LMFDB - Embedded newform 405.4.b.d.244.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(244,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("405.244");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.b (of order $2$, degree $1$, 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:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 70 x^{14} + 2191 x^{12} + 30544 x^{10} + 285007 x^{8} + 513982 x^{6} + 1874737 x^{4} + \cdots + 149328400 $ x^16 + 70x^14 + 2191x^12 + 30544x^10 + 285007x^8 + 513982x^6 + 1874737x^4 - 66369332*x^2 + 149328400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			244.1
Root			$-1.73205 + 5.49509i$ of defining polynomial
Character	$\chi$	$=$	405.244
Dual form			405.4.b.d.244.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.49509i q^{2} -22.1960 q^{4} +(-9.52216 - 5.85905i) q^{5} -19.7308i q^{7} +78.0086i q^{8} +O(q^{10})$	\(q-5.49509i q^{2} -22.1960 q^{4} +(-9.52216 - 5.85905i) q^{5} -19.7308i q^{7} +78.0086i q^{8} +(-32.1960 + 52.3251i) q^{10} -61.3874 q^{11} +7.73615i q^{13} -108.422 q^{14} +251.096 q^{16} -42.7556i q^{17} -19.5651 q^{19} +(211.354 + 130.048i) q^{20} +337.330i q^{22} -25.3673i q^{23} +(56.3430 + 111.582i) q^{25} +42.5109 q^{26} +437.945i q^{28} -74.0591 q^{29} +193.214 q^{31} -755.727i q^{32} -234.946 q^{34} +(-115.604 + 187.879i) q^{35} -273.787i q^{37} +107.512i q^{38} +(457.057 - 742.810i) q^{40} -91.6721 q^{41} +142.057i q^{43} +1362.56 q^{44} -139.396 q^{46} -548.650i q^{47} -46.3026 q^{49} +(613.152 - 309.610i) q^{50} -171.712i q^{52} +385.554i q^{53} +(584.541 + 359.672i) q^{55} +1539.17 q^{56} +406.961i q^{58} +228.067 q^{59} -113.246 q^{61} -1061.73i q^{62} -2144.02 q^{64} +(45.3265 - 73.6649i) q^{65} -286.672i q^{67} +949.006i q^{68} +(1032.41 + 635.252i) q^{70} -763.518 q^{71} +528.843i q^{73} -1504.49 q^{74} +434.267 q^{76} +1211.22i q^{77} +222.382 q^{79} +(-2390.98 - 1471.19i) q^{80} +503.747i q^{82} -484.072i q^{83} +(-250.508 + 407.126i) q^{85} +780.619 q^{86} -4788.75i q^{88} +1310.17 q^{89} +152.640 q^{91} +563.055i q^{92} -3014.88 q^{94} +(186.302 + 114.633i) q^{95} +813.532i q^{97} +254.437i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 60 q^{4}+O(q^{10}) $ 16 * q - 60 * q^4	$ 16 q - 60 q^{4} - 220 q^{10} + 788 q^{16} + 356 q^{19} + 550 q^{25} + 1520 q^{31} - 392 q^{34} + 1132 q^{40} + 724 q^{46} + 4 q^{49} + 1716 q^{55} + 1268 q^{61} - 9476 q^{64} - 672 q^{70} + 228 q^{76} - 472 q^{79} - 3562 q^{85} + 1524 q^{91} - 10700 q^{94}+O(q^{100}) $ 16 * q - 60 * q^4 - 220 * q^10 + 788 * q^16 + 356 * q^19 + 550 * q^25 + 1520 * q^31 - 392 * q^34 + 1132 * q^40 + 724 * q^46 + 4 * q^49 + 1716 * q^55 + 1268 * q^61 - 9476 * q^64 - 672 * q^70 + 228 * q^76 - 472 * q^79 - 3562 * q^85 + 1524 * q^91 - 10700 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	5.49509i		−	1.94281i	−0.237431	−	0.971404i	$-0.576305\pi$
$2$		−	5.49509i		−	1.94281i	0.237431	−	0.971404i	$-0.423695\pi$
$3$		0			0
$3$		0			0
$4$	−22.1960			−2.77451
$5$	−9.52216	−	5.85905i	−0.851688	−	0.524050i
$5$	−9.52216	−	5.85905i	−0.851688	−	0.524050i
$6$		0			0
$7$		−	19.7308i		−	1.06536i	−0.846317	−	0.532680i	$-0.821185\pi$
$7$		−	19.7308i		−	1.06536i	0.846317	−	0.532680i	$-0.178815\pi$
$8$			78.0086i			3.44753i
$9$		0			0
$10$	−32.1960	+	52.3251i	−1.01813	+	1.65467i
$11$	−61.3874			−1.68264			−0.841319	−	0.540540i	$-0.818220\pi$
$11$	−61.3874			−1.68264			−0.841319	+	0.540540i	$0.818220\pi$
$12$		0			0
$13$			7.73615i			0.165048i	0.996589	+	0.0825240i	$0.0262981\pi$
$13$			7.73615i			0.165048i	−0.996589	+	0.0825240i	$0.973702\pi$
$14$	−108.422			−2.06979
$15$		0			0
$16$	251.096			3.92338
$17$		−	42.7556i		−	0.609986i	−0.952355	−	0.304993i	$-0.901346\pi$
$17$		−	42.7556i		−	0.609986i	0.952355	−	0.304993i	$-0.0986541\pi$
$18$		0			0
$19$	−19.5651			−0.236239			−0.118119	−	0.992999i	$-0.537687\pi$
$19$	−19.5651			−0.236239			−0.118119	+	0.992999i	$0.537687\pi$
$20$	211.354	+	130.048i	2.36301	+	1.45398i
$21$		0			0
$22$			337.330i			3.26904i
$23$		−	25.3673i		−	0.229976i	−0.993367	−	0.114988i	$-0.963317\pi$
$23$		−	25.3673i		−	0.229976i	0.993367	−	0.114988i	$-0.0366830\pi$
$24$		0			0
$25$	56.3430	+	111.582i	0.450744	+	0.892653i
$26$	42.5109			0.320657
$27$		0			0
$28$			437.945i			2.95585i
$29$	−74.0591			−0.474221			−0.237111	−	0.971483i	$-0.576200\pi$
$29$	−74.0591			−0.474221			−0.237111	+	0.971483i	$0.576200\pi$
$30$		0			0
$31$	193.214			1.11943			0.559713	−	0.828687i	$-0.310911\pi$
$31$	193.214			1.11943			0.559713	+	0.828687i	$0.310911\pi$
$32$		−	755.727i		−	4.17484i
$33$		0			0
$34$	−234.946			−1.18509
$35$	−115.604	+	187.879i	−0.558302	+	0.907354i
$36$		0			0
$37$		−	273.787i		−	1.21650i	−0.793747	−	0.608248i	$-0.791872\pi$
$37$		−	273.787i		−	1.21650i	0.793747	−	0.608248i	$-0.208128\pi$
$38$			107.512i			0.458967i
$39$		0			0
$40$	457.057	−	742.810i	1.80667	−	2.93621i
$41$	−91.6721			−0.349190			−0.174595	−	0.984640i	$-0.555862\pi$
$41$	−91.6721			−0.349190			−0.174595	+	0.984640i	$0.555862\pi$
$42$		0			0
$43$			142.057i			0.503804i	0.967753	+	0.251902i	$0.0810560\pi$
$43$			142.057i			0.503804i	−0.967753	+	0.251902i	$0.918944\pi$
$44$	1362.56			4.66849
$45$		0			0
$46$	−139.396			−0.446800
$47$		−	548.650i		−	1.70274i	−0.524566	−	0.851370i	$-0.675772\pi$
$47$		−	548.650i		−	1.70274i	0.524566	−	0.851370i	$-0.324228\pi$
$48$		0			0
$49$	−46.3026			−0.134993
$50$	613.152	−	309.610i	1.73425	−	0.875709i
$51$		0			0
$52$		−	171.712i		−	0.457926i
$53$			385.554i			0.999245i	0.866243	+	0.499622i	$0.166528\pi$
$53$			385.554i			0.999245i	−0.866243	+	0.499622i	$0.833472\pi$
$54$		0			0
$55$	584.541	+	359.672i	1.43308	+	0.881786i
$56$	1539.17			3.67286
$57$		0			0
$58$			406.961i			0.921322i
$59$	228.067			0.503251			0.251625	−	0.967825i	$-0.419035\pi$
$59$	228.067			0.503251			0.251625	+	0.967825i	$0.419035\pi$
$60$		0			0
$61$	−113.246			−0.237699			−0.118850	−	0.992912i	$-0.537921\pi$
$61$	−113.246			−0.237699			−0.118850	+	0.992912i	$0.537921\pi$
$62$		−	1061.73i		−	2.17483i
$63$		0			0
