LMFDB - Embedded newform 270.3.b.d.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(269,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("270.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.31744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 31 $ x^4 + 14*x^2 + 31
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			269.2
Root			$3.35300i$ of defining polynomial
Character	$\chi$	$=$	270.269
Dual form			270.3.b.d.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421 q^{2} +2.00000 q^{4} +(1.58579 + 4.74186i) q^{5} -0.813575i q^{7} -2.82843 q^{8} +(-2.24264 - 6.70601i) q^{10} +15.3762i q^{11} -5.89243i q^{13} +1.15057i q^{14} +4.00000 q^{16} -12.8995 q^{17} +1.24264 q^{19} +(3.17157 + 9.48373i) q^{20} -21.7452i q^{22} -4.79899 q^{23} +(-19.9706 + 15.0392i) q^{25} +8.33316i q^{26} -1.62715i q^{28} +42.6768i q^{29} +4.21320 q^{31} -5.65685 q^{32} +18.2426 q^{34} +(3.85786 - 1.29016i) q^{35} +70.3144i q^{37} -1.75736 q^{38} +(-4.48528 - 13.4120i) q^{40} +7.04300i q^{41} +41.0496i q^{43} +30.7523i q^{44} +6.78680 q^{46} -79.7990 q^{47} +48.3381 q^{49} +(28.2426 - 21.2686i) q^{50} -11.7849i q^{52} +63.7279 q^{53} +(-72.9117 + 24.3833i) q^{55} +2.30114i q^{56} -60.3541i q^{58} -36.6448i q^{59} -82.9411 q^{61} -5.95837 q^{62} +8.00000 q^{64} +(27.9411 - 9.34414i) q^{65} -89.0027i q^{67} -25.7990 q^{68} +(-5.45584 + 1.82456i) q^{70} -69.6982i q^{71} +89.6188i q^{73} -99.4396i q^{74} +2.48528 q^{76} +12.5097 q^{77} +134.095 q^{79} +(6.34315 + 18.9675i) q^{80} -9.96031i q^{82} +109.024 q^{83} +(-20.4558 - 61.1677i) q^{85} -58.0529i q^{86} -43.4904i q^{88} -137.514i q^{89} -4.79394 q^{91} -9.59798 q^{92} +112.853 q^{94} +(1.97056 + 5.89243i) q^{95} +90.6298i q^{97} -68.3604 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 12 q^{5} + 8 q^{10} + 16 q^{16} - 12 q^{17} - 12 q^{19} + 24 q^{20} + 60 q^{23} - 12 q^{25} - 68 q^{31} + 56 q^{34} + 72 q^{35} - 24 q^{38} + 16 q^{40} + 112 q^{46} - 240 q^{47} - 180 q^{49}+ \cdots - 528 q^{98}+O(q^{100}) $ 4 * q + 8 * q^4 + 12 * q^5 + 8 * q^10 + 16 * q^16 - 12 * q^17 - 12 * q^19 + 24 * q^20 + 60 * q^23 - 12 * q^25 - 68 * q^31 + 56 * q^34 + 72 * q^35 - 24 * q^38 + 16 * q^40 + 112 * q^46 - 240 * q^47 - 180 * q^49 + 96 * q^50 + 204 * q^53 - 88 * q^55 - 196 * q^61 - 120 * q^62 + 32 * q^64 - 24 * q^65 - 24 * q^68 + 80 * q^70 - 24 * q^76 - 312 * q^77 + 180 * q^79 + 48 * q^80 + 108 * q^83 + 20 * q^85 + 456 * q^91 + 120 * q^92 + 112 * q^94 - 60 * q^95 - 528 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$		0			0
$3$		0			0
$4$	2.00000			0.500000
$5$	1.58579	+	4.74186i	0.317157	+	0.948373i
$5$	1.58579	+	4.74186i	0.317157	+	0.948373i
$6$		0			0
$7$		−	0.813575i		−	0.116225i	−0.998310	−	0.0581125i	$-0.981492\pi$
$7$		−	0.813575i		−	0.116225i	0.998310	−	0.0581125i	$-0.0185082\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−2.24264	−	6.70601i	−0.224264	−	0.670601i
$11$			15.3762i			1.39783i	0.715203	+	0.698917i	$0.246334\pi$
$11$			15.3762i			1.39783i	−0.715203	+	0.698917i	$0.753666\pi$
$12$		0			0
$13$		−	5.89243i		−	0.453264i	−0.973980	−	0.226632i	$-0.927229\pi$
$13$		−	5.89243i		−	0.453264i	0.973980	−	0.226632i	$-0.0727715\pi$
$14$			1.15057i			0.0821835i
$15$		0			0
$16$	4.00000			0.250000
$17$	−12.8995			−0.758794			−0.379397	−	0.925234i	$-0.623869\pi$
$17$	−12.8995			−0.758794			−0.379397	+	0.925234i	$0.623869\pi$
$18$		0			0
$19$	1.24264			0.0654021			0.0327011	−	0.999465i	$-0.489589\pi$
$19$	1.24264			0.0654021			0.0327011	+	0.999465i	$0.489589\pi$
$20$	3.17157	+	9.48373i	0.158579	+	0.474186i
$21$		0			0
$22$		−	21.7452i		−	0.988417i
$23$	−4.79899			−0.208652			−0.104326	−	0.994543i	$-0.533268\pi$
$23$	−4.79899			−0.208652			−0.104326	+	0.994543i	$0.533268\pi$
$24$		0			0
$25$	−19.9706	+	15.0392i	−0.798823	+	0.601567i
$26$			8.33316i			0.320506i
$27$		0			0
$28$		−	1.62715i		−	0.0581125i
$29$			42.6768i			1.47161i	0.677192	+	0.735807i	$0.263197\pi$
$29$			42.6768i			1.47161i	−0.677192	+	0.735807i	$0.736803\pi$
$30$		0			0
