LMFDB - Embedded newform 432.4.i.e.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,4,Mod(145,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, degree $2$, not 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:	$25.4888251225$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.5206055409.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + 9x^{5} - 23x^{4} + 27x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + 9x^5 - 23x^4 + 27x^3 + 9x^2 - 81x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.4
Root			$0.172469 + 1.72344i$ of defining polynomial
Character	$\chi$	$=$	432.289
Dual form			432.4.i.e.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.65944 + 14.9986i) q^{5} +(-1.18676 + 2.05553i) q^{7} +O(q^{10})$	$q+(8.65944 + 14.9986i) q^{5} +(-1.18676 + 2.05553i) q^{7} +(26.1082 - 45.2208i) q^{11} +(-6.84965 - 11.8639i) q^{13} +82.9217 q^{17} +126.803 q^{19} +(27.1831 + 47.0825i) q^{23} +(-87.4718 + 151.506i) q^{25} +(-106.425 + 184.334i) q^{29} +(-112.061 - 194.095i) q^{31} -41.1068 q^{35} -32.2229 q^{37} +(250.331 + 433.586i) q^{41} +(-6.41270 + 11.1071i) q^{43} +(-104.770 + 181.467i) q^{47} +(168.683 + 292.168i) q^{49} -371.213 q^{53} +904.331 q^{55} +(-2.90924 - 5.03895i) q^{59} +(302.016 - 523.107i) q^{61} +(118.628 - 205.470i) q^{65} +(377.033 + 653.040i) q^{67} +43.4780 q^{71} +671.029 q^{73} +(61.9686 + 107.333i) q^{77} +(-324.601 + 562.226i) q^{79} +(-67.2629 + 116.503i) q^{83} +(718.056 + 1243.71i) q^{85} +206.076 q^{89} +32.5156 q^{91} +(1098.04 + 1901.87i) q^{95} +(726.420 - 1258.20i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{5} - 3 q^{7}+O(q^{10}) $ 8 * q + 5 * q^5 - 3 * q^7	$ 8 q + 5 q^{5} - 3 q^{7} + 16 q^{11} + 29 q^{13} + 34 q^{17} + 218 q^{19} + 37 q^{23} + 97 q^{25} + 3 q^{29} - 331 q^{31} - 342 q^{35} - 732 q^{37} + 378 q^{41} - 506 q^{43} + 171 q^{47} + 829 q^{49} - 820 q^{53} + 2326 q^{55} + 616 q^{59} + 1331 q^{61} + 815 q^{65} - 1162 q^{67} - 688 q^{71} - 2614 q^{73} + 741 q^{77} - 1853 q^{79} + 1421 q^{83} + 2074 q^{85} - 1632 q^{89} + 3990 q^{91} + 1292 q^{95} + 2506 q^{97}+O(q^{100}) $ 8 * q + 5 * q^5 - 3 * q^7 + 16 * q^11 + 29 * q^13 + 34 * q^17 + 218 * q^19 + 37 * q^23 + 97 * q^25 + 3 * q^29 - 331 * q^31 - 342 * q^35 - 732 * q^37 + 378 * q^41 - 506 * q^43 + 171 * q^47 + 829 * q^49 - 820 * q^53 + 2326 * q^55 + 616 * q^59 + 1331 * q^61 + 815 * q^65 - 1162 * q^67 - 688 * q^71 - 2614 * q^73 + 741 * q^77 - 1853 * q^79 + 1421 * q^83 + 2074 * q^85 - 1632 * q^89 + 3990 * q^91 + 1292 * q^95 + 2506 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	8.65944	+	14.9986i	0.774524	+	1.34151i	0.935062	+	0.354485i	$0.115344\pi$
$5$	8.65944	+	14.9986i	0.774524	+	1.34151i	−0.160538	+	0.987030i	$0.551323\pi$
$6$		0			0
$7$	−1.18676	+	2.05553i	−0.0640792	+	0.110988i	−0.896285	−	0.443478i	$-0.853744\pi$
$7$	−1.18676	+	2.05553i	−0.0640792	+	0.110988i	0.832206	+	0.554467i	$0.187078\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	26.1082	−	45.2208i	0.715630	−	1.23951i	−0.247086	−	0.968994i	$-0.579473\pi$
$11$	26.1082	−	45.2208i	0.715630	−	1.23951i	0.962716	−	0.270514i	$-0.0871936\pi$
$12$		0			0
$13$	−6.84965	−	11.8639i	−0.146135	−	0.253113i	0.783661	−	0.621189i	$-0.213350\pi$
$13$	−6.84965	−	11.8639i	−0.146135	−	0.253113i	−0.929796	+	0.368076i	$0.880017\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	82.9217			1.18303			0.591514	−	0.806295i	$-0.298531\pi$
$17$	82.9217			1.18303			0.591514	+	0.806295i	$0.298531\pi$
$18$		0			0
$19$	126.803			1.53108			0.765542	−	0.643386i	$-0.222471\pi$
$19$	126.803			1.53108			0.765542	+	0.643386i	$0.222471\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	27.1831	+	47.0825i	0.246437	+	0.426842i	0.962535	−	0.271158i	$-0.0874067\pi$
$23$	27.1831	+	47.0825i	0.246437	+	0.426842i	−0.716097	+	0.698000i	$0.754073\pi$
$24$		0			0
$25$	−87.4718	+	151.506i	−0.699775	+	1.21205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−106.425	+	184.334i	−0.681471	+	1.18034i	0.293060	+	0.956094i	$0.405326\pi$
$29$	−106.425	+	184.334i	−0.681471	+	1.18034i	−0.974532	+	0.224249i	$0.928007\pi$
$30$		0			0
$31$	−112.061	−	194.095i	−0.649250	−	1.12453i	−0.983302	−	0.181980i	$-0.941749\pi$
$31$	−112.061	−	194.095i	−0.649250	−	1.12453i	0.334052	−	0.942555i	$-0.391584\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−41.1068			−0.198523
$36$		0			0
$37$	−32.2229			−0.143173			−0.0715866	−	0.997434i	$-0.522806\pi$
$37$	−32.2229			−0.143173			−0.0715866	+	0.997434i	$0.522806\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	250.331	+	433.586i	0.953540	+	1.65158i	0.737673	+	0.675158i	$0.235924\pi$
$41$	250.331	+	433.586i	0.953540	+	1.65158i	0.215867	+	0.976423i	$0.430742\pi$
$42$		0			0
$43$	−6.41270	+	11.1071i	−0.0227425	+	0.0393912i	−0.877173	−	0.480175i	$-0.840573\pi$
$43$	−6.41270	+	11.1071i	−0.0227425	+	0.0393912i	0.854430	+	0.519566i	$0.173906\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−104.770	+	181.467i	−0.325156	+	0.563186i	−0.981544	−	0.191237i	$-0.938750\pi$
$47$	−104.770	+	181.467i	−0.325156	+	0.563186i	0.656388	+	0.754423i	$0.272083\pi$
$48$		0			0
$49$	168.683	+	292.168i	0.491788	+	0.851801i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−371.213			−0.962075			−0.481038	−	0.876700i	$-0.659740\pi$
$53$	−371.213			−0.962075			−0.481038	+	0.876700i	$0.659740\pi$
$54$		0			0
$55$	904.331			2.21709
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.90924	−	5.03895i	−0.00641950	−	0.0111189i	0.862798	−	0.505549i	$-0.168710\pi$
$59$	−2.90924	−	5.03895i	−0.00641950	−	0.0111189i	−0.869217	+	0.494430i	$0.835377\pi$
$60$		0			0
$61$	302.016	−	523.107i	0.633921	−	1.09798i	−0.352822	−	0.935691i	$-0.614778\pi$
$61$	302.016	−	523.107i	0.633921	−	1.09798i	0.986743	−	0.162293i	$-0.0518889\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	118.628	−	205.470i	0.226370	−	0.392083i
$66$		0			0
$67$	377.033	+	653.040i	0.687491	+	1.19077i	0.972647	+	0.232288i	$0.0746213\pi$