$64$	−2144.02			−4.18755
$65$	45.3265	−	73.6649i	0.0864933	−	0.140569i
$66$		0			0
$67$		−	286.672i		−	0.522724i	−0.965241	−	0.261362i	$-0.915828\pi$
$67$		−	286.672i		−	0.522724i	0.965241	−	0.261362i	$-0.0841717\pi$
$68$			949.006i			1.69241i
$69$		0			0
$70$	1032.41	+	635.252i	1.76282	+	1.08467i
$71$	−763.518			−1.27624			−0.638119	−	0.769938i	$-0.720287\pi$
$71$	−763.518			−1.27624			−0.638119	+	0.769938i	$0.720287\pi$
$72$		0			0
$73$			528.843i			0.847895i	0.905687	+	0.423948i	$0.139356\pi$
$73$			528.843i			0.847895i	−0.905687	+	0.423948i	$0.860644\pi$
$74$	−1504.49			−2.36342
$75$		0			0
$76$	434.267			0.655446
$77$			1211.22i			1.79262i
$78$		0			0
$79$	222.382			0.316708			0.158354	−	0.987382i	$-0.449381\pi$
$79$	222.382			0.316708			0.158354	+	0.987382i	$0.449381\pi$
$80$	−2390.98	−	1471.19i	−3.34149	−	2.05604i
$81$		0			0
$82$			503.747i			0.678409i
$83$		−	484.072i		−	0.640167i	−0.947389	−	0.320083i	$-0.896289\pi$
$83$		−	484.072i		−	0.640167i	0.947389	−	0.320083i	$-0.103711\pi$
$84$		0			0
$85$	−250.508	+	407.126i	−0.319663	+	0.519518i
$86$	780.619			0.978794
$87$		0			0
$88$		−	4788.75i		−	5.80093i
$89$	1310.17			1.56043			0.780214	−	0.625513i	$-0.215110\pi$
$89$	1310.17			1.56043			0.780214	+	0.625513i	$0.215110\pi$
$90$		0			0
$91$	152.640			0.175836
$92$			563.055i			0.638071i
$93$		0			0
$94$	−3014.88			−3.30810
$95$	186.302	+	114.633i	0.201202	+	0.123801i
$96$		0			0
$97$			813.532i			0.851564i	0.904826	+	0.425782i	$0.140001\pi$
$97$			813.532i			0.851564i	−0.904826	+	0.425782i	$0.859999\pi$
$98$			254.437i			0.262266i
$99$		0			0
$100$	−1250.59	−	2476.67i	−1.25059	−	2.47667i
$101$	−1920.87			−1.89241			−0.946207	−	0.323562i	$-0.895120\pi$
$101$	−1920.87			−1.89241			−0.946207	+	0.323562i	$0.895120\pi$
$102$		0			0
$103$			1087.94i			1.04075i	0.853937	+	0.520377i	$0.174208\pi$
$103$			1087.94i			1.04075i	−0.853937	+	0.520377i	$0.825792\pi$
$104$	−603.486			−0.569007
$105$		0			0
$106$	2118.66			1.94134
$107$			1694.66i			1.53111i	0.643368	+	0.765557i	$0.277537\pi$
$107$			1694.66i			1.53111i	−0.643368	+	0.765557i	$0.722463\pi$
$108$		0			0
$109$	−1004.27			−0.882489			−0.441245	−	0.897387i	$-0.645463\pi$
$109$	−1004.27			−0.882489			−0.441245	+	0.897387i	$0.645463\pi$
$110$	1976.43	−	3212.11i	1.71314	−	2.78420i
$111$		0			0
$112$		−	4954.31i		−	4.17981i
$113$			1621.38i			1.34980i	0.737911	+	0.674898i	$0.235812\pi$
$113$			1621.38i			1.34980i	−0.737911	+	0.674898i	$0.764188\pi$
$114$		0			0
$115$	−148.629	+	241.552i	−0.120519	+	0.195868i
$116$	1643.82			1.31573
$117$		0			0
$118$		−	1253.25i		−	0.977720i
$119$	−843.601			−0.649855
$120$		0			0
$121$	2437.42			1.83127
$122$			622.297i			0.461804i
$123$		0			0
$124$	−4288.58			−3.10585
$125$	117.256	−	1392.61i	0.0839018	−	0.996474i
$126$		0			0
$127$			1335.29i			0.932978i	0.884527	+	0.466489i	$0.154481\pi$
$127$			1335.29i			0.932978i	−0.884527	+	0.466489i	$0.845519\pi$
$128$			5735.79i			3.96076i
$129$		0			0
$130$	−404.795	−	249.074i	−0.273099	−	0.168040i
$131$	606.535			0.404529			0.202264	−	0.979331i	$-0.435170\pi$
$131$	606.535			0.404529			0.202264	+	0.979331i	$0.435170\pi$
$132$		0			0
$133$			386.034i			0.251679i
$134$	−1575.29			−1.01555
$135$		0			0
$136$	3335.31			2.10294
$137$		−	760.948i		−	0.474542i	−0.971444	−	0.237271i	$-0.923747\pi$
$137$		−	760.948i		−	0.474542i	0.971444	−	0.237271i	$-0.0762529\pi$
$138$		0			0
$139$	2282.70			1.39292			0.696461	−	0.717595i	$-0.254757\pi$
$139$	2282.70			1.39292			0.696461	+	0.717595i	$0.254757\pi$
$140$	2565.94	−	4170.18i	1.54901	−	2.51746i
$141$		0			0
$142$			4195.60i			2.47949i
$143$		−	474.903i		−	0.277716i
$144$		0			0
$145$	705.202	+	433.916i	0.403889	+	0.248516i
$146$	2906.04			1.64730
$147$		0			0
$148$			6077.00i			3.37518i
$149$	−50.9345			−0.0280048			−0.0140024	−	0.999902i	$-0.504457\pi$
$149$	−50.9345			−0.0280048			−0.0140024	+	0.999902i	$0.504457\pi$
$150$		0			0
$151$	−1201.78			−0.647679			−0.323839	−	0.946112i	$-0.604974\pi$
$151$	−1201.78			−0.647679			−0.323839	+	0.946112i	$0.604974\pi$
$152$		−	1526.24i		−	0.814439i
$153$		0			0
$154$	6655.77			3.48271
$155$	−1839.81	−	1132.05i	−0.953401	−	0.586635i
$156$		0			0
$157$			742.899i			0.377642i	0.982012	+	0.188821i	$0.0604666\pi$
$157$			742.899i			0.377642i	−0.982012	+	0.188821i	$0.939533\pi$
$158$		−	1222.01i		−	0.615303i
$159$		0			0
$160$	−4427.85	+	7196.16i	−2.18783	+	3.55566i
$161$	−500.517			−0.245008
$162$		0			0
$163$			2819.44i			1.35482i	0.735605	+	0.677410i	$0.236898\pi$
$163$			2819.44i			1.35482i	−0.735605	+	0.677410i	$0.763102\pi$
$164$	2034.76			0.968829
$165$		0			0
$166$	−2660.02			−1.24372
$167$		−	2121.54i		−	0.983053i	−0.870863	−	0.491527i	$-0.836439\pi$
$167$		−	2121.54i		−	0.983053i	0.870863	−	0.491527i	$-0.163561\pi$
$168$		0			0
$169$	2137.15			0.972759
$170$	2237.19	+	1376.56i	1.00932	+	0.621044i
$171$		0			0
$172$		−	3153.11i		−	1.39781i
$173$		−	1212.11i		−	0.532690i	−0.963878	−	0.266345i	$-0.914184\pi$
$173$		−	1212.11i		−	0.532690i	0.963878	−	0.266345i	$-0.0858160\pi$
$174$		0			0
$175$	2201.59	−	1111.69i	0.950998	−	0.480205i
$176$	−15414.1			−6.60162
$177$		0			0
$178$		−	7199.52i		−	3.03161i
$179$	−1590.94			−0.664315			−0.332158	−	0.943224i	$-0.607777\pi$
$179$	−1590.94			−0.664315			−0.332158	+	0.943224i	$0.607777\pi$
$180$		0			0
$181$	−2392.55			−0.982522			−0.491261	−	0.871012i	$-0.663464\pi$
$181$	−2392.55			−0.982522			−0.491261	+	0.871012i	$0.663464\pi$
$182$		−	838.772i		−	0.341615i
$183$		0			0
$184$	1978.87			0.792849
$185$	−1604.14	+	2607.05i	−0.637505	+	1.03608i
$186$		0			0
$187$			2624.66i			1.02639i
$188$			12177.9i			4.72426i
$189$		0			0
$190$	629.918	−	1023.75i	0.240521	−	0.390896i
$191$	−338.416			−0.128204			−0.0641018	−	0.997943i	$-0.520418\pi$
$191$	−338.416			−0.128204			−0.0641018	+	0.997943i	$0.520418\pi$
$192$		0			0
$193$		−	1922.34i		−	0.716958i	−0.933538	−	0.358479i	$-0.883296\pi$
$193$		−	1922.34i		−	0.716958i	0.933538	−	0.358479i	$-0.116704\pi$
$194$	4470.44			1.65443
$195$		0			0