$31$	4.21320			0.135910			0.0679549	−	0.997688i	$-0.478353\pi$
$31$	4.21320			0.135910			0.0679549	+	0.997688i	$0.478353\pi$
$32$	−5.65685			−0.176777
$33$		0			0
$34$	18.2426			0.536548
$35$	3.85786	−	1.29016i	0.110225	−	0.0368616i
$36$		0			0
$37$			70.3144i			1.90039i	0.311657	+	0.950195i	$0.399116\pi$
$37$			70.3144i			1.90039i	−0.311657	+	0.950195i	$0.600884\pi$
$38$	−1.75736			−0.0462463
$39$		0			0
$40$	−4.48528	−	13.4120i	−0.112132	−	0.335300i
$41$			7.04300i			0.171781i	0.996305	+	0.0858903i	$0.0273735\pi$
$41$			7.04300i			0.171781i	−0.996305	+	0.0858903i	$0.972627\pi$
$42$		0			0
$43$			41.0496i			0.954643i	0.878729	+	0.477321i	$0.158392\pi$
$43$			41.0496i			0.954643i	−0.878729	+	0.477321i	$0.841608\pi$
$44$			30.7523i			0.698917i
$45$		0			0
$46$	6.78680			0.147539
$47$	−79.7990			−1.69785			−0.848925	−	0.528513i	$-0.822750\pi$
$47$	−79.7990			−1.69785			−0.848925	+	0.528513i	$0.822750\pi$
$48$		0			0
$49$	48.3381			0.986492
$50$	28.2426	−	21.2686i	0.564853	−	0.425372i
$51$		0			0
$52$		−	11.7849i		−	0.226632i
$53$	63.7279			1.20241			0.601207	−	0.799093i	$-0.294687\pi$
$53$	63.7279			1.20241			0.601207	+	0.799093i	$0.294687\pi$
$54$		0			0
$55$	−72.9117	+	24.3833i	−1.32567	+	0.443333i
$56$			2.30114i			0.0410918i
$57$		0			0
$58$		−	60.3541i		−	1.04059i
$59$		−	36.6448i		−	0.621098i	−0.950557	−	0.310549i	$-0.899487\pi$
$59$		−	36.6448i		−	0.621098i	0.950557	−	0.310549i	$-0.100513\pi$
$60$		0			0
$61$	−82.9411			−1.35969			−0.679845	−	0.733356i	$-0.737953\pi$
$61$	−82.9411			−1.35969			−0.679845	+	0.733356i	$0.737953\pi$
$62$	−5.95837			−0.0961027
$63$		0			0
$64$	8.00000			0.125000
$65$	27.9411	−	9.34414i	0.429863	−	0.143756i
$66$		0			0
$67$		−	89.0027i		−	1.32840i	−0.747556	−	0.664199i	$-0.768773\pi$
$67$		−	89.0027i		−	1.32840i	0.747556	−	0.664199i	$-0.231227\pi$
$68$	−25.7990			−0.379397
$69$		0			0
$70$	−5.45584	+	1.82456i	−0.0779406	+	0.0260651i
$71$		−	69.6982i		−	0.981665i	−0.871254	−	0.490833i	$-0.836693\pi$
$71$		−	69.6982i		−	0.981665i	0.871254	−	0.490833i	$-0.163307\pi$
$72$		0			0
$73$			89.6188i			1.22766i	0.789440	+	0.613828i	$0.210371\pi$
$73$			89.6188i			1.22766i	−0.789440	+	0.613828i	$0.789629\pi$
$74$		−	99.4396i		−	1.34378i
$75$		0			0
$76$	2.48528			0.0327011
$77$	12.5097			0.162463
$78$		0			0
$79$	134.095			1.69741			0.848705	−	0.528866i	$-0.177383\pi$
$79$	134.095			1.69741			0.848705	+	0.528866i	$0.177383\pi$
$80$	6.34315	+	18.9675i	0.0792893	+	0.237093i
$81$		0			0
$82$		−	9.96031i		−	0.121467i
$83$	109.024			1.31355			0.656773	−	0.754088i	$-0.271921\pi$
$83$	109.024			1.31355			0.656773	+	0.754088i	$0.271921\pi$
$84$		0			0
$85$	−20.4558	−	61.1677i	−0.240657	−	0.719620i
$86$		−	58.0529i		−	0.675034i
$87$		0			0
$88$		−	43.4904i		−	0.494209i
$89$		−	137.514i		−	1.54510i	−0.634953	−	0.772551i	$-0.718980\pi$
$89$		−	137.514i		−	1.54510i	0.634953	−	0.772551i	$-0.281020\pi$
$90$		0			0
$91$	−4.79394			−0.0526807
$92$	−9.59798			−0.104326
$93$		0			0
$94$	112.853			1.20056
$95$	1.97056	+	5.89243i	0.0207428	+	0.0620256i
$96$		0			0
$97$			90.6298i			0.934328i	0.884171	+	0.467164i	$0.154724\pi$
$97$			90.6298i			0.934328i	−0.884171	+	0.467164i	$0.845276\pi$
$98$	−68.3604			−0.697555
$99$		0			0
$100$	−39.9411	+	30.0783i	−0.399411	+	0.300783i
$101$		−	49.7198i		−	0.492275i	−0.969235	−	0.246138i	$-0.920839\pi$
$101$		−	49.7198i		−	0.492275i	0.969235	−	0.246138i	$-0.0791615\pi$
$102$		0			0
$103$		−	128.844i		−	1.25091i	−0.780259	−	0.625456i	$-0.784913\pi$
$103$		−	128.844i		−	1.25091i	0.780259	−	0.625456i	$-0.215087\pi$
$104$			16.6663i			0.160253i
$105$		0			0
$106$	−90.1249			−0.850235
$107$	6.42641			0.0600599			0.0300299	−	0.999549i	$-0.490440\pi$
$107$	6.42641			0.0600599			0.0300299	+	0.999549i	$0.490440\pi$
$108$		0			0
$109$	108.279			0.993387			0.496694	−	0.867926i	$-0.334547\pi$
$109$	108.279			0.993387			0.496694	+	0.867926i	$0.334547\pi$
$110$	103.113	−	34.4832i	0.937388	−	0.313484i
$111$		0			0
$112$		−	3.25430i		−	0.0290563i