$67$	377.033	+	653.040i	0.687491	+	1.19077i	−0.285156	+	0.958481i	$0.592045\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	43.4780			0.0726744			0.0363372	−	0.999340i	$-0.488431\pi$
$71$	43.4780			0.0726744			0.0363372	+	0.999340i	$0.488431\pi$
$72$		0			0
$73$	671.029			1.07586			0.537931	−	0.842989i	$-0.319206\pi$
$73$	671.029			1.07586			0.537931	+	0.842989i	$0.319206\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	61.9686	+	107.333i	0.0917139	+	0.158853i
$78$		0			0
$79$	−324.601	+	562.226i	−0.462284	+	0.800700i	−0.999074	−	0.0430157i	$-0.986303\pi$
$79$	−324.601	+	562.226i	−0.462284	+	0.800700i	0.536790	+	0.843716i	$0.319637\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−67.2629	+	116.503i	−0.0889526	+	0.154070i	−0.907069	−	0.420983i	$-0.861685\pi$
$83$	−67.2629	+	116.503i	−0.0889526	+	0.154070i	0.818116	+	0.575053i	$0.195019\pi$
$84$		0			0
$85$	718.056	+	1243.71i	0.916283	+	1.58705i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	206.076			0.245439			0.122719	−	0.992441i	$-0.460838\pi$
$89$	206.076			0.245439			0.122719	+	0.992441i	$0.460838\pi$
$90$		0			0
$91$	32.5156			0.0374567
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1098.04	+	1901.87i	1.18586	+	2.05397i
$96$		0			0
$97$	726.420	−	1258.20i	0.760379	−	1.31702i	−0.182276	−	0.983247i	$-0.558347\pi$
$97$	726.420	−	1258.20i	0.760379	−	1.31702i	0.942655	−	0.333768i	$-0.108320\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	101.980	−	176.634i	0.100469	−	0.174017i	−0.811409	−	0.584479i	$-0.801299\pi$
$101$	101.980	−	176.634i	0.100469	−	0.174017i	0.911878	+	0.410461i	$0.134632\pi$
$102$		0			0
$103$	−777.773	−	1347.14i	−0.744042	−	1.28872i	−0.950641	−	0.310292i	$-0.899573\pi$
$103$	−777.773	−	1347.14i	−0.744042	−	1.28872i	0.206600	−	0.978426i	$-0.433760\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−584.436			−0.528033			−0.264016	−	0.964518i	$-0.585047\pi$
$107$	−584.436			−0.528033			−0.264016	+	0.964518i	$0.585047\pi$
$108$		0			0
$109$	−782.671			−0.687764			−0.343882	−	0.939013i	$-0.611742\pi$
$109$	−782.671			−0.687764			−0.343882	+	0.939013i	$0.611742\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−435.124	−	753.658i	−0.362239	−	0.627417i	0.626090	−	0.779751i	$-0.284654\pi$
$113$	−435.124	−	753.658i	−0.362239	−	0.627417i	−0.988329	+	0.152334i	$0.951321\pi$
$114$		0			0
$115$	−470.780	+	815.415i	−0.381743	+	0.661199i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−98.4084	+	170.448i	−0.0758074	+	0.131302i
$120$		0			0
$121$	−697.780	−	1208.59i	−0.524253	−	0.908032i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−864.968			−0.618921
$126$		0			0
$127$	−994.050			−0.694548			−0.347274	−	0.937764i	$-0.612893\pi$
$127$	−994.050			−0.694548			−0.347274	+	0.937764i	$0.612893\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	401.039	+	694.620i	0.267473	+	0.463277i	0.968209	−	0.250144i	$-0.0804781\pi$
$131$	401.039	+	694.620i	0.267473	+	0.463277i	−0.700736	+	0.713421i	$0.747145\pi$
$132$		0			0
$133$	−150.485	+	260.648i	−0.0981106	+	0.169933i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	659.936	−	1143.04i	0.411548	−	0.712822i	−0.583511	−	0.812105i	$-0.698322\pi$
$137$	659.936	−	1143.04i	0.411548	−	0.712822i	0.995059	+	0.0992828i	$0.0316549\pi$
$138$		0			0
$139$	263.397	+	456.216i	0.160727	+	0.278387i	0.935130	−	0.354306i	$-0.115283\pi$
$139$	263.397	+	456.216i	0.160727	+	0.278387i	−0.774403	+	0.632693i	$0.781950\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−715.329			−0.418313
$144$		0			0
$145$	−3686.33			−2.11126
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1538.88	+	2665.41i	0.846105	+	1.46550i	0.884659	+	0.466239i	$0.154391\pi$
$149$	1538.88	+	2665.41i	0.846105	+	1.46550i	−0.0385540	+	0.999257i	$0.512275\pi$
$150$		0			0
$151$	41.0954	−	71.1794i	0.0221477	−	0.0383609i	−0.854739	−	0.519058i	$-0.826283\pi$
$151$	41.0954	−	71.1794i	0.0221477	−	0.0383609i	0.876887	+	0.480697i	$0.159616\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1940.77	−	3361.52i	1.00572	−	1.74196i
$156$		0			0
$157$	1192.09	+	2064.76i	0.605981	+	1.04959i	0.991896	+	0.127055i	$0.0405526\pi$
$157$	1192.09	+	2064.76i	0.605981	+	1.04959i	−0.385915	+	0.922534i	$0.626114\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−129.039			−0.0631660
$162$		0			0
$163$	−1226.77			−0.589496			−0.294748	−	0.955575i	$-0.595236\pi$
$163$	−1226.77			−0.589496			−0.294748	+	0.955575i	$0.595236\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1948.20	−	3374.38i	−0.902733	−	1.56358i	−0.823932	−	0.566689i	$-0.808224\pi$
$167$	−1948.20	−	3374.38i	−0.902733	−	1.56358i	−0.0788009	−	0.996890i	$-0.525109\pi$
$168$		0			0
$169$	1004.66	−	1740.13i	0.457289	−	0.792048i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	73.2019	−	126.789i	0.0321701	−	0.0557203i	−0.849492	−	0.527601i	$-0.823091\pi$
$173$	73.2019	−	126.789i	0.0321701	−	0.0557203i	0.881662	+	0.471881i	$0.156425\pi$
$174$		0			0
$175$	−207.617	−	359.602i	−0.0896819	−	0.155334i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1540.84			−0.643396			−0.321698	−	0.946842i	$-0.604254\pi$
$179$	−1540.84			−0.643396			−0.321698	+	0.946842i	$0.604254\pi$
$180$		0			0
$181$	1173.94			0.482090			0.241045	−	0.970514i	$-0.422510\pi$
$181$	1173.94			0.482090			0.241045	+	0.970514i	$0.422510\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−279.032	−	483.298i	−0.110891	−	0.192069i
$186$		0			0
$187$	2164.94	−	3749.79i	0.846610	−	1.46637i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1096.82	−	1899.74i	0.415513	−	0.719689i	−0.579969	−	0.814638i	$-0.696935\pi$
$191$	1096.82	−	1899.74i	0.415513	−	0.719689i	0.995482	+	0.0949489i	$0.0302688\pi$
$192$		0			0
$193$	−1231.66	−	2133.29i	−0.459360	−	0.795635i	0.539567	−	0.841943i	$-0.318588\pi$
$193$	−1231.66	−	2133.29i	−0.459360	−	0.795635i	−0.998927	+	0.0463073i	$0.985255\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3593.52			−1.29963			−0.649816	−	0.760091i	$-0.725154\pi$