$196$	1027.73			0.374539
$197$			3719.82i			1.34531i	0.739956	+	0.672655i	$0.234846\pi$
$197$			3719.82i			1.34531i	−0.739956	+	0.672655i	$0.765154\pi$
$198$		0			0
$199$	−1616.51			−0.575837			−0.287919	−	0.957655i	$-0.592963\pi$
$199$	−1616.51			−0.575837			−0.287919	+	0.957655i	$0.592963\pi$
$200$	−8704.33	+	4395.24i	−3.07744	+	1.55395i
$201$		0			0
$202$			10555.4i			3.67660i
$203$			1461.24i			0.505217i
$204$		0			0
$205$	872.917	+	537.112i	0.297401	+	0.182993i
$206$	5978.31			2.02198
$207$		0			0
$208$			1942.52i			0.647545i
$209$	1201.05			0.397504
$210$		0			0
$211$	−4006.06			−1.30706			−0.653528	−	0.756902i	$-0.726712\pi$
$211$	−4006.06			−1.30706			−0.653528	+	0.756902i	$0.726712\pi$
$212$		−	8557.78i		−	2.77241i
$213$		0			0
$214$	9312.33			2.97466
$215$	832.322	−	1352.69i	0.264018	−	0.429083i
$216$		0			0
$217$		−	3812.25i		−	1.19259i
$218$			5518.54i			1.71451i
$219$		0			0
$220$	−12974.5	−	7983.30i	−3.97609	−	2.44652i
$221$	330.764			0.100677
$222$		0			0
$223$			728.351i			0.218717i	0.994002	+	0.109359i	$0.0348797\pi$
$223$			728.351i			0.218717i	−0.994002	+	0.109359i	$0.965120\pi$
$224$	−14911.1			−4.44771
$225$		0			0
$226$	8909.65			2.62239
$227$			1463.63i			0.427949i	0.976839	+	0.213975i	$0.0686410\pi$
$227$			1463.63i			0.427949i	−0.976839	+	0.213975i	$0.931359\pi$
$228$		0			0
$229$	1890.60			0.545565			0.272783	−	0.962076i	$-0.412056\pi$
$229$	1890.60			0.545565			0.272783	+	0.962076i	$0.412056\pi$
$230$	1327.35	+	816.728i	0.380534	+	0.234145i
$231$		0			0
$232$		−	5777.24i		−	1.63489i
$233$		−	434.333i		−	0.122121i	−0.998134	−	0.0610603i	$-0.980552\pi$
$233$		−	434.333i		−	0.122121i	0.998134	−	0.0610603i	$-0.0194482\pi$
$234$		0			0
$235$	−3214.57	+	5224.33i	−0.892320	+	1.45020i
$236$	−5062.18			−1.39627
$237$		0			0
$238$			4635.66i			1.26254i
$239$	−1670.68			−0.452164			−0.226082	−	0.974108i	$-0.572592\pi$
$239$	−1670.68			−0.452164			−0.226082	+	0.974108i	$0.572592\pi$
$240$		0			0
$241$	1361.11			0.363803			0.181901	−	0.983317i	$-0.441775\pi$
$241$	1361.11			0.363803			0.181901	+	0.983317i	$0.441775\pi$
$242$		−	13393.8i		−	3.55780i
$243$		0			0
$244$	2513.61			0.659498
$245$	440.901	+	271.289i	0.114972	+	0.0707430i
$246$		0			0
$247$		−	151.358i		−	0.0389907i
$248$			15072.3i			3.85925i
$249$		0			0
$250$	−7652.55	−	644.334i	−1.93596	−	0.163005i
$251$	2369.11			0.595766			0.297883	−	0.954602i	$-0.403720\pi$
$251$	2369.11			0.595766			0.297883	+	0.954602i	$0.403720\pi$
$252$		0			0
$253$			1557.24i			0.386967i
$254$	7337.57			1.81260
$255$		0			0
$256$	14366.5			3.50745
$257$			5349.58i			1.29843i	0.760603	+	0.649217i	$0.224903\pi$
$257$			5349.58i			1.29843i	−0.760603	+	0.649217i	$0.775097\pi$
$258$		0			0
$259$	−5402.03			−1.29601
$260$	−1006.07	+	1635.07i	−0.239976	+	0.390010i
$261$		0			0
$262$		−	3332.97i		−	0.785922i
$263$			3271.43i			0.767016i	0.923538	+	0.383508i	$0.125284\pi$
$263$			3271.43i			0.767016i	−0.923538	+	0.383508i	$0.874716\pi$
$264$		0			0
$265$	2258.98	−	3671.31i	0.523654	−	0.851044i
$266$	2121.29			0.488965
$267$		0			0
$268$			6362.98i			1.45030i
$269$	−6631.50			−1.50308			−0.751542	−	0.659685i	$-0.770690\pi$
$269$	−6631.50			−1.50308			−0.751542	+	0.659685i	$0.770690\pi$
$270$		0			0
$271$	−39.0882			−0.00876177			−0.00438089	−	0.999990i	$-0.501394\pi$
$271$	−39.0882			−0.00876177			−0.00438089	+	0.999990i	$0.501394\pi$
$272$		−	10735.8i		−	2.39320i
$273$		0			0
$274$	−4181.48			−0.921944
$275$	−3458.75	−	6849.71i	−0.758438	−	1.50201i
$276$		0			0
$277$		−	3155.82i		−	0.684530i	−0.939603	−	0.342265i	$-0.888806\pi$
$277$		−	3155.82i		−	0.684530i	0.939603	−	0.342265i	$-0.111194\pi$
$278$		−	12543.7i		−	2.70618i
$279$		0			0
$280$	−14656.2	−	9018.07i	−3.12813	−	1.92476i
$281$	−1084.72			−0.230281			−0.115141	−	0.993349i	$-0.536732\pi$
$281$	−1084.72			−0.230281			−0.115141	+	0.993349i	$0.536732\pi$
$282$		0			0
$283$		−	5748.10i		−	1.20738i	−0.797218	−	0.603691i	$-0.793696\pi$
$283$		−	5748.10i		−	1.20738i	0.797218	−	0.603691i	$-0.206304\pi$
$284$	16947.1			3.54093
$285$		0			0
$286$	−2609.63			−0.539549
$287$			1808.76i			0.372013i
$288$		0			0
$289$	3084.96			0.627917
$290$	2384.41	−	3875.15i	0.482818	−	0.784678i
$291$		0			0
$292$		−	11738.2i		−	2.35249i
$293$		−	6933.77i		−	1.38251i	−0.722612	−	0.691254i	$-0.757059\pi$
$293$		−	6933.77i		−	1.38251i	0.722612	−	0.691254i	$-0.242941\pi$
$294$		0			0
$295$	−2171.69	−	1336.26i	−0.428612	−	0.263728i
$296$	21357.8			4.19390
$297$		0			0
$298$			279.890i			0.0544080i
$299$	196.246			0.0379571
$300$		0			0
$301$	2802.90			0.536733
$302$			6603.90i			1.25832i
$303$		0			0
$304$	−4912.71			−0.926853
$305$	1078.35	+	663.514i	0.202445	+	0.124566i
$306$		0			0
$307$		−	10020.5i		−	1.86286i	−0.363917	−	0.931431i	$-0.618561\pi$
$307$		−	10020.5i		−	1.86286i	0.363917	−	0.931431i	$-0.381439\pi$
$308$		−	26884.3i		−	4.97362i
$309$		0			0
$310$	−6220.72	+	10109.9i	−1.13972	+	1.85228i
$311$	6830.44			1.24540			0.622699	−	0.782461i	$-0.286036\pi$
$311$	6830.44			1.24540			0.622699	+	0.782461i	$0.286036\pi$
$312$		0			0
$313$		−	7535.37i		−	1.36078i	−0.732850	−	0.680390i	$-0.761810\pi$
$313$		−	7535.37i		−	1.36078i	0.732850	−	0.680390i	$-0.238190\pi$
$314$	4082.30			0.733686
$315$		0			0
$316$	−4936.00			−0.878708
$317$			6233.88i			1.10451i	0.833676	+	0.552255i	$0.186232\pi$
$317$			6233.88i			1.10451i	−0.833676	+	0.552255i	$0.813768\pi$
$318$		0			0
$319$	4546.30			0.797943
$320$	20415.7	+	12562.0i	3.56648	+	2.19448i
$321$		0			0
$322$			2750.39i			0.476003i
$323$			836.517i			0.144102i
$324$		0			0
$325$	−863.213	+	435.878i	−0.147331	+	0.0743943i
$326$	15493.1			2.63216
$327$		0			0
$328$		−	7151.21i		−	1.20384i
$329$	−10825.3			−1.81403
$330$		0			0
$331$	−3370.75			−0.559737			−0.279869	−	0.960038i	$-0.590291\pi$
$331$	−3370.75			−0.559737			−0.279869	+	0.960038i	$0.590291\pi$
$332$			10744.5i			1.77615i
$333$		0			0
$334$	−11658.1			−1.90988
$335$	−1679.62	+	2729.73i	−0.273933	+	0.445198i
$336$		0			0
$337$		−	7960.36i		−	1.28673i	−0.765559	−	0.643366i	$-0.777538\pi$