$113$	−30.4264			−0.269260			−0.134630	−	0.990896i	$-0.542985\pi$
$113$	−30.4264			−0.269260			−0.134630	+	0.990896i	$0.542985\pi$
$114$		0			0
$115$	−7.61017	−	22.7562i	−0.0661754	−	0.197880i
$116$			85.3536i			0.735807i
$117$		0			0
$118$			51.8235i			0.439182i
$119$			10.4947i			0.0881909i
$120$		0			0
$121$	−115.426			−0.953937
$122$	117.296			0.961446
$123$		0			0
$124$	8.42641			0.0679549
$125$	−102.983	−	70.8488i	−0.823862	−	0.566790i
$126$		0			0
$127$		−	133.725i		−	1.05296i	−0.850189	−	0.526478i	$-0.823512\pi$
$127$		−	133.725i		−	1.05296i	0.850189	−	0.526478i	$-0.176488\pi$
$128$	−11.3137			−0.0883883
$129$		0			0
$130$	−39.5147	+	13.2146i	−0.303959	+	0.101651i
$131$			61.7838i			0.471632i	0.971798	+	0.235816i	$0.0757763\pi$
$131$			61.7838i			0.471632i	−0.971798	+	0.235816i	$0.924224\pi$
$132$		0			0
$133$		−	1.01098i		−	0.00760137i
$134$			125.869i			0.939319i
$135$		0			0
$136$	36.4853			0.268274
$137$	−163.919			−1.19649			−0.598244	−	0.801314i	$-0.704135\pi$
$137$	−163.919			−1.19649			−0.598244	+	0.801314i	$0.704135\pi$
$138$		0			0
$139$	182.250			1.31115			0.655575	−	0.755130i	$-0.272426\pi$
$139$	182.250			1.31115			0.655575	+	0.755130i	$0.272426\pi$
$140$	7.71573	−	2.58031i	0.0551123	−	0.0184308i
$141$		0			0
$142$			98.5682i			0.694142i
$143$	90.6030			0.633588
$144$		0			0
$145$	−202.368	+	67.6763i	−1.39564	+	0.466733i
$146$		−	126.740i		−	0.868084i
$147$		0			0
$148$			140.629i			0.950195i
$149$			189.535i			1.27205i	0.771670	+	0.636023i	$0.219422\pi$
$149$			189.535i			1.27205i	−0.771670	+	0.636023i	$0.780578\pi$
$150$		0			0
$151$	−113.338			−0.750583			−0.375292	−	0.926907i	$-0.622457\pi$
$151$	−113.338			−0.750583			−0.375292	+	0.926907i	$0.622457\pi$
$152$	−3.51472			−0.0231231
$153$		0			0
$154$	−17.6913			−0.114879
$155$	6.68124	+	19.9784i	0.0431048	+	0.128893i
$156$		0			0
$157$			113.189i			0.720946i	0.932770	+	0.360473i	$0.117385\pi$
$157$			113.189i			0.720946i	−0.932770	+	0.360473i	$0.882615\pi$
$158$	−189.640			−1.20025
$159$		0			0
$160$	−8.97056	−	26.8240i	−0.0560660	−	0.167650i
$161$			3.90434i			0.0242506i
$162$		0			0
$163$		−	152.414i		−	0.935053i	−0.883979	−	0.467527i	$-0.845145\pi$
$163$		−	152.414i		−	0.935053i	0.883979	−	0.467527i	$-0.154855\pi$
$164$			14.0860i			0.0858903i
$165$		0			0
$166$	−154.184			−0.928818
$167$	105.853			0.633849			0.316925	−	0.948451i	$-0.397350\pi$
$167$	105.853			0.633849			0.316925	+	0.948451i	$0.397350\pi$
$168$		0			0
$169$	134.279			0.794552
$170$	28.9289	+	86.5041i	0.170170	+	0.508848i
$171$		0			0
$172$			82.0993i			0.477321i
$173$	110.012			0.635909			0.317954	−	0.948106i	$-0.397004\pi$
$173$	110.012			0.635909			0.317954	+	0.948106i	$0.397004\pi$
$174$		0			0
$175$	12.2355	+	16.2476i	0.0699171	+	0.0928432i
$176$			61.5047i			0.349458i
$177$		0			0
$178$			194.474i			1.09255i
$179$			118.407i			0.661492i	0.943720	+	0.330746i	$0.107300\pi$
$179$			118.407i			0.661492i	−0.943720	+	0.330746i	$0.892700\pi$
$180$		0			0
$181$	172.397			0.952469			0.476235	−	0.879318i	$-0.342001\pi$
$181$	172.397			0.952469			0.476235	+	0.879318i	$0.342001\pi$
$182$	6.77965			0.0372508
$183$		0			0
$184$	13.5736			0.0737695
$185$	−333.421	+	111.504i	−1.80228	+	0.602722i
$186$		0			0
$187$		−	198.345i		−	1.06067i
$188$	−159.598			−0.848925
$189$		0			0
$190$	−2.78680	−	8.33316i	−0.0146674	−	0.0438587i
$191$			289.393i			1.51515i	0.652749	+	0.757574i	$0.273616\pi$
$191$			289.393i			1.51515i	−0.652749	+	0.757574i	$0.726384\pi$
$192$		0			0
$193$			127.833i			0.662347i	0.943570	+	0.331173i	$0.107445\pi$
$193$			127.833i			0.662347i	−0.943570	+	0.331173i	$0.892555\pi$
$194$		−	128.170i		−	0.660670i
$195$		0			0
$196$	96.6762			0.493246
$197$	280.414			1.42342			0.711711	−	0.702472i	$-0.247920\pi$
$197$	280.414			1.42342			0.711711	+	0.702472i	$0.247920\pi$
$198$		0			0
$199$	156.426			0.786062			0.393031	−	0.919525i	$-0.371426\pi$
$199$	156.426			0.786062			0.393031	+	0.919525i	$0.371426\pi$
$200$	56.4853	−	42.5372i	0.282426	−	0.212686i