$197$	−3593.52			−1.29963			−0.649816	+	0.760091i	$0.725154\pi$
$198$		0			0
$199$	4599.36			1.63839			0.819197	−	0.573513i	$-0.194420\pi$
$199$	4599.36			1.63839			0.819197	+	0.573513i	$0.194420\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−252.603	−	437.521i	−0.0873362	−	0.151271i
$204$		0			0
$205$	−4335.46	+	7509.23i	−1.47708	+	2.55838i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3310.60	−	5734.13i	1.09569	−	1.89779i
$210$		0			0
$211$	−1166.12	−	2019.78i	−0.380469	−	0.658992i	0.610660	−	0.791893i	$-0.290904\pi$
$211$	−1166.12	−	2019.78i	−0.380469	−	0.658992i	−0.991129	+	0.132901i	$0.957571\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−222.122			−0.0704584
$216$		0			0
$217$	531.959			0.166414
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−567.984	−	983.778i	−0.172881	−	0.299439i
$222$		0			0
$223$	−2028.55	+	3513.55i	−0.609156	+	1.05509i	0.382224	+	0.924070i	$0.375158\pi$
$223$	−2028.55	+	3513.55i	−0.609156	+	1.05509i	−0.991380	+	0.131019i	$0.958175\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−648.626	+	1123.45i	−0.189651	+	0.328486i	−0.945134	−	0.326683i	$-0.894069\pi$
$227$	−648.626	+	1123.45i	−0.189651	+	0.328486i	0.755483	+	0.655169i	$0.227402\pi$
$228$		0			0
$229$	−1555.98	−	2695.04i	−0.449005	−	0.777699i	0.549317	−	0.835614i	$-0.314888\pi$
$229$	−1555.98	−	2695.04i	−0.449005	−	0.777699i	−0.998322	+	0.0579149i	$0.981555\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2034.74			−0.572103			−0.286052	−	0.958214i	$-0.592343\pi$
$233$	−2034.74			−0.572103			−0.286052	+	0.958214i	$0.592343\pi$
$234$		0			0
$235$	−3629.01			−1.00736
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−734.229	−	1271.72i	−0.198717	−	0.344188i	0.749396	−	0.662122i	$-0.230344\pi$
$239$	−734.229	−	1271.72i	−0.198717	−	0.344188i	−0.948113	+	0.317935i	$0.897011\pi$
$240$		0			0
$241$	−329.582	+	570.852i	−0.0880922	+	0.152580i	−0.906705	−	0.421766i	$-0.861410\pi$
$241$	−329.582	+	570.852i	−0.0880922	+	0.152580i	0.818612	+	0.574346i	$0.194744\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2921.40	+	5060.02i	−0.761803	+	1.31948i
$246$		0			0
$247$	−868.555	−	1504.38i	−0.223744	−	0.387537i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5509.13			−1.38539			−0.692696	−	0.721230i	$-0.743577\pi$
$251$	−5509.13			−1.38539			−0.692696	+	0.721230i	$0.743577\pi$
$252$		0			0
$253$	2838.81			0.705432
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1833.82	+	3176.26i	0.445098	+	0.770933i	0.998059	−	0.0622742i	$-0.0198353\pi$
$257$	1833.82	+	3176.26i	0.445098	+	0.770933i	−0.552961	+	0.833207i	$0.686502\pi$
$258$		0			0
$259$	38.2409	−	66.2352i	0.00917443	−	0.0158906i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2496.38	−	4323.86i	0.585299	−	1.01377i	−0.409539	−	0.912292i	$-0.634311\pi$
$263$	2496.38	−	4323.86i	0.585299	−	1.01377i	0.994838	−	0.101475i	$-0.0323561\pi$
$264$		0			0
$265$	−3214.49	−	5567.67i	−0.745150	−	1.29064i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−88.5142			−0.0200625			−0.0100312	−	0.999950i	$-0.503193\pi$
$269$	−88.5142			−0.0200625			−0.0100312	+	0.999950i	$0.503193\pi$
$270$		0			0
$271$	−5226.56			−1.17155			−0.585777	−	0.810472i	$-0.699211\pi$
$271$	−5226.56			−1.17155			−0.585777	+	0.810472i	$0.699211\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4567.47	+	7911.09i	1.00156	+	1.73475i
$276$		0			0
$277$	1056.13	−	1829.26i	0.229085	−	0.396787i	−0.728452	−	0.685097i	$-0.759760\pi$
$277$	1056.13	−	1829.26i	0.229085	−	0.396787i	0.957537	+	0.288310i	$0.0930933\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	862.569	−	1494.01i	0.183120	−	0.317172i	−0.759822	−	0.650131i	$-0.774714\pi$
$281$	862.569	−	1494.01i	0.183120	−	0.317172i	0.942941	+	0.332959i	$0.108047\pi$
$282$		0			0
$283$	1670.90	+	2894.08i	0.350970	+	0.607898i	0.986420	−	0.164244i	$-0.0525186\pi$
$283$	1670.90	+	2894.08i	0.350970	+	0.607898i	−0.635450	+	0.772142i	$0.719185\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1188.33			−0.244408
$288$		0			0
$289$	1963.01			0.399554
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2629.21	−	4553.92i	−0.524232	−	0.907997i	−0.999602	−	0.0282107i	$-0.991019\pi$
$293$	−2629.21	−	4553.92i	−0.524232	−	0.907997i	0.475370	−	0.879786i	$-0.342314\pi$
$294$		0			0
$295$	50.3848	−	87.2690i	0.00994412	−	0.0172237i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	372.389	−	644.996i	0.0720261	−	0.124753i
$300$		0			0
$301$	−15.2207	−	26.3630i	−0.00291464	−	0.00504831i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	10461.2			1.96395
$306$		0			0
$307$	−2582.56			−0.480112			−0.240056	−	0.970759i	$-0.577166\pi$
$307$	−2582.56			−0.480112			−0.240056	+	0.970759i	$0.577166\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2544.26	+	4406.79i	0.463897	+	0.803493i	0.999151	−	0.0411980i	$-0.0131174\pi$
$311$	2544.26	+	4406.79i	0.463897	+	0.803493i	−0.535254	+	0.844691i	$0.679784\pi$
$312$		0			0
$313$	1465.53	−	2538.38i	0.264654	−	0.458395i	−0.702819	−	0.711369i	$-0.748076\pi$
$313$	1465.53	−	2538.38i	0.264654	−	0.458395i	0.967473	+	0.252974i	$0.0814088\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1799.78	−	3117.32i	0.318883	−	0.552322i	−0.661372	−	0.750058i	$-0.730026\pi$
$317$	1799.78	−	3117.32i	0.318883	−	0.552322i	0.980255	+	0.197736i	$0.0633589\pi$
$318$		0			0
$319$	5557.15	+	9625.27i	0.975363	+	1.68938i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	10514.7			1.81131
$324$		0			0
$325$	2396.60			0.409045
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−248.675	−	430.718i	−0.0416714	−	0.0721770i
$330$		0			0
$331$	1838.91	−	3185.08i	0.305364	−	0.528905i	−0.671979	−	0.740571i	$-0.734555\pi$
$331$	1838.91	−	3185.08i	0.305364	−	0.528905i	0.977342	+	0.211665i	$0.0678886\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6529.79	+	11309.9i	−1.06496	+	1.84456i
$336$		0			0
$337$	2778.02	+	4811.67i	0.449046	+	0.777770i	0.998324	−	0.0578696i	$-0.0184308\pi$
