{71} +(-130.574 - 226.161i) q^{73} +(-73.6440 - 127.555i) q^{74} +414.810 q^{76} +(318.229 - 451.131i) q^{77} +(-618.075 + 1070.54i) q^{79} +(-143.570 - 248.670i) q^{80} +(285.800 - 495.020i) q^{82} +1225.79 q^{83} -932.367 q^{85} +(-183.820 + 318.386i) q^{86} +(360.933 + 625.154i) q^{88} +(395.991 - 685.876i) q^{89} +(103.570 + 224.139i) q^{91} +72.7211 q^{92} +(547.659 + 948.573i) q^{94} +(-800.260 - 1386.09i) q^{95} -935.253 q^{97} +(236.966 + 665.425i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 32 q^{4} - 26 q^{7}+O(q^{10}) \) 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

Introduction

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