$337$		−	7960.36i		−	1.28673i	0.765559	−	0.643366i	$-0.222462\pi$
$338$		−	11743.8i		−	1.88989i
$339$		0			0
$340$	5560.28	−	9036.58i	0.886907	−	1.44140i
$341$	−11860.9			−1.88359
$342$		0			0
$343$		−	5854.06i		−	0.921544i
$344$	−11081.7			−1.73688
$345$		0			0
$346$	−6660.68			−1.03491
$347$			6475.03i			1.00172i	0.865527	+	0.500862i	$0.166983\pi$
$347$			6475.03i			1.00172i	−0.865527	+	0.500862i	$0.833017\pi$
$348$		0			0
$349$	−5035.27			−0.772298			−0.386149	−	0.922436i	$-0.626195\pi$
$349$	−5035.27			−0.772298			−0.386149	+	0.922436i	$0.626195\pi$
$350$	−6108.84	−	12097.9i	−0.932946	−	1.84761i
$351$		0			0
$352$			46392.2i			7.02475i
$353$			5969.49i			0.900068i	0.893011	+	0.450034i	$0.148588\pi$
$353$			5969.49i			0.900068i	−0.893011	+	0.450034i	$0.851412\pi$
$354$		0			0
$355$	7270.34	+	4473.49i	1.08696	+	0.668812i
$356$	−29080.7			−4.32941
$357$		0			0
$358$			8742.36i			1.29064i
$359$	−1254.16			−0.184379			−0.0921895	−	0.995741i	$-0.529387\pi$
$359$	−1254.16			−0.184379			−0.0921895	+	0.995741i	$0.529387\pi$
$360$		0			0
$361$	−6476.21			−0.944191
$362$			13147.3i			1.90885i
$363$		0			0
$364$	−3388.01			−0.487857
$365$	3098.52	−	5035.72i	0.444339	−	0.722142i
$366$		0			0
$367$			6284.06i			0.893802i	0.894583	+	0.446901i	$0.147472\pi$
$367$			6284.06i			0.893802i	−0.894583	+	0.446901i	$0.852528\pi$
$368$		−	6369.64i		−	0.902284i
$369$		0			0
$370$	14326.0	+	8814.87i	2.01290	+	1.23855i
$371$	7607.28			1.06456
$372$		0			0
$373$			5229.54i			0.725939i	0.931801	+	0.362969i	$0.118237\pi$
$373$			5229.54i			0.725939i	−0.931801	+	0.362969i	$0.881763\pi$
$374$	14422.7			1.99407
$375$		0			0
$376$	42799.4			5.87024
$377$		−	572.932i		−	0.0782693i
$378$		0			0
$379$	−2282.25			−0.309318			−0.154659	−	0.987968i	$-0.549428\pi$
$379$	−2282.25			−0.309318			−0.154659	+	0.987968i	$0.549428\pi$
$380$	−4135.16	−	2544.40i	−0.558235	−	0.343486i
$381$		0			0
$382$			1859.63i			0.249075i
$383$		−	1460.90i		−	0.194904i	−0.995240	−	0.0974521i	$-0.968931\pi$
$383$		−	1460.90i		−	0.194904i	0.995240	−	0.0974521i	$-0.0310693\pi$
$384$		0			0
$385$	7096.61	−	11533.4i	0.939419	−	1.52675i
$386$	−10563.4			−1.39291
$387$		0			0
$388$		−	18057.2i		−	2.36267i
$389$	953.470			0.124275			0.0621373	−	0.998068i	$-0.480208\pi$
$389$	953.470			0.124275			0.0621373	+	0.998068i	$0.480208\pi$
$390$		0			0
$391$	−1084.60			−0.140282
$392$		−	3612.00i		−	0.465392i
$393$		0			0
$394$	20440.7			2.61368
$395$	−2117.56	−	1302.95i	−0.269736	−	0.165971i
$396$		0			0
$397$		−	6109.68i		−	0.772383i	−0.922419	−	0.386192i	$-0.873790\pi$
$397$		−	6109.68i		−	0.772383i	0.922419	−	0.386192i	$-0.126210\pi$
$398$			8882.89i			1.11874i
$399$		0			0
$400$	14147.5	+	28017.7i	1.76844	+	3.50221i
$401$	−10738.4			−1.33728			−0.668640	−	0.743586i	$-0.733123\pi$
$401$	−10738.4			−1.33728			−0.668640	+	0.743586i	$0.733123\pi$
$402$		0			0
$403$			1494.73i			0.184759i
$404$	42635.7			5.25051
$405$		0			0
$406$	8029.65			0.981540
$407$			16807.1i			2.04692i
$408$		0			0
$409$	−15868.3			−1.91842			−0.959211	−	0.282691i	$-0.908773\pi$
$409$	−15868.3			−1.91842			−0.959211	+	0.282691i	$0.908773\pi$
$410$	2951.48	−	4796.76i	0.355520	−	0.577793i
$411$		0			0
$412$		−	24147.9i		−	2.88758i
$413$		−	4499.93i		−	0.536143i
$414$		0			0
$415$	−2836.21	+	4609.41i	−0.335479	+	0.545222i
$416$	5846.42			0.689049
$417$		0			0
$418$		−	6599.88i		−	0.772274i
$419$	−10218.9			−1.19146			−0.595732	−	0.803183i	$-0.703138\pi$
$419$	−10218.9			−1.19146			−0.595732	+	0.803183i	$0.703138\pi$
$420$		0			0
$421$	−7998.04			−0.925892			−0.462946	−	0.886386i	$-0.653208\pi$
$421$	−7998.04			−0.925892			−0.462946	+	0.886386i	$0.653208\pi$
$422$			22013.7i			2.53936i
$423$		0			0
$424$	−30076.6			−3.44492
$425$	4770.74	−	2408.98i	0.544506	−	0.274947i
$426$		0			0
$427$			2234.43i			0.253235i
$428$		−	37614.8i		−	4.24809i
$429$		0			0
$430$	−7433.18	−	4573.69i	−0.833627	−	0.512937i
$431$	5393.13			0.602733			0.301367	−	0.953508i	$-0.402557\pi$
$431$	5393.13			0.602733			0.301367	+	0.953508i	$0.402557\pi$
$432$		0			0
$433$			15682.5i			1.74054i	0.492578	+	0.870268i	$0.336055\pi$
$433$			15682.5i			1.74054i	−0.492578	+	0.870268i	$0.663945\pi$
$434$	−20948.7			−2.31698
$435$		0			0
$436$	22290.8			2.44847
$437$			496.314i			0.0543293i
$438$		0			0
$439$	−7234.17			−0.786488			−0.393244	−	0.919434i	$-0.628647\pi$
$439$	−7234.17			−0.786488			−0.393244	+	0.919434i	$0.628647\pi$
$440$	−28057.5	+	45599.2i	−3.03998	+	4.94058i
$441$		0			0
$442$		−	1817.58i		−	0.195596i
$443$		−	7621.24i		−	0.817373i	−0.912675	−	0.408686i	$-0.865987\pi$
$443$		−	7621.24i		−	0.817373i	0.912675	−	0.408686i	$-0.134013\pi$
$444$		0			0
$445$	−12475.7	−	7676.37i	−1.32900	−	0.817741i
$446$	4002.35			0.424926
$447$		0			0
$448$			42303.2i			4.46125i
$449$	9045.31			0.950723			0.475362	−	0.879790i	$-0.342317\pi$
$449$	9045.31			0.950723			0.475362	+	0.879790i	$0.342317\pi$
$450$		0			0
$451$	5627.52			0.587560
$452$		−	35988.3i		−	3.74501i
$453$		0			0
$454$	8042.78			0.831424
$455$	−1453.46	−	894.327i	−0.149757	−	0.0921466i
$456$		0			0
$457$			13852.4i			1.41792i	0.705248	+	0.708961i	$0.250836\pi$
$457$			13852.4i			1.41792i	−0.705248	+	0.708961i	$0.749164\pi$
$458$		−	10389.0i		−	1.05993i
$459$		0			0
$460$	3298.97	−	5361.50i	0.334381	−	0.543437i
$461$	−14615.1			−1.47656			−0.738281	−	0.674493i	$-0.764362\pi$
$461$	−14615.1			−1.47656			−0.738281	+	0.674493i	$0.764362\pi$
$462$		0			0
$463$		−	14705.6i		−	1.47608i	−0.674757	−	0.738040i	$-0.735751\pi$
$463$		−	14705.6i		−	1.47608i	0.674757	−	0.738040i	$-0.264249\pi$
$464$	−18595.9			−1.86055
$465$		0			0
$466$	−2386.70			−0.237257
$467$			57.7497i			0.00572235i	0.999996	+	0.00286117i	$0.000910741\pi$
$467$			57.7497i			0.00572235i	−0.999996	+	0.00286117i	$0.999089\pi$
$468$		0			0
$469$	−5656.25			−0.556890
$470$	28708.2	+	17664.4i	2.81747	+	1.73361i
$471$		0			0
$472$			17791.2i			1.73497i
$473$		−	8720.54i		−	0.847719i
$474$		0			0
$475$	−1102.35	−	2183.10i	−0.106483	−	0.210879i
$476$	18724.6			1.80303