$337$	2778.02	+	4811.67i	0.449046	+	0.777770i	−0.549279	+	0.835639i	$0.685097\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−11702.9			−1.85849
$342$		0			0
$343$	−1614.87			−0.254212
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1534.56	+	2657.94i	0.237405	+	0.411198i	0.959969	−	0.280106i	$-0.0903698\pi$
$347$	1534.56	+	2657.94i	0.237405	+	0.411198i	−0.722564	+	0.691304i	$0.757036\pi$
$348$		0			0
$349$	595.716	−	1031.81i	0.0913694	−	0.158256i	−0.816718	−	0.577037i	$-0.804209\pi$
$349$	595.716	−	1031.81i	0.0913694	−	0.158256i	0.908088	+	0.418780i	$0.137542\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3215.50	−	5569.41i	0.484827	−	0.839745i	−0.515021	−	0.857177i	$-0.672216\pi$
$353$	3215.50	−	5569.41i	0.484827	−	0.839745i	0.999848	+	0.0174329i	$0.00554933\pi$
$354$		0			0
$355$	376.495	+	652.108i	0.0562881	+	0.0974938i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4236.73			0.622858			0.311429	−	0.950270i	$-0.399192\pi$
$359$	4236.73			0.622858			0.311429	+	0.950270i	$0.399192\pi$
$360$		0			0
$361$	9219.99			1.34422
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5810.73	+	10064.5i	0.833281	+	1.44329i
$366$		0			0
$367$	3686.39	−	6385.02i	0.524327	−	0.908161i	−0.475272	−	0.879839i	$-0.657650\pi$
$367$	3686.39	−	6385.02i	0.524327	−	0.908161i	0.999599	−	0.0283220i	$-0.00901638\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	440.541	−	763.040i	0.0616490	−	0.106779i
$372$		0			0
$373$	5992.51	+	10379.3i	0.831852	+	1.44081i	0.896568	+	0.442905i	$0.146052\pi$
$373$	5992.51	+	10379.3i	0.831852	+	1.44081i	−0.0647168	+	0.997904i	$0.520614\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2915.90			0.398346
$378$		0			0
$379$	3872.02			0.524782			0.262391	−	0.964962i	$-0.415489\pi$
$379$	3872.02			0.524782			0.262391	+	0.964962i	$0.415489\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3621.33	−	6272.33i	−0.483137	−	0.836818i	0.516676	−	0.856181i	$-0.327169\pi$
$383$	−3621.33	−	6272.33i	−0.483137	−	0.836818i	−0.999813	+	0.0193636i	$0.993836\pi$
$384$		0			0
$385$	−1073.23	+	1858.88i	−0.142069	+	0.246071i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4866.16	+	8428.44i	−0.634253	+	1.09856i	0.352420	+	0.935842i	$0.385359\pi$
$389$	−4866.16	+	8428.44i	−0.634253	+	1.09856i	−0.986673	+	0.162716i	$0.947975\pi$
$390$		0			0
$391$	2254.07	+	3904.16i	0.291542	+	0.504966i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11243.5			−1.43220
$396$		0			0
$397$	−1393.66			−0.176186			−0.0880930	−	0.996112i	$-0.528077\pi$
$397$	−1393.66			−0.176186			−0.0880930	+	0.996112i	$0.528077\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−612.828	−	1061.45i	−0.0763171	−	0.132185i	0.825341	−	0.564634i	$-0.190983\pi$
$401$	−612.828	−	1061.45i	−0.0763171	−	0.132185i	−0.901658	+	0.432449i	$0.857649\pi$
$402$		0			0
$403$	−1535.16	+	2658.97i	−0.189756	+	0.328667i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−841.283	+	1457.15i	−0.102459	+	0.177464i
$408$		0			0
$409$	−4081.41	−	7069.22i	−0.493430	−	0.854646i	0.506541	−	0.862216i	$-0.330924\pi$
$409$	−4081.41	−	7069.22i	−0.493430	−	0.854646i	−0.999971	+	0.00756956i	$0.997591\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	13.8103			0.00164543
$414$		0			0
$415$	−2329.84			−0.275584
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1410.80	−	2443.58i	−0.164492	−	0.284908i	0.771983	−	0.635643i	$-0.219265\pi$
$419$	−1410.80	−	2443.58i	−0.164492	−	0.284908i	−0.936475	+	0.350735i	$0.885932\pi$
$420$		0			0
$421$	2319.95	−	4018.27i	0.268569	−	0.465175i	−0.699924	−	0.714218i	$-0.746783\pi$
$421$	2319.95	−	4018.27i	0.268569	−	0.465175i	0.968492	+	0.249043i	$0.0801160\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7253.31	+	12563.1i	−0.827853	+	1.43388i
$426$		0			0
$427$	716.843	+	1241.61i	0.0812423	+	0.140716i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	5998.72			0.670413			0.335207	−	0.942145i	$-0.391194\pi$
$431$	5998.72			0.670413			0.335207	+	0.942145i	$0.391194\pi$
$432$		0			0
$433$	−10187.5			−1.13067			−0.565334	−	0.824862i	$-0.691253\pi$
$433$	−10187.5			−1.13067			−0.565334	+	0.824862i	$0.691253\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3446.89	+	5970.19i	0.377316	+	0.653531i
$438$		0			0
$439$	7872.72	−	13636.0i	0.855910	−	1.48248i	−0.0198884	−	0.999802i	$-0.506331\pi$
$439$	7872.72	−	13636.0i	0.855910	−	1.48248i	0.875798	−	0.482677i	$-0.160336\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1216.83	+	2107.61i	−0.130504	+	0.226040i	−0.923871	−	0.382704i	$-0.874993\pi$
$443$	−1216.83	+	2107.61i	−0.130504	+	0.226040i	0.793367	+	0.608744i	$0.208326\pi$
$444$		0			0
$445$	1784.51	+	3090.86i	0.190098	+	0.329260i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7394.75			−0.777238			−0.388619	−	0.921399i	$-0.627048\pi$
$449$	−7394.75			−0.777238			−0.388619	+	0.921399i	$0.627048\pi$
$450$		0			0
$451$	26142.8			2.72953
$452$		0			0
$453$		0			0
$454$		0			0
$455$	281.567	+	487.688i	0.0290111	+	0.0502488i
$456$		0			0
$457$	−1064.96	+	1844.56i	−0.109008	+	0.188807i	−0.915369	−	0.402617i	$-0.868101\pi$
$457$	−1064.96	+	1844.56i	−0.109008	+	0.188807i	0.806361	+	0.591424i	$0.201434\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4156.89	+	7199.95i	−0.419969	+	0.727408i	−0.995936	−	0.0900653i	$-0.971292\pi$
$461$	−4156.89	+	7199.95i	−0.419969	+	0.727408i	0.575967	+	0.817473i	$0.304626\pi$
$462$		0			0
$463$	−922.797	−	1598.33i	−0.0926263	−	0.160434i	0.815989	−	0.578067i	$-0.196193\pi$
$463$	−922.797	−	1598.33i	−0.0926263	−	0.160434i	−0.908615	+	0.417634i	$0.862860\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15653.2			−1.55106			−0.775529	−	0.631312i	$-0.782517\pi$
$467$	−15653.2			−1.55106			−0.775529	+	0.631312i	$0.782517\pi$
$468$		0			0
$469$	−1789.79			−0.176215
$470$		0			0
$471$		0			0
$472$		0			0
$473$	334.849	+	579.975i	0.0325504	+	0.0563790i
$474$		0			0