$201$		0			0
$202$			70.3144i			0.348091i
$203$	34.7208			0.171038
$204$		0			0
$205$	−33.3970	+	11.1687i	−0.162912	+	0.0544815i
$206$			182.213i			0.884528i
$207$		0			0
$208$		−	23.5697i		−	0.113316i
$209$			19.1070i			0.0914213i
$210$		0			0
$211$	22.5076			0.106671			0.0533355	−	0.998577i	$-0.483015\pi$
$211$	22.5076			0.106671			0.0533355	+	0.998577i	$0.483015\pi$
$212$	127.456			0.601207
$213$		0			0
$214$	−9.08831			−0.0424687
$215$	−194.652	+	65.0959i	−0.905357	+	0.302772i
$216$		0			0
$217$		−	3.42776i		−	0.0157961i
$218$	−153.130			−0.702431
$219$		0			0
$220$	−145.823	+	48.7666i	−0.662834	+	0.221666i
$221$			76.0094i			0.343934i
$222$		0			0
$223$		−	354.826i		−	1.59115i	−0.605856	−	0.795575i	$-0.707169\pi$
$223$		−	354.826i		−	1.59115i	0.605856	−	0.795575i	$-0.292831\pi$
$224$			4.60228i			0.0205459i
$225$		0			0
$226$	43.0294			0.190396
$227$	−415.098			−1.82862			−0.914312	−	0.405011i	$-0.867268\pi$
$227$	−415.098			−1.82862			−0.914312	+	0.405011i	$0.867268\pi$
$228$		0			0
$229$	−220.220			−0.961661			−0.480830	−	0.876814i	$-0.659665\pi$
$229$	−220.220			−0.961661			−0.480830	+	0.876814i	$0.659665\pi$
$230$	10.7624	+	32.1821i	0.0467931	+	0.139922i
$231$		0			0
$232$		−	120.708i		−	0.520294i
$233$	10.0345			0.0430665			0.0215332	−	0.999768i	$-0.493145\pi$
$233$	10.0345			0.0430665			0.0215332	+	0.999768i	$0.493145\pi$
$234$		0			0
$235$	−126.544	−	378.396i	−0.538486	−	1.61020i
$236$		−	73.2895i		−	0.310549i
$237$		0			0
$238$		−	14.8418i		−	0.0623603i
$239$		−	114.363i		−	0.478507i	−0.970957	−	0.239253i	$-0.923097\pi$
$239$		−	114.363i		−	0.478507i	0.970957	−	0.239253i	$-0.0769027\pi$
$240$		0			0
$241$	−63.7208			−0.264402			−0.132201	−	0.991223i	$-0.542204\pi$
$241$	−63.7208			−0.264402			−0.132201	+	0.991223i	$0.542204\pi$
$242$	163.238			0.674535
$243$		0			0
$244$	−165.882			−0.679845
$245$	76.6539	+	229.213i	0.312873	+	0.935562i
$246$		0			0
$247$		−	7.32218i		−	0.0296444i
$248$	−11.9167			−0.0480514
$249$		0			0
$250$	145.640	+	100.195i	0.582558	+	0.400781i
$251$		−	229.631i		−	0.914866i	−0.889244	−	0.457433i	$-0.848769\pi$
$251$		−	229.631i		−	0.914866i	0.889244	−	0.457433i	$-0.151231\pi$
$252$		0			0
$253$		−	73.7901i		−	0.291660i
$254$			189.116i			0.744552i
$255$		0			0
$256$	16.0000			0.0625000
$257$	388.227			1.51061			0.755306	−	0.655372i	$-0.227488\pi$
$257$	388.227			1.51061			0.755306	+	0.655372i	$0.227488\pi$
$258$		0			0
$259$	57.2061			0.220873
$260$	55.8823	−	18.6883i	0.214932	−	0.0718780i
$261$		0			0
$262$		−	87.3755i		−	0.333494i
$263$	226.877			0.862651			0.431325	−	0.902196i	$-0.358046\pi$
$263$	226.877			0.862651			0.431325	+	0.902196i	$0.358046\pi$
$264$		0			0
$265$	101.059	+	302.189i	0.381354	+	1.14034i
$266$			1.42974i			0.00537498i
$267$		0			0
$268$		−	178.005i		−	0.664199i
$269$		−	226.772i		−	0.843019i	−0.906824	−	0.421509i	$-0.861500\pi$
$269$		−	226.772i		−	0.843019i	0.906824	−	0.421509i	$-0.138500\pi$
$270$		0			0
$271$	322.889			1.19147			0.595737	−	0.803180i	$-0.296860\pi$
$271$	322.889			1.19147			0.595737	+	0.803180i	$0.296860\pi$
$272$	−51.5980			−0.189698
$273$		0			0
$274$	231.816			0.846045
$275$	−231.245	−	307.071i	−0.840890	−	1.11662i
$276$		0			0
$277$		−	200.564i		−	0.724058i	−0.932167	−	0.362029i	$-0.882084\pi$
$277$		−	200.564i		−	0.724058i	0.932167	−	0.362029i	$-0.117916\pi$
$278$	−257.740			−0.927123
$279$		0			0
$280$	−10.9117	+	3.64911i	−0.0389703	+	0.0130326i
$281$		−	128.030i		−	0.455624i	−0.973705	−	0.227812i	$-0.926843\pi$
$281$		−	128.030i		−	0.455624i	0.973705	−	0.227812i	$-0.0731572\pi$
$282$		0			0
$283$			420.235i			1.48493i	0.669885	+	0.742465i	$0.266344\pi$
$283$			420.235i			1.48493i	−0.669885	+	0.742465i	$0.733656\pi$
$284$		−	139.396i		−	0.490833i
$285$		0			0
$286$	−128.132			−0.448014
$287$	5.73001			0.0199652
$288$		0			0
$289$	−122.603			−0.424232
$290$	286.191	−	95.7087i	0.986865	−	0.330030i
$291$		0			0
$292$			179.238i			0.613828i
$293$	137.434			0.469056			0.234528	−	0.972109i	$-0.424645\pi$