$477$		0			0
$478$			9180.54i			0.878469i
$479$	14388.0			1.37245			0.686225	−	0.727389i	$-0.259266\pi$
$479$	14388.0			1.37245			0.686225	+	0.727389i	$0.259266\pi$
$480$		0			0
$481$	2118.06			0.200780
$482$		−	7479.40i		−	0.706799i
$483$		0			0
$484$	−54101.0			−5.08086
$485$	4766.53	−	7746.58i	0.446262	−	0.725267i
$486$		0			0
$487$		−	15397.6i		−	1.43271i	−0.697736	−	0.716355i	$-0.745809\pi$
$487$		−	15397.6i		−	1.43271i	0.697736	−	0.716355i	$-0.254191\pi$
$488$		−	8834.15i		−	0.819474i
$489$		0			0
$490$	1490.76	−	2422.79i	0.137440	−	0.223368i
$491$	13165.6			1.21009			0.605047	−	0.796190i	$-0.293154\pi$
$491$	13165.6			1.21009			0.605047	+	0.796190i	$0.293154\pi$
$492$		0			0
$493$			3166.44i			0.289268i
$494$	−831.729			−0.0757515
$495$		0			0
$496$	48515.2			4.39193
$497$			15064.8i			1.35965i
$498$		0			0
$499$	−5340.12			−0.479071			−0.239536	−	0.970888i	$-0.576995\pi$
$499$	−5340.12			−0.479071			−0.239536	+	0.970888i	$0.576995\pi$
$500$	−2602.63	+	30910.5i	−0.232786	+	2.76472i
$501$		0			0
$502$		−	13018.5i		−	1.15746i
$503$		−	12895.5i		−	1.14311i	−0.820565	−	0.571553i	$-0.806341\pi$
$503$		−	12895.5i		−	1.14311i	0.820565	−	0.571553i	$-0.193659\pi$
$504$		0			0
$505$	18290.8	+	11254.5i	1.61175	+	0.991719i
$506$	8557.16			0.751802
$507$		0			0
$508$		−	29638.3i		−	2.58855i
$509$	8352.05			0.727305			0.363652	−	0.931535i	$-0.381530\pi$
$509$	8352.05			0.727305			0.363652	+	0.931535i	$0.381530\pi$
$510$		0			0
$511$	10434.5			0.903314
$512$		−	33059.0i		−	2.85355i
$513$		0			0
$514$	29396.4			2.52261
$515$	6374.28	−	10359.5i	0.545406	−	0.886397i
$516$		0			0
$517$			33680.2i			2.86509i
$518$			29684.7i			2.51789i
$519$		0			0
$520$	5746.49	+	3535.86i	0.484616	+	0.298188i
$521$	−3927.19			−0.330237			−0.165119	−	0.986274i	$-0.552801\pi$
$521$	−3927.19			−0.330237			−0.165119	+	0.986274i	$0.552801\pi$
$522$		0			0
$523$		−	10611.0i		−	0.887161i	−0.896235	−	0.443580i	$-0.853708\pi$
$523$		−	10611.0i		−	0.887161i	0.896235	−	0.443580i	$-0.146292\pi$
$524$	−13462.7			−1.12237
$525$		0			0
$526$	17976.8			1.49017
$527$		−	8260.97i		−	0.682834i
$528$		0			0
$529$	11523.5			0.947111
$530$	−20174.2	−	12413.3i	−1.65342	−	1.01736i
$531$		0			0
$532$		−	8568.42i		−	0.698286i
$533$		−	709.190i		−	0.0576331i
$534$		0			0
$535$	9929.12	−	16136.8i	0.802380	−	1.30403i
$536$	22362.9			1.80210
$537$		0			0
$538$			36440.7i			2.92021i
$539$	2842.40			0.227144
$540$		0			0
$541$	−18685.5			−1.48494			−0.742469	−	0.669881i	$-0.766345\pi$
$541$	−18685.5			−1.48494			−0.742469	+	0.669881i	$0.766345\pi$
$542$			214.793i			0.0170224i
$543$		0			0
$544$	−32311.6			−2.54660
$545$	9562.79	+	5884.06i	0.751605	+	0.462468i
$546$		0			0
$547$			17948.8i			1.40299i	0.712673	+	0.701496i	$0.247484\pi$
$547$			17948.8i			1.40299i	−0.712673	+	0.701496i	$0.752516\pi$
$548$			16890.0i			1.31662i
$549$		0			0
$550$	−37639.8	+	19006.2i	−2.91812	+	1.47350i
$551$	1448.97			0.112029
$552$		0			0
$553$		−	4387.76i		−	0.337408i
$554$	−17341.5			−1.32991
$555$		0			0
$556$	−50666.9			−3.86467
$557$			8386.29i			0.637951i	0.947763	+	0.318975i	$0.103339\pi$
$557$			8386.29i			0.637951i	−0.947763	+	0.318975i	$0.896661\pi$
$558$		0			0
$559$	−1098.98			−0.0831518
$560$	−29027.6	+	47175.8i	−2.19043	+	3.55989i
$561$		0			0
$562$			5960.64i			0.447393i
$563$			11613.5i			0.869360i	0.900585	+	0.434680i	$0.143139\pi$
$563$			11613.5i			0.869360i	−0.900585	+	0.434680i	$0.856861\pi$
$564$		0			0
$565$	9499.77	−	15439.1i	0.707360	−	1.14960i
$566$	−31586.3			−2.34571
$567$		0			0
$568$		−	59560.9i		−	4.39986i
$569$	−2834.90			−0.208867			−0.104433	−	0.994532i	$-0.533303\pi$
$569$	−2834.90			−0.208867			−0.104433	+	0.994532i	$0.533303\pi$
$570$		0			0
$571$	10401.4			0.762318			0.381159	−	0.924509i	$-0.375525\pi$
$571$	10401.4			0.762318			0.381159	+	0.924509i	$0.375525\pi$
$572$			10541.0i			0.770524i
$573$		0			0
$574$	9939.31			0.722750
$575$	2830.53	−	1429.27i	0.205289	−	0.103660i
$576$		0			0
$577$		−	10769.8i		−	0.777043i	−0.921440	−	0.388522i	$-0.872986\pi$
$577$		−	10769.8i		−	0.777043i	0.921440	−	0.388522i	$-0.127014\pi$
$578$		−	16952.1i		−	1.21992i
$579$		0			0
$580$	−15652.7	−	9631.22i	−1.12059	−	0.689508i
$581$	−9551.11			−0.682008
$582$		0			0
$583$		−	23668.2i		−	1.68137i
$584$	−41254.3			−2.92314
$585$		0			0
$586$	−38101.7			−2.68595
$587$		−	10879.9i		−	0.765014i	−0.923953	−	0.382507i	$-0.875061\pi$
$587$		−	10879.9i		−	0.765014i	0.923953	−	0.382507i	$-0.124939\pi$
$588$		0			0
$589$	−3780.24			−0.264452
$590$	−7342.85	+	11933.6i	−0.512374	+	0.832712i
$591$		0			0
$592$		−	68746.9i		−	4.77277i
$593$			16369.0i			1.13355i	0.823872	+	0.566775i	$0.191809\pi$
$593$			16369.0i			1.13355i	−0.823872	+	0.566775i	$0.808191\pi$
$594$		0			0
$595$	8032.90	+	4942.70i	0.553474	+	0.340556i
$596$	1130.54			0.0776995
$597$		0			0
$598$		−	1078.39i		−	0.0737434i
$599$	15480.8			1.05597			0.527985	−	0.849254i	$-0.322948\pi$
$599$	15480.8			1.05597			0.527985	+	0.849254i	$0.322948\pi$
$600$		0			0
$601$	8606.99			0.584170			0.292085	−	0.956392i	$-0.405651\pi$
$601$	8606.99			0.584170			0.292085	+	0.956392i	$0.405651\pi$
$602$		−	15402.2i		−	1.04277i
$603$		0			0
$604$	26674.8			1.79699
$605$	−23209.5	−	14281.0i	−1.55967	−	0.959675i
$606$		0			0
$607$			8497.67i			0.568221i	0.958792	+	0.284110i	$0.0916982\pi$
$607$			8497.67i			0.568221i	−0.958792	+	0.284110i	$0.908302\pi$
$608$			14785.9i			0.986260i
$609$		0			0
$610$	3646.07	−	5925.61i	0.242008	−	0.393313i
$611$	4244.44			0.281034
$612$		0			0
$613$			16596.5i			1.09352i	0.837289	+	0.546760i	$0.184139\pi$
$613$			16596.5i			1.09352i	−0.837289	+	0.546760i	$0.815861\pi$
$614$	−55063.5			−3.61919
$615$		0			0
$616$	−94485.6			−6.18009
$617$			18944.7i			1.23612i	0.786133	+	0.618058i	$0.212080\pi$
$617$			18944.7i			1.23612i	−0.786133	+	0.618058i	$0.787920\pi$
$618$		0			0
$619$	−1529.97			−0.0993452			−0.0496726	−	0.998766i	$-0.515818\pi$
$619$	−1529.97			−0.0993452			−0.0496726	+	0.998766i	$0.515818\pi$
$620$	40836.5	+	25127.0i	2.64522	+	1.62762i