$475$	−11091.7	+	19211.4i	−1.07141	+	1.85574i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−986.975	+	1709.49i	−0.0941462	+	0.163066i	−0.909252	−	0.416246i	$-0.863345\pi$
$479$	−986.975	+	1709.49i	−0.0941462	+	0.163066i	0.815106	+	0.579312i	$0.196679\pi$
$480$		0			0
$481$	220.715	+	382.290i	0.0209226	+	0.0362390i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	25161.6			2.35573
$486$		0			0
$487$	1753.49			0.163158			0.0815792	−	0.996667i	$-0.474004\pi$
$487$	1753.49			0.163158			0.0815792	+	0.996667i	$0.474004\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3111.09	−	5388.56i	−0.285950	−	0.495280i	0.686889	−	0.726762i	$-0.258976\pi$
$491$	−3111.09	−	5388.56i	−0.285950	−	0.495280i	−0.972839	+	0.231482i	$0.925642\pi$
$492$		0			0
$493$	−8824.96	+	15285.3i	−0.806199	+	1.39638i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−51.5980	+	89.3704i	−0.00465692	+	0.00806602i
$498$		0			0
$499$	−8646.88	−	14976.8i	−0.775727	−	1.34360i	−0.934385	−	0.356264i	$-0.884050\pi$
$499$	−8646.88	−	14976.8i	−0.775727	−	1.34360i	0.158659	−	0.987333i	$-0.449283\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20578.6			1.82416			0.912082	−	0.410007i	$-0.134474\pi$
$503$	20578.6			1.82416			0.912082	+	0.410007i	$0.134474\pi$
$504$		0			0
$505$	3532.35			0.311263
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9277.57	−	16069.2i	−0.807900	−	1.39932i	−0.914316	−	0.405003i	$-0.867271\pi$
$509$	−9277.57	−	16069.2i	−0.807900	−	1.39932i	0.106415	−	0.994322i	$-0.466063\pi$
$510$		0			0
$511$	−796.352	+	1379.32i	−0.0689404	+	0.119408i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	13470.2	−	23331.0i	1.15256	−	1.99629i
$516$		0			0
$517$	5470.73	+	9475.59i	0.465382	+	0.806066i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5321.51			0.447485			0.223742	−	0.974648i	$-0.428173\pi$
$521$	5321.51			0.447485			0.223742	+	0.974648i	$0.428173\pi$
$522$		0			0
$523$	−7766.94			−0.649378			−0.324689	−	0.945821i	$-0.605260\pi$
$523$	−7766.94			−0.649378			−0.324689	+	0.945821i	$0.605260\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9292.29	−	16094.7i	−0.768081	−	1.33036i
$528$		0			0
$529$	4605.66	−	7977.24i	0.378537	−	0.655646i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3429.36	−	5939.83i	0.278691	−	0.482706i
$534$		0			0
$535$	−5060.88	−	8765.71i	−0.408974	−	0.708364i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	17616.1			1.40775
$540$		0			0
$541$	−1292.25			−0.102695			−0.0513476	−	0.998681i	$-0.516352\pi$
$541$	−1292.25			−0.102695			−0.0513476	+	0.998681i	$0.516352\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6777.49	−	11739.0i	−0.532690	−	0.922646i
$546$		0			0
$547$	3766.48	−	6523.73i	0.294411	−	0.509935i	−0.680437	−	0.732807i	$-0.738210\pi$
$547$	3766.48	−	6523.73i	0.294411	−	0.509935i	0.974848	+	0.222872i	$0.0715432\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13495.0	+	23374.1i	−1.04339	+	1.80720i
$552$		0			0
$553$	−770.449	−	1334.46i	−0.0592456	−	0.102616i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9856.22			0.749769			0.374884	−	0.927072i	$-0.377682\pi$
$557$	9856.22			0.749769			0.374884	+	0.927072i	$0.377682\pi$
$558$		0			0
$559$	175.699			0.0132939
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5141.10	+	8904.65i	0.384852	+	0.666583i	0.991749	−	0.128198i	$-0.0409192\pi$
$563$	5141.10	+	8904.65i	0.384852	+	0.666583i	−0.606897	+	0.794781i	$0.707586\pi$
$564$		0			0
$565$	7535.87	−	13052.5i	0.561126	−	0.971899i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−661.321	+	1145.44i	−0.0487241	+	0.0843927i	−0.889359	−	0.457210i	$-0.848849\pi$
$569$	−661.321	+	1145.44i	−0.0487241	+	0.0843927i	0.840635	+	0.541602i	$0.182182\pi$
$570$		0			0
$571$	−2127.29	−	3684.57i	−0.155909	−	0.270043i	0.777480	−	0.628907i	$-0.216497\pi$
$571$	−2127.29	−	3684.57i	−0.155909	−	0.270043i	−0.933390	+	0.358864i	$0.883164\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9511.01			−0.689803
$576$		0			0
$577$	−13268.4			−0.957312			−0.478656	−	0.878003i	$-0.658876\pi$
$577$	−13268.4			−0.957312			−0.478656	+	0.878003i	$0.658876\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−159.650	−	276.522i	−0.0114000	−	0.0197454i
$582$		0			0
$583$	−9691.71	+	16786.5i	−0.688490	+	1.19250i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2355.25	+	4079.42i	−0.165608	+	0.286841i	−0.936871	−	0.349676i	$-0.886292\pi$
$587$	−2355.25	+	4079.42i	−0.165608	+	0.286841i	0.771263	+	0.636516i	$0.219625\pi$
$588$		0			0
$589$	−14209.7	−	24611.9i	−0.994057	−	1.72176i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16303.6			−1.12902			−0.564510	−	0.825426i	$-0.690935\pi$
$593$	−16303.6			−1.12902			−0.564510	+	0.825426i	$0.690935\pi$
$594$		0			0
$595$	−3408.65			−0.234859
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5279.43	+	9144.25i	0.360120	+	0.623746i	0.987980	−	0.154580i	$-0.0494024\pi$
$599$	5279.43	+	9144.25i	0.360120	+	0.623746i	−0.627860	+	0.778326i	$0.716069\pi$
$600$		0			0
$601$	936.177	−	1621.51i	0.0635399	−	0.110054i	−0.832505	−	0.554017i	$-0.813094\pi$
$601$	936.177	−	1621.51i	0.0635399	−	0.110054i	0.896045	+	0.443962i	$0.146428\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12084.8	−	20931.4i	0.812092	−	1.40659i
$606$		0			0
$607$	−11535.9	−	19980.7i	−0.771378	−	1.33607i	−0.936808	−	0.349844i	$-0.886235\pi$
$607$	−11535.9	−	19980.7i	−0.771378	−	1.33607i	0.165430	−	0.986222i	$-0.447099\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2870.56			0.190066
$612$		0			0
$613$	−24292.0			−1.60056			−0.800281	−	0.599625i	$-0.795317\pi$
$613$	−24292.0			−1.60056			−0.800281	+	0.599625i	$0.795317\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3886.97	−	6732.43i	−0.253620	−	0.439283i	0.710900	−	0.703293i	$-0.248288\pi$
$617$	−3886.97	−	6732.43i	−0.253620	−	0.439283i	−0.964520	+	0.264010i	$0.914955\pi$
$618$		0			0
$619$	−15287.6	+	26478.8i	−0.992664	+	1.71934i	−0.391626	+	0.920125i	$0.628087\pi$