$293$	137.434			0.469056			0.234528	+	0.972109i	$0.424645\pi$
$294$		0			0
$295$	173.765	−	58.1108i	0.589032	−	0.196986i
$296$		−	198.879i		−	0.671889i
$297$		0			0
$298$		−	268.043i		−	0.899473i
$299$			28.2777i			0.0945744i
$300$		0			0
$301$	33.3970			0.110953
$302$	160.284			0.530743
$303$		0			0
$304$	4.97056			0.0163505
$305$	−131.527	−	393.296i	−0.431236	−	1.28949i
$306$		0			0
$307$			117.849i			0.383872i	0.981407	+	0.191936i	$0.0614766\pi$
$307$			117.849i			0.383872i	−0.981407	+	0.191936i	$0.938523\pi$
$308$	25.0193			0.0812316
$309$		0			0
$310$	−9.44870	−	28.2538i	−0.0304797	−	0.0911412i
$311$		−	499.326i		−	1.60555i	−0.596283	−	0.802774i	$-0.703356\pi$
$311$		−	499.326i		−	1.60555i	0.596283	−	0.802774i	$-0.296644\pi$
$312$		0			0
$313$			491.806i			1.57127i	0.618693	+	0.785633i	$0.287662\pi$
$313$			491.806i			1.57127i	−0.618693	+	0.785633i	$0.712338\pi$
$314$		−	160.073i		−	0.509786i
$315$		0			0
$316$	268.191			0.848705
$317$	−241.399			−0.761511			−0.380756	−	0.924676i	$-0.624336\pi$
$317$	−241.399			−0.761511			−0.380756	+	0.924676i	$0.624336\pi$
$318$		0			0
$319$	−656.205			−2.05707
$320$	12.6863	+	37.9349i	0.0396447	+	0.118547i
$321$		0			0
$322$		−	5.52157i		−	0.0171477i
$323$	−16.0294			−0.0496267
$324$		0			0
$325$	88.6173	+	117.675i	0.272669	+	0.362078i
$326$			215.545i			0.661182i
$327$		0			0
$328$		−	19.9206i		−	0.0607336i
$329$			64.9225i			0.197333i
$330$		0			0
$331$	−87.8091			−0.265284			−0.132642	−	0.991164i	$-0.542346\pi$
$331$	−87.8091			−0.265284			−0.132642	+	0.991164i	$0.542346\pi$
$332$	218.049			0.656773
$333$		0			0
$334$	−149.698			−0.448199
$335$	422.039	−	141.139i	1.25982	−	0.421311i
$336$		0			0
$337$			452.138i			1.34166i	0.741613	+	0.670828i	$0.234061\pi$
$337$			452.138i			1.34166i	−0.741613	+	0.670828i	$0.765939\pi$
$338$	−189.899			−0.561833
$339$		0			0
$340$	−40.9117	−	122.335i	−0.120328	−	0.359810i
$341$			64.7829i			0.189979i
$342$		0			0
$343$		−	79.1919i		−	0.230880i
$344$		−	116.106i		−	0.337517i
$345$		0			0
$346$	−155.581			−0.449655
$347$	189.411			0.545854			0.272927	−	0.962035i	$-0.412008\pi$
$347$	189.411			0.545854			0.272927	+	0.962035i	$0.412008\pi$
$348$		0			0
$349$	−155.794			−0.446401			−0.223200	−	0.974773i	$-0.571650\pi$
$349$	−155.794			−0.446401			−0.223200	+	0.974773i	$0.571650\pi$
$350$	−17.3036	−	22.9775i	−0.0494389	−	0.0656500i
$351$		0			0
$352$		−	86.9807i		−	0.247104i
$353$	263.387			0.746138			0.373069	−	0.927804i	$-0.378305\pi$
$353$	263.387			0.746138			0.373069	+	0.927804i	$0.378305\pi$
$354$		0			0
$355$	330.500	−	110.527i	0.930985	−	0.311342i
$356$		−	275.028i		−	0.772551i
$357$		0			0
$358$		−	167.453i		−	0.467745i
$359$			79.6346i			0.221823i	0.993830	+	0.110912i	$0.0353771\pi$
$359$			79.6346i			0.221823i	−0.993830	+	0.110912i	$0.964623\pi$
$360$		0			0
$361$	−359.456			−0.995723
$362$	−243.806			−0.673498
$363$		0			0
$364$	−9.58788			−0.0263403
$365$	−424.960	+	142.116i	−1.16428	+	0.389360i
$366$		0			0
$367$			475.953i			1.29688i	0.761268	+	0.648438i	$0.224577\pi$
$367$			475.953i			1.29688i	−0.761268	+	0.648438i	$0.775423\pi$
$368$	−19.1960			−0.0521629
$369$		0			0
$370$	471.529	−	157.690i	1.27440	−	0.426189i
$371$		−	51.8475i		−	0.139751i
$372$		0			0
$373$			61.7838i			0.165640i	0.996565	+	0.0828201i	$0.0263927\pi$
$373$			61.7838i			0.165640i	−0.996565	+	0.0828201i	$0.973607\pi$
$374$			280.502i			0.750005i
$375$		0			0
$376$	225.706			0.600281
$377$	251.470			0.667030
$378$		0			0
$379$	−142.345			−0.375581			−0.187791	−	0.982209i	$-0.560133\pi$
$379$	−142.345			−0.375581			−0.187791	+	0.982209i	$0.560133\pi$
$380$	3.94113	+	11.7849i	0.0103714	+	0.0310128i
$381$		0			0
$382$		−	409.264i		−	1.07137i
$383$	357.520			0.933472			0.466736	−	0.884397i	$-0.345430\pi$
$383$	357.520			0.933472			0.466736	+	0.884397i	$0.345430\pi$
$384$		0			0
$385$	19.8377	+	59.3192i	0.0515264	+	0.154076i
$386$		−	180.783i		−	0.468350i
$387$		0			0
$388$			181.260i			0.467164i