$621$		0			0
$622$		−	37533.9i		−	2.41957i
$623$		−	25850.7i		−	1.66242i
$624$		0			0
$625$	−9275.94	+	12573.7i	−0.593660	+	0.804716i
$626$	−41407.6			−2.64374
$627$		0			0
$628$		−	16489.4i		−	1.04777i
$629$	−11706.0			−0.742046
$630$		0			0
$631$	29030.4			1.83151			0.915755	−	0.401737i	$-0.131593\pi$
$631$	29030.4			1.83151			0.915755	+	0.401737i	$0.131593\pi$
$632$			17347.7i			1.09186i
$633$		0			0
$634$	34255.7			2.14585
$635$	7823.56	−	12714.9i	0.488927	−	0.794606i
$636$		0			0
$637$		−	358.204i		−	0.0222803i
$638$		−	24982.3i		−	1.55025i
$639$		0			0
$640$	33606.3	−	54617.1i	2.07563	−	3.37333i
$641$	−6163.82			−0.379807			−0.189904	−	0.981803i	$-0.560818\pi$
$641$	−6163.82			−0.379807			−0.189904	+	0.981803i	$0.560818\pi$
$642$		0			0
$643$			13740.3i			0.842714i	0.906895	+	0.421357i	$0.138446\pi$
$643$			13740.3i			0.842714i	−0.906895	+	0.421357i	$0.861554\pi$
$644$	11109.5			0.679775
$645$		0			0
$646$	4596.74			0.279963
$647$			8072.80i			0.490533i	0.969456	+	0.245266i	$0.0788754\pi$
$647$			8072.80i			0.490533i	−0.969456	+	0.245266i	$0.921125\pi$
$648$		0			0
$649$	−14000.4			−0.846788
$650$	2395.19	+	4743.44i	0.144534	+	0.286235i
$651$		0			0
$652$		−	62580.5i		−	3.75896i
$653$		−	18600.4i		−	1.11469i	−0.830282	−	0.557343i	$-0.811821\pi$
$653$		−	18600.4i		−	1.11469i	0.830282	−	0.557343i	$-0.188179\pi$
$654$		0			0
$655$	−5775.53	−	3553.72i	−0.344532	−	0.211993i
$656$	−23018.5			−1.37000
$657$		0			0
$658$			59485.9i			3.52432i
$659$	23183.1			1.37039			0.685194	−	0.728360i	$-0.259717\pi$
$659$	23183.1			1.37039			0.685194	+	0.728360i	$0.259717\pi$
$660$		0			0
$661$	−6171.22			−0.363136			−0.181568	−	0.983378i	$-0.558117\pi$
$661$	−6171.22			−0.363136			−0.181568	+	0.983378i	$0.558117\pi$
$662$			18522.6i			1.08746i
$663$		0			0
$664$	37761.8			2.20699
$665$	2261.79	−	3675.87i	0.131893	−	0.214352i
$666$		0			0
$667$			1878.68i			0.109060i
$668$			47089.9i			2.72749i
$669$		0			0
$670$	15000.1	+	9229.69i	0.864934	+	0.532200i
$671$	6951.87			0.399961
$672$		0			0
$673$			6313.78i			0.361632i	0.983517	+	0.180816i	$0.0578739\pi$
$673$			6313.78i			0.361632i	−0.983517	+	0.180816i	$0.942126\pi$
$674$	−43742.9			−2.49987
$675$		0			0
$676$	−47436.3			−2.69893
$677$		−	9133.85i		−	0.518527i	−0.965807	−	0.259263i	$-0.916520\pi$
$677$		−	9133.85i		−	0.518527i	0.965807	−	0.259263i	$-0.0834797\pi$
$678$		0			0
$679$	16051.6			0.907223
$680$	−31759.3	−	19541.7i	−1.79105	−	1.10205i
$681$		0			0
$682$			65176.7i			3.65945i
$683$		−	20251.5i		−	1.13455i	−0.823527	−	0.567277i	$-0.807997\pi$
$683$		−	20251.5i		−	1.13455i	0.823527	−	0.567277i	$-0.192003\pi$
$684$		0			0
$685$	−4458.44	+	7245.87i	−0.248683	+	0.404161i
$686$	−32168.6			−1.79038
$687$		0			0
$688$			35670.1i			1.97661i
$689$	−2982.71			−0.164923
$690$		0			0
$691$	−16958.3			−0.933610			−0.466805	−	0.884360i	$-0.654595\pi$
$691$	−16958.3			−0.933610			−0.466805	+	0.884360i	$0.654595\pi$
$692$			26904.1i			1.47795i
$693$		0			0
$694$	35580.9			1.94616
$695$	−21736.2	−	13374.5i	−1.18633	−	0.729960i
$696$		0			0
$697$			3919.50i			0.213001i
$698$			27669.3i			1.50043i
$699$		0			0
$700$	−48866.6	+	24675.1i	−2.63855	+	1.33233i
$701$	13678.0			0.736963			0.368481	−	0.929635i	$-0.379878\pi$
$701$	13678.0			0.736963			0.368481	+	0.929635i	$0.379878\pi$
$702$		0			0
$703$			5356.67i			0.287384i
$704$	131616.			7.04612
$705$		0			0
$706$	32802.9			1.74866
$707$			37900.2i			2.01610i
$708$		0			0
$709$	18368.4			0.972976			0.486488	−	0.873687i	$-0.338278\pi$
$709$	18368.4			0.972976			0.486488	+	0.873687i	$0.338278\pi$
$710$	24582.2	−	39951.2i	1.29937	−	2.11175i
$711$		0			0
$712$			102205.i			5.37961i
$713$		−	4901.32i		−	0.257441i
$714$		0			0
$715$	−2782.48	+	4522.10i	−0.145537	+	0.236527i
$716$	35312.6			1.84315
$717$		0			0
$718$			6891.73i			0.358213i
$719$	24647.1			1.27842			0.639209	−	0.769033i	$-0.279262\pi$
$719$	24647.1			1.27842			0.639209	+	0.769033i	$0.279262\pi$
$720$		0			0
$721$	21465.8			1.10878
$722$			35587.4i			1.83438i
$723$		0			0
$724$	53105.0			2.72601
$725$	−4172.71	−	8263.63i	−0.213752	−	0.423315i
$726$		0			0
$727$			18618.7i			0.949832i	0.880031	+	0.474916i	$0.157522\pi$
$727$			18618.7i			0.949832i	−0.880031	+	0.474916i	$0.842478\pi$
$728$			11907.2i			0.606197i
$729$		0			0
$730$	−27671.8	−	17026.6i	−1.40298	−	0.863266i
$731$	6073.76			0.307313
$732$		0			0
$733$			34638.5i			1.74543i	0.488230	+	0.872715i	$0.337643\pi$
$733$			34638.5i			1.74543i	−0.488230	+	0.872715i	$0.662357\pi$
$734$	34531.5			1.73649
$735$		0			0
$736$	−19170.8			−0.960116
$737$			17598.0i			0.879555i
$738$		0			0
$739$	4520.66			0.225027			0.112514	−	0.993650i	$-0.464110\pi$
$739$	4520.66			0.225027			0.112514	+	0.993650i	$0.464110\pi$
$740$	35605.5	−	57866.1i	1.76876	−	2.87460i
$741$		0			0
$742$		−	41802.7i		−	2.06823i
$743$			5935.02i			0.293048i	0.989207	+	0.146524i	$0.0468086\pi$
$743$			5935.02i			0.293048i	−0.989207	+	0.146524i	$0.953191\pi$
$744$		0			0
$745$	485.006	+	298.428i	0.0238513	+	0.0146759i
$746$	28736.8			1.41036
$747$		0			0
$748$		−	58257.0i		−	2.84771i
$749$	33437.0			1.63119
$750$		0			0
$751$	−15021.3			−0.729874			−0.364937	−	0.931032i	$-0.618909\pi$
$751$	−15021.3			−0.729874			−0.364937	+	0.931032i	$0.618909\pi$
$752$		−	137764.i		−	6.68049i
$753$		0			0
$754$	−3148.32			−0.152062
$755$	11443.5	+	7041.30i	0.551620	+	0.339416i
$756$		0			0
$757$		−	27194.0i		−	1.30566i	−0.757505	−	0.652829i	$-0.773582\pi$
$757$		−	27194.0i		−	1.30566i	0.757505	−	0.652829i	$-0.226418\pi$
$758$			12541.2i			0.600946i
$759$		0			0
$760$	−8942.35	+	14533.1i	−0.426807	+	0.693648i
$761$	34060.8			1.62248			0.811238	−	0.584716i	$-0.198794\pi$
$761$	34060.8			1.62248			0.811238	+	0.584716i	$0.198794\pi$
$762$		0			0
$763$			19814.9i			0.940169i
$764$	7511.49			0.355702
$765$		0			0
$766$	−8027.76			−0.378661
$767$			1764.36i			0.0830605i
$768$		0			0
$769$	−30159.1			−1.41426			−0.707129	−	0.707085i	$-0.750010\pi$
$769$	−30159.1			−1.41426			−0.707129	+	0.707085i	$0.750010\pi$