$619$	−15287.6	+	26478.8i	−0.992664	+	1.71934i	−0.601038	+	0.799220i	$0.705246\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−244.564	+	423.597i	−0.0157275	+	0.0272409i
$624$		0			0
$625$	3443.84	+	5964.90i	0.220406	+	0.381754i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2671.98			−0.169378
$630$		0			0
$631$	−14474.9			−0.913209			−0.456605	−	0.889670i	$-0.650935\pi$
$631$	−14474.9			−0.913209			−0.456605	+	0.889670i	$0.650935\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8607.91	−	14909.3i	−0.537944	−	0.931747i
$636$		0			0
$637$	2310.84	−	4002.49i	0.143734	−	0.248955i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6841.90	+	11850.5i	−0.421589	+	0.730214i	−0.996095	−	0.0882864i	$-0.971861\pi$
$641$	−6841.90	+	11850.5i	−0.421589	+	0.730214i	0.574506	+	0.818501i	$0.305194\pi$
$642$		0			0
$643$	8007.76	+	13869.8i	0.491128	+	0.850658i	0.999948	−	0.0102148i	$-0.00325153\pi$
$643$	8007.76	+	13869.8i	0.491128	+	0.850658i	−0.508820	+	0.860873i	$0.669918\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12224.1			0.742783			0.371392	−	0.928476i	$-0.378881\pi$
$647$	12224.1			0.742783			0.371392	+	0.928476i	$0.378881\pi$
$648$		0			0
$649$	−303.821			−0.0183760
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8064.97	−	13968.9i	−0.483318	−	0.837131i	0.516498	−	0.856288i	$-0.327235\pi$
$653$	−8064.97	−	13968.9i	−0.483318	−	0.837131i	−0.999816	+	0.0191568i	$0.993902\pi$
$654$		0			0
$655$	−6945.55	+	12030.0i	−0.414328	+	0.717638i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3579.31	+	6199.55i	−0.211579	+	0.366465i	−0.952209	−	0.305448i	$-0.901194\pi$
$659$	−3579.31	+	6199.55i	−0.211579	+	0.366465i	0.740630	+	0.671913i	$0.234527\pi$
$660$		0			0
$661$	−4760.03	−	8244.61i	−0.280096	−	0.485141i	0.691312	−	0.722556i	$-0.257033\pi$
$661$	−4760.03	−	8244.61i	−0.280096	−	0.485141i	−0.971408	+	0.237415i	$0.923700\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5212.46			−0.303956
$666$		0			0
$667$	−11571.9			−0.671760
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15770.2	−	27314.8i	−0.907306	−	1.57150i
$672$		0			0
$673$	3801.82	−	6584.95i	0.217755	−	0.377163i	−0.736366	−	0.676583i	$-0.763460\pi$
$673$	3801.82	−	6584.95i	0.217755	−	0.377163i	0.954121	+	0.299420i	$0.0967932\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2475.98	+	4288.53i	−0.140561	+	0.243459i	−0.927708	−	0.373307i	$-0.878224\pi$
$677$	−2475.98	+	4288.53i	−0.140561	+	0.243459i	0.787147	+	0.616765i	$0.211557\pi$
$678$		0			0
$679$	1724.18	+	2986.36i	0.0974489	+	0.168786i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−28231.4			−1.58162			−0.790809	−	0.612063i	$-0.790340\pi$
$683$	−28231.4			−1.58162			−0.790809	+	0.612063i	$0.790340\pi$
$684$		0			0
$685$	22858.7			1.27502
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2542.68	+	4404.04i	0.140592	+	0.243513i
$690$		0			0
$691$	12755.1	−	22092.5i	0.702212	−	1.21627i	−0.265477	−	0.964117i	$-0.585529\pi$
$691$	12755.1	−	22092.5i	0.702212	−	1.21627i	0.967688	−	0.252149i	$-0.0811373\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4561.73	+	7901.16i	−0.248973	+	0.431234i
$696$		0			0
$697$	20757.9	+	35953.7i	1.12806	+	1.95387i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−17524.1			−0.944191			−0.472095	−	0.881547i	$-0.656502\pi$
$701$	−17524.1			−0.944191			−0.472095	+	0.881547i	$0.656502\pi$
$702$		0			0
$703$	−4085.96			−0.219210
$704$		0			0
$705$		0			0
$706$		0			0
$707$	242.052	+	419.246i	0.0128759	+	0.0223018i
$708$		0			0
$709$	17490.8	−	30295.0i	0.926490	−	1.60473i	0.137343	−	0.990524i	$-0.456144\pi$
$709$	17490.8	−	30295.0i	0.926490	−	1.60473i	0.789147	−	0.614205i	$-0.210523\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6092.32	−	10552.2i	0.319999	−	0.554255i
$714$		0			0
$715$	−6194.35	−	10728.9i	−0.323994	−	0.561173i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	30485.5			1.58125			0.790623	−	0.612303i	$-0.209757\pi$
$719$	30485.5			1.58125			0.790623	+	0.612303i	$0.209757\pi$
$720$		0			0
$721$	3692.13			0.190710
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−18618.4	−	32248.0i	−0.953753	−	1.65195i
$726$		0			0
$727$	13348.9	−	23121.0i	0.680994	−	1.17952i	−0.293683	−	0.955903i	$-0.594881\pi$
$727$	13348.9	−	23121.0i	0.680994	−	1.17952i	0.974678	−	0.223614i	$-0.0717856\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−531.752	+	921.022i	−0.0269050	+	0.0466008i
$732$		0			0
$733$	−15258.5	−	26428.4i	−0.768874	−	1.33173i	−0.938174	−	0.346164i	$-0.887484\pi$
$733$	−15258.5	−	26428.4i	−0.768874	−	1.33173i	0.169301	−	0.985564i	$-0.445849\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	39374.7			1.96796
$738$		0			0
$739$	20020.0			0.996544			0.498272	−	0.867021i	$-0.333968\pi$
$739$	20020.0			0.996544			0.498272	+	0.867021i	$0.333968\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8017.35	−	13886.5i	−0.395866	−	0.685659i	0.597346	−	0.801984i	$-0.296222\pi$
$743$	−8017.35	−	13886.5i	−0.395866	−	0.685659i	−0.993211	+	0.116325i	$0.962889\pi$
$744$		0			0
$745$	−26651.6	+	46161.9i	−1.31066	+	2.27012i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	693.586	−	1201.33i	0.0338359	−	0.0586055i
$750$		0			0
$751$	12362.5	+	21412.5i	0.600686	+	1.04042i	0.992717	+	0.120467i	$0.0384392\pi$
$751$	12362.5	+	21412.5i	0.600686	+	1.04042i	−0.392031	+	0.919952i	$0.628227\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1423.45			0.0686156
$756$		0			0
$757$	−13567.6			−0.651419			−0.325709	−	0.945470i	$-0.605603\pi$
$757$	−13567.6			−0.651419			−0.325709	+	0.945470i	$0.605603\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1108.70	−	1920.32i	−0.0528124	−	0.0914737i	0.838411	−	0.545039i	$-0.183485\pi$
$761$	−1108.70	−	1920.32i	−0.0528124	−	0.0914737i	−0.891223	+	0.453565i	$0.850152\pi$
$762$		0			0
$763$	928.845	−	1608.81i	0.0440713	−	0.0763338i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−39.8545	+	69.0301i	−0.00187622	+	0.00324971i
$768$		0			0