$389$		−	411.079i		−	1.05676i	−0.849009	−	0.528379i	$-0.822800\pi$
$389$		−	411.079i		−	1.05676i	0.849009	−	0.528379i	$-0.177200\pi$
$390$		0			0
$391$	61.9045			0.158324
$392$	−136.721			−0.348777
$393$		0			0
$394$	−396.566			−1.00651
$395$	212.647	+	635.863i	0.538346	+	1.60978i
$396$		0			0
$397$		−	457.462i		−	1.15230i	−0.817345	−	0.576149i	$-0.804555\pi$
$397$		−	457.462i		−	1.15230i	0.817345	−	0.576149i	$-0.195445\pi$
$398$	−221.220			−0.555830
$399$		0			0
$400$	−79.8823	+	60.1567i	−0.199706	+	0.150392i
$401$			467.283i			1.16529i	0.812725	+	0.582647i	$0.197983\pi$
$401$			467.283i			1.16529i	−0.812725	+	0.582647i	$0.802017\pi$
$402$		0			0
$403$		−	24.8260i		−	0.0616030i
$404$		−	99.4396i		−	0.246138i
$405$		0			0
$406$	−49.1026			−0.120942
$407$	−1081.17			−2.65643
$408$		0			0
$409$	−448.574			−1.09676			−0.548378	−	0.836230i	$-0.684755\pi$
$409$	−448.574			−1.09676			−0.548378	+	0.836230i	$0.684755\pi$
$410$	47.2304	−	15.7949i	0.115196	−	0.0385242i
$411$		0			0
$412$		−	257.688i		−	0.625456i
$413$	−29.8133			−0.0721871
$414$		0			0
$415$	172.889	+	516.979i	0.416601	+	1.24573i
$416$			33.3326i			0.0801265i
$417$		0			0
$418$		−	27.0214i		−	0.0646446i
$419$		−	360.834i		−	0.861180i	−0.902548	−	0.430590i	$-0.858306\pi$
$419$		−	360.834i		−	0.861180i	0.902548	−	0.430590i	$-0.141694\pi$
$420$		0			0
$421$	357.059			0.848121			0.424060	−	0.905634i	$-0.360604\pi$
$421$	357.059			0.848121			0.424060	+	0.905634i	$0.360604\pi$
$422$	−31.8305			−0.0754278
$423$		0			0
$424$	−180.250			−0.425117
$425$	257.610	−	193.998i	0.606142	−	0.456465i
$426$		0			0
$427$			67.4789i			0.158030i
$428$	12.8528			0.0300299
$429$		0			0
$430$	275.279	−	92.0596i	0.640184	−	0.214092i
$431$			655.947i			1.52192i	0.648800	+	0.760959i	$0.275271\pi$
$431$			655.947i			1.52192i	−0.648800	+	0.760959i	$0.724729\pi$
$432$		0			0
$433$			164.372i			0.379612i	0.981822	+	0.189806i	$0.0607859\pi$
$433$			164.372i			0.379612i	−0.981822	+	0.189806i	$0.939214\pi$
$434$			4.84758i			0.0111695i
$435$		0			0
$436$	216.558			0.496694
$437$	−5.96342			−0.0136463
$438$		0			0
$439$	−132.286			−0.301336			−0.150668	−	0.988584i	$-0.548142\pi$
$439$	−132.286			−0.301336			−0.150668	+	0.988584i	$0.548142\pi$
$440$	206.225	−	68.9664i	0.468694	−	0.156742i
$441$		0			0
$442$		−	107.494i		−	0.243198i
$443$	455.485			1.02818			0.514092	−	0.857735i	$-0.328129\pi$
$443$	455.485			1.02818			0.514092	+	0.857735i	$0.328129\pi$
$444$		0			0
$445$	652.073	−	218.068i	1.46533	−	0.490040i
$446$			501.800i			1.12511i
$447$		0			0
$448$		−	6.50860i		−	0.0145281i
$449$			415.749i			0.925944i	0.886373	+	0.462972i	$0.153217\pi$
$449$			415.749i			0.925944i	−0.886373	+	0.462972i	$0.846783\pi$
$450$		0			0
$451$	−108.294			−0.240121
$452$	−60.8528			−0.134630
$453$		0			0
$454$	587.037			1.29303
$455$	−7.60216	−	22.7322i	−0.0167081	−	0.0499609i
$456$		0			0
$457$			303.643i			0.664426i	0.943204	+	0.332213i	$0.107795\pi$
$457$			303.643i			0.664426i	−0.943204	+	0.332213i	$0.892205\pi$
$458$	311.439			0.679997
$459$		0			0
$460$	−15.2203	−	45.5123i	−0.0330877	−	0.0989398i
$461$		−	428.790i		−	0.930130i	−0.885277	−	0.465065i	$-0.846031\pi$
$461$		−	428.790i		−	0.930130i	0.885277	−	0.465065i	$-0.153969\pi$
$462$		0			0
$463$		−	814.484i		−	1.75914i	−0.475765	−	0.879572i	$-0.657829\pi$
$463$		−	814.484i		−	1.75914i	0.475765	−	0.879572i	$-0.342171\pi$
$464$			170.707i			0.367903i
$465$		0			0
$466$	−14.1909			−0.0304526
$467$	−607.118			−1.30004			−0.650019	−	0.759918i	$-0.725239\pi$
$467$	−607.118			−1.30004			−0.650019	+	0.759918i	$0.725239\pi$
$468$		0			0
$469$	−72.4104			−0.154393
$470$	178.960	+	535.133i	0.380767	+	1.13858i
$471$		0			0
$472$			103.647i			0.219591i
$473$	−631.186			−1.33443
$474$		0			0
$475$	−24.8162	+	18.6883i	−0.0522447	+	0.0393438i
$476$			20.9894i			0.0440954i
$477$		0			0
$478$			161.734i			0.338355i
$479$			343.889i			0.717931i	0.933351	+	0.358965i	$0.116870\pi$
$479$			343.889i			0.717931i	−0.933351	+	0.358965i	$0.883130\pi$
$480$		0			0
$481$	414.323			0.861378