$770$	−63377.3	−	38996.5i	−2.96618	−	1.82511i
$771$		0			0
$772$			42668.3i			1.98920i
$773$			36455.0i			1.69624i	0.529801	+	0.848122i	$0.322267\pi$
$773$			36455.0i			1.69624i	−0.529801	+	0.848122i	$0.677733\pi$
$774$		0			0
$775$	10886.2	+	21559.1i	0.504574	+	0.999259i
$776$	−63462.5			−2.93579
$777$		0			0
$778$		−	5239.40i		−	0.241442i
$779$	1793.57			0.0824922
$780$		0			0
$781$	46870.4			2.14744
$782$			5959.96i			0.272542i
$783$		0			0
$784$	−11626.4			−0.529628
$785$	4352.69	−	7074.00i	0.197903	−	0.321633i
$786$		0			0
$787$			3825.03i			0.173250i	0.996241	+	0.0866249i	$0.0276082\pi$
$787$			3825.03i			0.173250i	−0.996241	+	0.0866249i	$0.972392\pi$
$788$		−	82565.2i		−	3.73257i
$789$		0			0
$790$	−7159.82	+	11636.2i	−0.322449	+	0.524046i
$791$	31991.1			1.43802
$792$		0			0
$793$		−	876.087i		−	0.0392318i
$794$	−33573.3			−1.50059
$795$		0			0
$796$	35880.2			1.59766
$797$			35109.7i			1.56041i	0.625521	+	0.780207i	$0.284886\pi$
$797$			35109.7i			1.56041i	−0.625521	+	0.780207i	$0.715114\pi$
$798$		0			0
$799$	−23457.9			−1.03865
$800$	84325.3	−	42579.9i	3.72669	−	1.88178i
$801$		0			0
$802$			59008.4i			2.59808i
$803$		−	32464.3i		−	1.42670i
$804$		0			0
$805$	4766.00	+	2932.55i	0.208670	+	0.128396i
$806$	8213.68			0.358951
$807$		0			0
$808$		−	149844.i		−	6.52414i
$809$	−34444.8			−1.49693			−0.748464	−	0.663176i	$-0.769208\pi$
$809$	−34444.8			−1.49693			−0.748464	+	0.663176i	$0.769208\pi$
$810$		0			0
$811$	29534.7			1.27880			0.639398	−	0.768876i	$-0.279184\pi$
$811$	29534.7			1.27880			0.639398	+	0.768876i	$0.279184\pi$
$812$		−	32433.8i		−	1.40173i
$813$		0			0
$814$	92356.6			3.97678
$815$	16519.3	−	26847.2i	0.709993	−	1.15388i
$816$		0			0
$817$		−	2779.36i		−	0.119018i
$818$			87197.5i			3.72713i
$819$		0			0
$820$	−19375.3	−	11921.8i	−0.825140	−	0.507715i
$821$	−18325.4			−0.779001			−0.389501	−	0.921026i	$-0.627352\pi$
$821$	−18325.4			−0.779001			−0.389501	+	0.921026i	$0.627352\pi$
$822$		0			0
$823$		−	27790.9i		−	1.17707i	−0.808471	−	0.588536i	$-0.799705\pi$
$823$		−	27790.9i		−	1.17707i	0.808471	−	0.588536i	$-0.200295\pi$
$824$	−84868.4			−3.58802
$825$		0			0
$826$	−24727.5			−1.04162
$827$			8611.07i			0.362075i	0.983476	+	0.181038i	$0.0579455\pi$
$827$			8611.07i			0.362075i	−0.983476	+	0.181038i	$0.942054\pi$
$828$		0			0
$829$	20602.5			0.863154			0.431577	−	0.902076i	$-0.357957\pi$
$829$	20602.5			0.863154			0.431577	+	0.902076i	$0.357957\pi$
$830$	25329.1	+	15585.2i	1.05926	+	0.651772i
$831$		0			0
$832$		−	16586.5i		−	0.691146i
$833$			1979.70i			0.0823439i
$834$		0			0
$835$	−12430.2	+	20201.7i	−0.515169	+	0.837254i
$836$	−26658.6			−1.10288
$837$		0			0
$838$			56153.6i			2.31479i
$839$	−8540.58			−0.351434			−0.175717	−	0.984441i	$-0.556224\pi$
$839$	−8540.58			−0.351434			−0.175717	+	0.984441i	$0.556224\pi$
$840$		0			0
$841$	−18904.3			−0.775114
$842$			43950.0i			1.79883i
$843$		0			0
$844$	88918.8			3.62643
$845$	−20350.3	−	12521.7i	−0.828487	−	0.509774i
$846$		0			0
$847$		−	48092.1i		−	1.95096i
$848$			96811.2i			3.92041i
$849$		0			0
$850$	−13237.6	−	26215.7i	−0.534170	−	1.05787i
$851$	−6945.26			−0.279766
$852$		0			0
$853$		−	25929.3i		−	1.04080i	−0.853922	−	0.520401i	$-0.825783\pi$
$853$		−	25929.3i		−	1.04080i	0.853922	−	0.520401i	$-0.174217\pi$
$854$	12278.4			0.491988
$855$		0			0
$856$	−132198.			−5.27856
$857$			9529.37i			0.379833i	0.981800	+	0.189917i	$0.0608217\pi$
$857$			9529.37i			0.379833i	−0.981800	+	0.189917i	$0.939178\pi$
$858$		0			0
$859$	−12520.9			−0.497330			−0.248665	−	0.968590i	$-0.579992\pi$
$859$	−12520.9			−0.497330			−0.248665	+	0.968590i	$0.579992\pi$
$860$	−18474.3	+	30024.4i	−0.732520	+	1.19049i
$861$		0			0
$862$		−	29635.8i		−	1.17100i
$863$		−	45333.7i		−	1.78815i	−0.447913	−	0.894077i	$-0.647832\pi$
$863$		−	45333.7i		−	1.78815i	0.447913	−	0.894077i	$-0.352168\pi$
$864$		0			0
$865$	−7101.84	+	11541.9i	−0.279156	+	0.453685i
$866$	86176.7			3.38153
$867$		0			0
$868$			84616.9i			3.30885i
$869$	−13651.5			−0.532905
$870$		0			0
$871$	2217.74			0.0862745
$872$		−	78341.5i		−	3.04240i
$873$		0			0
$874$	2727.29			0.105551
$875$	−27477.3	−	2313.56i	−1.06160	−	0.0893857i
$876$		0			0
$877$		−	7099.47i		−	0.273355i	−0.990616	−	0.136677i	$-0.956358\pi$
$877$		−	7099.47i		−	0.273355i	0.990616	−	0.136677i	$-0.0436424\pi$
$878$			39752.4i			1.52799i
$879$		0			0
$880$	146776.	+	90312.3i	5.62252	+	3.45958i
$881$	1110.63			0.0424722			0.0212361	−	0.999774i	$-0.493240\pi$
$881$	1110.63			0.0424722			0.0212361	+	0.999774i	$0.493240\pi$
$882$		0			0
$883$			46972.2i			1.79019i	0.445872	+	0.895097i	$0.352894\pi$
$883$			46972.2i			1.79019i	−0.445872	+	0.895097i	$0.647106\pi$
$884$	−7341.65			−0.279329
$885$		0			0
$886$	−41879.4			−1.58800
$887$		−	34620.2i		−	1.31052i	−0.755403	−	0.655261i	$-0.772559\pi$
$887$		−	34620.2i		−	1.31052i	0.755403	−	0.655261i	$-0.227441\pi$
$888$		0			0
$889$	26346.4			0.993958
$890$	−42182.4	+	68555.0i	−1.58872	+	2.58199i
$891$		0			0
$892$		−	16166.5i		−	0.606833i
$893$			10734.4i			0.402253i
$894$		0			0
$895$	15149.2	+	9321.40i	0.565789	+	0.348134i
$896$	113171.			4.21964
$897$		0			0
$898$		−	49704.8i		−	1.84707i
$899$	−14309.2			−0.530856
$900$		0			0
$901$	16484.6			0.609525
$902$		−	30923.7i		−	1.14152i
$903$		0			0
$904$	−126482.			−4.65345
$905$	22782.2	+	14018.1i	0.836802	+	0.514890i
$906$		0			0
$907$			18079.3i			0.661867i	0.943654	+	0.330934i	$0.107364\pi$
$907$			18079.3i			0.661867i	−0.943654	+	0.330934i	$0.892636\pi$
$908$		−	32486.8i		−	1.18735i
$909$		0			0
$910$	−4914.41	+	7986.92i	−0.179023	+	0.290949i
$911$	11420.7			0.415353			0.207676	−	0.978198i	$-0.433410\pi$
$911$	11420.7			0.415353			0.207676	+	0.978198i	$0.433410\pi$
$912$		0			0
$913$			29716.0i			1.07717i
$914$	76120.5			2.75475
$915$		0			0
$916$	−41963.9			−1.51367
$917$		−	11967.4i		−	0.430969i
$918$		0			0
$919$	−5641.95			−0.202515			−0.101257	−	0.994860i	$-0.532287\pi$
$919$	−5641.95			−0.202515			−0.101257	+	0.994860i	$0.532287\pi$