$769$	17449.5	+	30223.4i	0.818263	+	1.41727i	0.906961	+	0.421215i	$0.138396\pi$
$769$	17449.5	+	30223.4i	0.818263	+	1.41727i	−0.0886978	+	0.996059i	$0.528271\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10244.1			0.476656			0.238328	−	0.971185i	$-0.423401\pi$
$773$	10244.1			0.476656			0.238328	+	0.971185i	$0.423401\pi$
$774$		0			0
$775$	39208.7			1.81732
$776$		0			0
$777$		0			0
$778$		0			0
$779$	31742.7	+	54980.0i	1.45995	+	2.52871i
$780$		0			0
$781$	1135.13	−	1966.11i	0.0520080	−	0.0900805i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−20645.6	+	35759.3i	−0.938693	+	1.62586i
$786$		0			0
$787$	−5430.76	−	9406.36i	−0.245979	−	0.426049i	0.716427	−	0.697662i	$-0.245776\pi$
$787$	−5430.76	−	9406.36i	−0.245979	−	0.426049i	−0.962407	+	0.271613i	$0.912443\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2065.56			0.0928480
$792$		0			0
$793$	−8274.81			−0.370551
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17802.4	+	30834.7i	0.791209	+	1.37041i	0.925219	+	0.379434i	$0.123881\pi$
$797$	17802.4	+	30834.7i	0.791209	+	1.37041i	−0.134010	+	0.990980i	$0.542786\pi$
$798$		0			0
$799$	−8687.73	+	15047.6i	−0.384668	+	0.666265i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17519.4	−	30344.4i	0.769919	−	1.33354i
$804$		0			0
$805$	−1117.41	−	1935.41i	−0.0489236	−	0.0847381i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−13929.4			−0.605355			−0.302678	−	0.953093i	$-0.597881\pi$
$809$	−13929.4			−0.605355			−0.302678	+	0.953093i	$0.597881\pi$
$810$		0			0
$811$	−41996.6			−1.81837			−0.909187	−	0.416388i	$-0.863296\pi$
$811$	−41996.6			−1.81837			−0.909187	+	0.416388i	$0.863296\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−10623.1	−	18399.8i	−0.456579	−	0.790817i
$816$		0			0
$817$	−813.149	+	1408.42i	−0.0348207	+	0.0603112i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10540.1	−	18255.9i	0.448052	−	0.776049i	−0.550207	−	0.835028i	$-0.685451\pi$
$821$	10540.1	−	18255.9i	0.448052	−	0.776049i	0.998259	+	0.0589791i	$0.0187845\pi$
$822$		0			0
$823$	17182.6	+	29761.1i	0.727760	+	1.26052i	0.957828	+	0.287343i	$0.0927719\pi$
$823$	17182.6	+	29761.1i	0.727760	+	1.26052i	−0.230068	+	0.973175i	$0.573895\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32925.7			−1.38445			−0.692225	−	0.721682i	$-0.743369\pi$
$827$	−32925.7			−1.38445			−0.692225	+	0.721682i	$0.743369\pi$
$828$		0			0
$829$	21195.7			0.888008			0.444004	−	0.896025i	$-0.353558\pi$
$829$	21195.7			0.888008			0.444004	+	0.896025i	$0.353558\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	13987.5	+	24227.1i	0.581798	+	1.00770i
$834$		0			0
$835$	33740.7	−	58440.6i	1.39838	−	2.42206i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11868.4	−	20556.7i	0.488370	−	0.845882i	−0.511541	−	0.859259i	$-0.670925\pi$
$839$	11868.4	−	20556.7i	0.488370	−	0.845882i	0.999911	+	0.0133775i	$0.00425831\pi$
$840$		0			0
$841$	−10458.2	−	18114.1i	−0.428806	−	0.742715i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	34799.3			1.41673
$846$		0			0
$847$	3312.40			0.134375
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−875.917	−	1517.13i	−0.0352833	−	0.0611124i
$852$		0			0
$853$	−10964.2	+	18990.6i	−0.440104	+	0.762282i	−0.997697	−	0.0678324i	$-0.978392\pi$
$853$	−10964.2	+	18990.6i	−0.440104	+	0.762282i	0.557593	+	0.830114i	$0.311725\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20166.3	+	34929.1i	−0.803814	+	1.39225i	0.113275	+	0.993564i	$0.463866\pi$
$857$	−20166.3	+	34929.1i	−0.803814	+	1.39225i	−0.917089	+	0.398683i	$0.869467\pi$
$858$		0			0
$859$	11472.6	+	19871.1i	0.455691	+	0.789280i	0.998728	−	0.0504289i	$-0.0160588\pi$
$859$	11472.6	+	19871.1i	0.455691	+	0.789280i	−0.543037	+	0.839709i	$0.682725\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−40453.2			−1.59565			−0.797824	−	0.602890i	$-0.794016\pi$
$863$	−40453.2			−1.59565			−0.797824	+	0.602890i	$0.794016\pi$
$864$		0			0
$865$	2535.55			0.0996662
$866$		0			0
$867$		0			0
$868$		0			0
$869$	16949.5	+	29357.4i	0.661649	+	1.14601i
$870$		0			0
$871$	5165.08	−	8946.19i	0.200932	−	0.348025i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1026.51	−	1777.97i	0.0396599	−	0.0686930i
$876$		0			0
$877$	−2280.71	−	3950.30i	−0.0878153	−	0.152101i	0.818772	−	0.574119i	$-0.194655\pi$
$877$	−2280.71	−	3950.30i	−0.0878153	−	0.152101i	−0.906587	+	0.422018i	$0.861322\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−31553.9			−1.20667			−0.603336	−	0.797487i	$-0.706162\pi$
$881$	−31553.9			−1.20667			−0.603336	+	0.797487i	$0.706162\pi$
$882$		0			0
$883$	−22726.0			−0.866128			−0.433064	−	0.901363i	$-0.642568\pi$
$883$	−22726.0			−0.866128			−0.433064	+	0.901363i	$0.642568\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−817.180	−	1415.40i	−0.0309337	−	0.0535788i	0.850144	−	0.526550i	$-0.176515\pi$
$887$	−817.180	−	1415.40i	−0.0309337	−	0.0535788i	−0.881078	+	0.472971i	$0.843181\pi$
$888$		0			0
$889$	1179.70	−	2043.30i	0.0445061	−	0.0770868i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13285.2	+	23010.6i	−0.497841	+	0.862285i
$894$		0			0
$895$	−13342.8	−	23110.4i	−0.498325	−	0.863125i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	47704.5			1.76978
$900$		0			0
$901$	−30781.6			−1.13816
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10165.7	+	17607.5i	0.373390	+	0.646731i
$906$		0			0
$907$	−3267.67	+	5659.76i	−0.119626	+	0.207199i	−0.919620	−	0.392810i	$-0.871503\pi$
$907$	−3267.67	+	5659.76i	−0.119626	+	0.207199i	0.799993	+	0.600009i	$0.204836\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23043.3	+	39912.2i	−0.838046	+	1.45154i	0.0534801	+	0.998569i	$0.482969\pi$
$911$	−23043.3	+	39912.2i	−0.838046	+	1.45154i	−0.891526	+	0.452969i	$0.850365\pi$
$912$		0			0
$913$	3512.23	+	6083.37i	0.127314	+	0.220515i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1903.75			−0.0685578
$918$		0			0
$919$	−1857.94			−0.0666898			−0.0333449	−	0.999444i	$-0.510616\pi$