$482$	90.1148			0.186960
$483$		0			0
$484$	−230.853			−0.476969
$485$	−429.754	+	143.720i	−0.886092	+	0.296329i
$486$		0			0
$487$			300.759i			0.617576i	0.951131	+	0.308788i	$0.0999233\pi$
$487$			300.759i			0.617576i	−0.951131	+	0.308788i	$0.900077\pi$
$488$	234.593			0.480723
$489$		0			0
$490$	−108.405	−	324.156i	−0.221235	−	0.661542i
$491$			173.914i			0.354203i	0.984193	+	0.177101i	$0.0566720\pi$
$491$			173.914i			0.354203i	−0.984193	+	0.177101i	$0.943328\pi$
$492$		0			0
$493$		−	550.509i		−	1.11665i
$494$			10.3551i			0.0209618i
$495$		0			0
$496$	16.8528			0.0339774
$497$	−56.7048			−0.114094
$498$		0			0
$499$	−761.610			−1.52627			−0.763136	−	0.646237i	$-0.776342\pi$
$499$	−761.610			−1.52627			−0.763136	+	0.646237i	$0.776342\pi$
$500$	−205.966	−	141.698i	−0.411931	−	0.283395i
$501$		0			0
$502$			324.748i			0.646908i
$503$	−280.632			−0.557917			−0.278959	−	0.960303i	$-0.589989\pi$
$503$	−280.632			−0.557917			−0.278959	+	0.960303i	$0.589989\pi$
$504$		0			0
$505$	235.765	−	78.8450i	0.466860	−	0.156129i
$506$			104.355i			0.206235i
$507$		0			0
$508$		−	267.451i		−	0.526478i
$509$			633.176i			1.24396i	0.783032	+	0.621981i	$0.213672\pi$
$509$			633.176i			1.24396i	−0.783032	+	0.621981i	$0.786328\pi$
$510$		0			0
$511$	72.9117			0.142684
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−549.037			−1.06816
$515$	610.960	−	204.319i	1.18633	−	0.396736i
$516$		0			0
$517$		−	1227.00i		−	2.37331i
$518$	−80.9016			−0.156181
$519$		0			0
$520$	−79.0294	+	26.4292i	−0.151980	+	0.0508254i
$521$		−	92.3966i		−	0.177345i	−0.996061	−	0.0886723i	$-0.971738\pi$
$521$		−	92.3966i		−	0.177345i	0.996061	−	0.0886723i	$-0.0282624\pi$
$522$		0			0
$523$			818.552i			1.56511i	0.622582	+	0.782554i	$0.286084\pi$
$523$			818.552i			1.56511i	−0.622582	+	0.782554i	$0.713916\pi$
$524$			123.568i			0.235816i
$525$		0			0
$526$	−320.853			−0.609986
$527$	−54.3482			−0.103128
$528$		0			0
$529$	−505.970			−0.956464
$530$	−142.919	−	427.360i	−0.269658	−	0.806340i
$531$		0			0
$532$		−	2.02196i		−	0.00380068i
$533$	41.5004			0.0778620
$534$		0			0
$535$	10.1909	+	30.4732i	0.0190484	+	0.0569592i
$536$			251.738i			0.469660i
$537$		0			0
$538$			320.704i			0.596104i
$539$			743.254i			1.37895i
$540$		0			0
$541$	−376.985			−0.696830			−0.348415	−	0.937340i	$-0.613280\pi$
$541$	−376.985			−0.696830			−0.348415	+	0.937340i	$0.613280\pi$
$542$	−456.635			−0.842499
$543$		0			0
$544$	72.9706			0.134137
$545$	171.708	+	513.445i	0.315060	+	0.942102i
$546$		0			0
$547$		−	337.346i		−	0.616721i	−0.951270	−	0.308360i	$-0.900220\pi$
$547$		−	337.346i		−	0.616721i	0.951270	−	0.308360i	$-0.0997803\pi$
$548$	−327.838			−0.598244
$549$		0			0
$550$	327.029	+	434.263i	0.594599	+	0.789570i
$551$			53.0319i			0.0962467i
$552$		0			0
$553$		−	109.097i		−	0.197282i
$554$			283.640i			0.511986i
$555$		0			0
$556$	364.500			0.655575
$557$	303.338			0.544593			0.272296	−	0.962213i	$-0.412217\pi$
$557$	303.338			0.544593			0.272296	+	0.962213i	$0.412217\pi$
$558$		0			0
$559$	241.882			0.432705
$560$	15.4315	−	5.16063i	0.0275562	−	0.00921541i
$561$		0			0
$562$			181.062i			0.322175i
$563$	234.093			0.415796			0.207898	−	0.978150i	$-0.433338\pi$
$563$	234.093			0.415796			0.207898	+	0.978150i	$0.433338\pi$
$564$		0			0
$565$	−48.2498	−	144.278i	−0.0853978	−	0.255359i
$566$		−	594.302i		−	1.05000i
$567$		0			0
$568$			197.136i			0.347071i
$569$			66.5257i			0.116917i	0.998290	+	0.0584584i	$0.0186185\pi$
$569$			66.5257i			0.116917i	−0.998290	+	0.0584584i	$0.981381\pi$
$570$		0			0
$571$	1115.54			1.95365			0.976826	−	0.214035i	$-0.0686607\pi$
$571$	1115.54			1.95365			0.976826	+	0.214035i	$0.0686607\pi$
$572$	181.206			0.316794
$573$		0			0
$574$	−8.10346			−0.0141175
$575$	95.8385	−	72.1728i	0.166676	−	0.125518i
$576$		0			0
$577$			957.356i			1.65920i	0.558361	+	0.829598i	$0.311430\pi$
$577$			957.356i			1.65920i	−0.558361	+	0.829598i	$0.688570\pi$
$578$	173.387			0.299977
$579$		0			0
$580$	−404.735	+	135.353i	−0.697819	+	0.233366i