$920$	−18843.1	−	11594.3i	−0.675260	−	0.415492i
$921$		0			0
$922$			80311.6i			2.86868i
$923$		−	5906.69i		−	0.210640i
$924$		0			0
$925$	30549.7	−	15426.0i	1.08591	−	0.548328i
$926$	−80808.4			−2.86774
$927$		0			0
$928$			55968.5i			1.97980i
$929$	−12713.0			−0.448977			−0.224489	−	0.974477i	$-0.572071\pi$
$929$	−12713.0			−0.448977			−0.224489	+	0.974477i	$0.572071\pi$
$930$		0			0
$931$	905.914			0.0318906
$932$			9640.48i			0.338824i
$933$		0			0
$934$	317.340			0.0111174
$935$	15378.0	−	24992.4i	0.537877	−	0.874160i
$936$		0			0
$937$		−	13459.0i		−	0.469249i	−0.972086	−	0.234624i	$-0.924614\pi$
$937$		−	13459.0i		−	0.469249i	0.972086	−	0.234624i	$-0.0753860\pi$
$938$			31081.6i			1.08193i
$939$		0			0
$940$	71350.7	−	115959.i	2.47575	−	4.02360i
$941$	−43559.6			−1.50903			−0.754517	−	0.656281i	$-0.772129\pi$
$941$	−43559.6			−1.50903			−0.754517	+	0.656281i	$0.772129\pi$
$942$		0			0
$943$			2325.48i			0.0803054i
$944$	57266.7			1.97444
$945$		0			0
$946$	−47920.2			−1.64696
$947$		−	9153.54i		−	0.314097i	−0.987591	−	0.157049i	$-0.949802\pi$
$947$		−	9153.54i		−	0.314097i	0.987591	−	0.157049i	$-0.0501980\pi$
$948$		0			0
$949$	−4091.21			−0.139943
$950$	−11996.4	+	6057.54i	−0.409698	+	0.206876i
$951$		0			0
$952$		−	65808.1i		−	2.24039i
$953$			5520.98i			0.187662i	0.995588	+	0.0938311i	$0.0299114\pi$
$953$			5520.98i			0.187662i	−0.995588	+	0.0938311i	$0.970089\pi$
$954$		0			0
$955$	3222.45	+	1982.80i	0.109189	+	0.0671851i
$956$	37082.5			1.25453
$957$		0			0
$958$		−	79063.3i		−	2.66641i
$959$	−15014.1			−0.505558
$960$		0			0
$961$	7540.51			0.253114
$962$		−	11638.9i		−	0.390078i
$963$		0			0
$964$	−30211.2			−1.00937
$965$	−11263.1	+	18304.8i	−0.375722	+	0.610624i
$966$		0			0
$967$			19640.0i			0.653134i	0.945174	+	0.326567i	$0.105892\pi$
$967$			19640.0i			0.653134i	−0.945174	+	0.326567i	$0.894108\pi$
$968$			190139.i			6.31334i
$969$		0			0
$970$	−42568.2	−	26192.5i	−1.40905	−	0.867001i
$971$	9759.09			0.322538			0.161269	−	0.986911i	$-0.448441\pi$
$971$	9759.09			0.322538			0.161269	+	0.986911i	$0.448441\pi$
$972$		0			0
$973$		−	45039.4i		−	1.48396i
$974$	−84611.0			−2.78348
$975$		0			0
$976$	−28435.6			−0.932583
$977$		−	27944.0i		−	0.915055i	−0.889196	−	0.457527i	$-0.848735\pi$
$977$		−	27944.0i		−	0.915055i	0.889196	−	0.457527i	$-0.151265\pi$
$978$		0			0
$979$	−80428.1			−2.62563
$980$	−9786.25	−	6021.55i	−0.318990	−	0.196277i
$981$		0			0
$982$		−	72346.3i		−	2.35098i
$983$			44818.1i			1.45420i	0.686534	+	0.727098i	$0.259131\pi$
$983$			44818.1i			1.45420i	−0.686534	+	0.727098i	$0.740869\pi$
$984$		0			0
$985$	21794.6	−	35420.7i	0.705009	−	1.14578i
$986$	17399.9			0.561993
$987$		0			0
$988$			3359.56i			0.108180i
$989$	3603.62			0.115863
$990$		0			0
$991$	−28185.8			−0.903483			−0.451741	−	0.892149i	$-0.649197\pi$
$991$	−28185.8			−0.903483			−0.451741	+	0.892149i	$0.649197\pi$
$992$		−	146017.i		−	4.67343i
$993$		0			0
$994$	82782.4			2.64155
$995$	15392.7	+	9471.24i	0.490433	+	0.301767i
$996$		0			0
$997$			8721.92i			0.277057i	0.990358	+	0.138529i	$0.0442373\pi$
$997$			8721.92i			0.277057i	−0.990358	+	0.138529i	$0.955763\pi$
$998$			29344.4i			0.930743i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.b.d.244.1	✓	16
3.2	odd	2	inner	405.4.b.d.244.16	yes	16
5.2	odd	4		2025.4.a.bm.1.16		16
5.3	odd	4		2025.4.a.bm.1.1		16
5.4	even	2	inner	405.4.b.d.244.15	yes	16
15.2	even	4		2025.4.a.bm.1.2		16
15.8	even	4		2025.4.a.bm.1.15		16
15.14	odd	2	inner	405.4.b.d.244.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.b.d.244.1	✓	16	1.1	even	1	trivial
405.4.b.d.244.2	yes	16	15.14	odd	2	inner
405.4.b.d.244.15	yes	16	5.4	even	2	inner
405.4.b.d.244.16	yes	16	3.2	odd	2	inner
2025.4.a.bm.1.1		16	5.3	odd	4
2025.4.a.bm.1.2		16	15.2	even	4
2025.4.a.bm.1.15		16	15.8	even	4
2025.4.a.bm.1.16		16	5.2	odd	4

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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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.49509i q^{2} -22.1960 q^{4} +(-9.52216 - 5.85905i) q^{5} -19.7308i q^{7} +78.0086i q^{8} +O(q^{10})\)	\(q-5.49509i q^{2} -22.1960 q^{4} +(-9.52216 - 5.85905i) q^{5} -19.7308i q^{7} +78.0086i q^{8} +(-32.1960 + 52.3251i) q^{10} -61.3874 q^{11} +7.73615i q^{13} -108.422 q^{14} +251.096 q^{16} -42.7556i q^{17} -19.5651 q^{19} +(211.354 + 130.048i) q^{20} +337.330i q^{22} -25.3673i q^{23} +(56.3430 + 111.582i) q^{25} +42.5109 q^{26} +437.945i q^{28} -74.0591 q^{29} +193.214 q^{31} -755.727i q^{32} -234.946 q^{34} +(-115.604 + 187.879i) q^{35} -273.787i q^{37} +107.512i q^{38} +(457.057 - 742.810i) q^{40} -91.6721 q^{41} +142.057i q^{43} +1362.56 q^{44} -139.396 q^{46} -548.650i q^{47} -46.3026 q^{49} +(613.152 - 309.610i) q^{50} -171.712i q^{52} +385.554i q^{53} +(584.541 + 359.672i) q^{55} +1539.17 q^{56} +406.961i q^{58} +228.067 q^{59} -113.246 q^{61} -1061.73i q^{62} -2144.02 q^{64} +(45.3265 - 73.6649i) q^{65} -286.672i q^{67} +949.006i q^{68} +(1032.41 + 635.252i) q^{70} -763.518 q^{71} +528.843i q^{73} -1504.49 q^{74} +434.267 q^{76} +1211.22i q^{77} +222.382 q^{79} +(-2390.98 - 1471.19i) q^{80} +503.747i q^{82} -484.072i q^{83} +(-250.508 + 407.126i) q^{85} +780.619 q^{86} -4788.75i q^{88} +1310.17 q^{89} +152.640 q^{91} +563.055i q^{92} -3014.88 q^{94} +(186.302 + 114.633i) q^{95} +813.532i q^{97} +254.437i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 60 q^{4}+O(q^{10}) \) 16 * q - 60 * q^4	\( 16 q - 60 q^{4} - 220 q^{10} + 788 q^{16} + 356 q^{19} + 550 q^{25} + 1520 q^{31} - 392 q^{34} + 1132 q^{40} + 724 q^{46} + 4 q^{49} + 1716 q^{55} + 1268 q^{61} - 9476 q^{64} - 672 q^{70} + 228 q^{76} - 472 q^{79} - 3562 q^{85} + 1524 q^{91} - 10700 q^{94}+O(q^{100}) \) 16 * q - 60 * q^4 - 220 * q^10 + 788 * q^16 + 356 * q^19 + 550 * q^25 + 1520 * q^31 - 392 * q^34 + 1132 * q^40 + 724 * q^46 + 4 * q^49 + 1716 * q^55 + 1268 * q^61 - 9476 * q^64 - 672 * q^70 + 228 * q^76 - 472 * q^79 - 3562 * q^85 + 1524 * q^91 - 10700 * q^94

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