$919$	−1857.94			−0.0666898			−0.0333449	+	0.999444i	$0.510616\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−297.809	−	515.820i	−0.0106202	−	0.0183948i
$924$		0			0
$925$	2818.60	−	4881.95i	0.100189	−	0.173532i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12150.8	−	21045.8i	0.429123	−	0.743263i	−0.567672	−	0.823254i	$-0.692156\pi$
$929$	12150.8	−	21045.8i	0.429123	−	0.743263i	0.996796	+	0.0799916i	$0.0254893\pi$
$930$		0			0
$931$	21389.5	+	37047.8i	0.752968	+	1.30418i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	74988.7			2.62288
$936$		0			0
$937$	52069.9			1.81542			0.907710	−	0.419597i	$-0.137829\pi$
$937$	52069.9			1.81542			0.907710	+	0.419597i	$0.137829\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7854.48	+	13604.4i	0.272103	+	0.471296i	0.969400	−	0.245486i	$-0.0789476\pi$
$941$	7854.48	+	13604.4i	0.272103	+	0.471296i	−0.697297	+	0.716782i	$0.745614\pi$
$942$		0			0
$943$	−13609.5	+	23572.4i	−0.469976	+	0.814023i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−26244.3	+	45456.5i	−0.900556	+	1.55981i	−0.0737816	+	0.997274i	$0.523507\pi$
$947$	−26244.3	+	45456.5i	−0.900556	+	1.55981i	−0.826774	+	0.562534i	$0.809827\pi$
$948$		0			0
$949$	−4596.31	−	7961.04i	−0.157221	−	0.272314i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−2447.37			−0.0831880			−0.0415940	−	0.999135i	$-0.513244\pi$
$953$	−2447.37			−0.0831880			−0.0415940	+	0.999135i	$0.513244\pi$
$954$		0			0
$955$	37991.3			1.28730
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1566.37	+	2713.04i	0.0527433	+	0.0913541i
$960$		0			0
$961$	−10219.9	+	17701.3i	−0.343052	+	0.594183i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	21330.9	−	36946.2i	0.711571	−	1.23248i
$966$		0			0
$967$	−14696.1	−	25454.4i	−0.488723	−	0.846494i	0.511193	−	0.859466i	$-0.329204\pi$
$967$	−14696.1	−	25454.4i	−0.488723	−	0.846494i	−0.999916	+	0.0129726i	$0.995871\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−32763.9			−1.08285			−0.541423	−	0.840751i	$-0.682114\pi$
$971$	−32763.9			−1.08285			−0.541423	+	0.840751i	$0.682114\pi$
$972$		0			0
$973$	−1250.36			−0.0411969
$974$		0			0
$975$		0			0
$976$		0			0
$977$	334.690	+	579.701i	0.0109598	+	0.0189829i	0.871453	−	0.490479i	$-0.163178\pi$
$977$	334.690	+	579.701i	0.0109598	+	0.0189829i	−0.860494	+	0.509461i	$0.829845\pi$
$978$		0			0
$979$	5380.29	−	9318.94i	0.175643	−	0.304223i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11895.5	+	20603.6i	−0.385969	+	0.668518i	−0.991903	−	0.126997i	$-0.959466\pi$
$983$	−11895.5	+	20603.6i	−0.385969	+	0.668518i	0.605934	+	0.795515i	$0.292800\pi$
$984$		0			0
$985$	−31117.9	−	53897.7i	−1.00660	−	1.74348i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−697.267			−0.0224184
$990$		0			0
$991$	−7069.41			−0.226607			−0.113303	−	0.993560i	$-0.536143\pi$
$991$	−7069.41			−0.226607			−0.113303	+	0.993560i	$0.536143\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	39827.9	+	68984.0i	1.26897	+	2.19793i
$996$		0			0
$997$	−17162.3	+	29726.0i	−0.545172	+	0.944266i	0.453424	+	0.891295i	$0.350202\pi$
$997$	−17162.3	+	29726.0i	−0.545172	+	0.944266i	−0.998596	+	0.0529711i	$0.983131\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.4.i.e.289.4		8
3.2	odd	2		144.4.i.e.97.3		8
4.3	odd	2		216.4.i.a.73.4		8
9.2	odd	6		1296.4.a.ba.1.4		4
9.4	even	3	inner	432.4.i.e.145.4		8
9.5	odd	6		144.4.i.e.49.3		8
9.7	even	3		1296.4.a.y.1.1		4
12.11	even	2		72.4.i.a.25.2	✓	8
36.7	odd	6		648.4.a.h.1.1		4
36.11	even	6		648.4.a.i.1.4		4
36.23	even	6		72.4.i.a.49.2	yes	8
36.31	odd	6		216.4.i.a.145.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.i.a.25.2	✓	8	12.11	even	2
72.4.i.a.49.2	yes	8	36.23	even	6
144.4.i.e.49.3		8	9.5	odd	6
144.4.i.e.97.3		8	3.2	odd	2
216.4.i.a.73.4		8	4.3	odd	2
216.4.i.a.145.4		8	36.31	odd	6
432.4.i.e.145.4		8	9.4	even	3	inner
432.4.i.e.289.4		8	1.1	even	1	trivial
648.4.a.h.1.1		4	36.7	odd	6
648.4.a.i.1.4		4	36.11	even	6
1296.4.a.y.1.1		4	9.7	even	3
1296.4.a.ba.1.4		4	9.2	odd	6

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.65944 + 14.9986i) q^{5} +(-1.18676 + 2.05553i) q^{7} +O(q^{10})\)	\(q+(8.65944 + 14.9986i) q^{5} +(-1.18676 + 2.05553i) q^{7} +(26.1082 - 45.2208i) q^{11} +(-6.84965 - 11.8639i) q^{13} +82.9217 q^{17} +126.803 q^{19} +(27.1831 + 47.0825i) q^{23} +(-87.4718 + 151.506i) q^{25} +(-106.425 + 184.334i) q^{29} +(-112.061 - 194.095i) q^{31} -41.1068 q^{35} -32.2229 q^{37} +(250.331 + 433.586i) q^{41} +(-6.41270 + 11.1071i) q^{43} +(-104.770 + 181.467i) q^{47} +(168.683 + 292.168i) q^{49} -371.213 q^{53} +904.331 q^{55} +(-2.90924 - 5.03895i) q^{59} +(302.016 - 523.107i) q^{61} +(118.628 - 205.470i) q^{65} +(377.033 + 653.040i) q^{67} +43.4780 q^{71} +671.029 q^{73} +(61.9686 + 107.333i) q^{77} +(-324.601 + 562.226i) q^{79} +(-67.2629 + 116.503i) q^{83} +(718.056 + 1243.71i) q^{85} +206.076 q^{89} +32.5156 q^{91} +(1098.04 + 1901.87i) q^{95} +(726.420 - 1258.20i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{5} - 3 q^{7}+O(q^{10}) \) 8 * q + 5 * q^5 - 3 * q^7	\( 8 q + 5 q^{5} - 3 q^{7} + 16 q^{11} + 29 q^{13} + 34 q^{17} + 218 q^{19} + 37 q^{23} + 97 q^{25} + 3 q^{29} - 331 q^{31} - 342 q^{35} - 732 q^{37} + 378 q^{41} - 506 q^{43} + 171 q^{47} + 829 q^{49} - 820 q^{53} + 2326 q^{55} + 616 q^{59} + 1331 q^{61} + 815 q^{65} - 1162 q^{67} - 688 q^{71} - 2614 q^{73} + 741 q^{77} - 1853 q^{79} + 1421 q^{83} + 2074 q^{85} - 1632 q^{89} + 3990 q^{91} + 1292 q^{95} + 2506 q^{97}+O(q^{100}) \) 8 * q + 5 * q^5 - 3 * q^7 + 16 * q^11 + 29 * q^13 + 34 * q^17 + 218 * q^19 + 37 * q^23 + 97 * q^25 + 3 * q^29 - 331 * q^31 - 342 * q^35 - 732 * q^37 + 378 * q^41 - 506 * q^43 + 171 * q^47 + 829 * q^49 - 820 * q^53 + 2326 * q^55 + 616 * q^59 + 1331 * q^61 + 815 * q^65 - 1162 * q^67 - 688 * q^71 - 2614 * q^73 + 741 * q^77 - 1853 * q^79 + 1421 * q^83 + 2074 * q^85 - 1632 * q^89 + 3990 * q^91 + 1292 * q^95 + 2506 * q^97

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