$581$		−	88.6996i		−	0.152667i
$582$		0			0
$583$			979.891i			1.68077i
$584$		−	253.480i		−	0.434042i
$585$		0			0
$586$	−194.360			−0.331673
$587$	−79.8974			−0.136111			−0.0680557	−	0.997682i	$-0.521680\pi$
$587$	−79.8974			−0.136111			−0.0680557	+	0.997682i	$0.521680\pi$
$588$		0			0
$589$	5.23550			0.00888879
$590$	−245.740	+	82.1810i	−0.416509	+	0.139290i
$591$		0			0
$592$			281.258i			0.475097i
$593$	−213.831			−0.360593			−0.180296	−	0.983612i	$-0.557706\pi$
$593$	−213.831			−0.360593			−0.180296	+	0.983612i	$0.557706\pi$
$594$		0			0
$595$	−49.7645	+	16.6424i	−0.0836378	+	0.0279704i
$596$			379.070i			0.636023i
$597$		0			0
$598$		−	39.9908i		−	0.0668742i
$599$		−	915.493i		−	1.52837i	−0.644998	−	0.764184i	$-0.723142\pi$
$599$		−	915.493i		−	1.52837i	0.644998	−	0.764184i	$-0.276858\pi$
$600$		0			0
$601$	479.426			0.797714			0.398857	−	0.917013i	$-0.369407\pi$
$601$	479.426			0.797714			0.398857	+	0.917013i	$0.369407\pi$
$602$	−47.2304			−0.0784559
$603$		0			0
$604$	−226.676			−0.375292
$605$	−183.042	−	547.336i	−0.302548	−	0.904688i
$606$		0			0
$607$		−	219.893i		−	0.362261i	−0.983459	−	0.181131i	$-0.942024\pi$
$607$		−	219.893i		−	0.362261i	0.983459	−	0.181131i	$-0.0579757\pi$
$608$	−7.02944			−0.0115616
$609$		0			0
$610$	186.007	+	556.204i	0.304930	+	0.911810i
$611$			470.210i			0.769575i
$612$		0			0
$613$		−	862.066i		−	1.40631i	−0.711038	−	0.703154i	$-0.751775\pi$
$613$		−	862.066i		−	1.40631i	0.711038	−	0.703154i	$-0.248225\pi$
$614$		−	166.663i		−	0.271438i
$615$		0			0
$616$	−35.3827			−0.0574394
$617$	695.423			1.12710			0.563552	−	0.826080i	$-0.309434\pi$
$617$	695.423			1.12710			0.563552	+	0.826080i	$0.309434\pi$
$618$		0			0
$619$	−512.073			−0.827259			−0.413629	−	0.910445i	$-0.635739\pi$
$619$	−512.073			−0.827259			−0.413629	+	0.910445i	$0.635739\pi$
$620$	13.3625	+	39.9569i	0.0215524	+	0.0644466i
$621$		0			0
$622$			706.153i			1.13529i
$623$	−111.878			−0.179580
$624$		0			0
$625$	172.647	−	600.681i	0.276235	−	0.961090i
$626$		−	695.519i		−	1.11105i
$627$		0			0
$628$			226.377i			0.360473i
$629$		−	907.020i		−	1.44200i
$630$		0			0
$631$	−643.375			−1.01961			−0.509806	−	0.860290i	$-0.670283\pi$
$631$	−643.375			−1.01961			−0.509806	+	0.860290i	$0.670283\pi$
$632$	−379.279			−0.600125
$633$		0			0
$634$	341.390			0.538470
$635$	634.108	−	212.060i	0.998595	−	0.333953i
$636$		0			0
$637$		−	284.829i		−	0.447141i
$638$	928.014			1.45457
$639$		0			0
$640$	−17.9411	−	53.6481i	−0.0280330	−	0.0838251i
$641$		−	196.925i		−	0.307215i	−0.988132	−	0.153608i	$-0.950911\pi$
$641$		−	196.925i		−	0.307215i	0.988132	−	0.153608i	$-0.0490892\pi$
$642$		0			0
$643$			236.954i			0.368513i	0.982878	+	0.184256i	$0.0589877\pi$
$643$			236.954i			0.368513i	−0.982878	+	0.184256i	$0.941012\pi$
$644$			7.80868i			0.0121253i
$645$		0			0
$646$	22.6690			0.0350914
$647$	17.3818			0.0268653			0.0134326	−	0.999910i	$-0.495724\pi$
$647$	17.3818			0.0268653			0.0134326	+	0.999910i	$0.495724\pi$
$648$		0			0
$649$	563.456			0.868191
$650$	−125.324	−	166.418i	−0.192806	−	0.256028i
$651$		0			0
$652$		−	304.827i		−	0.467527i
$653$	−785.704			−1.20322			−0.601611	−	0.798789i	$-0.705474\pi$
$653$	−785.704			−1.20322			−0.601611	+	0.798789i	$0.705474\pi$
$654$		0			0
$655$	−292.971	+	97.9760i	−0.447283	+	0.149582i
$656$			28.1720i			0.0429451i
$657$		0			0
$658$		−	91.8143i		−	0.139535i
$659$		−	498.767i		−	0.756855i	−0.925631	−	0.378427i	$-0.876465\pi$
$659$		−	498.767i		−	0.756855i	0.925631	−	0.378427i	$-0.123535\pi$
$660$		0			0
$661$	303.133			0.458597			0.229299	−	0.973356i	$-0.426357\pi$
$661$	303.133			0.458597			0.229299	+	0.973356i	$0.426357\pi$
$662$	124.181			0.187584
$663$		0			0
$664$	−308.368			−0.464409
$665$	4.79394	−	1.60320i	0.00720893	−	0.00241083i
$666$		0			0
$667$		−	204.805i		−	0.307055i
$668$	211.706			0.316925
$669$		0			0
$670$	−596.853	+	199.601i	−0.890825	+	0.297912i
$671$		−	1275.32i		−	1.90062i
$672$		0			0
$673$		−	463.133i		−	0.688163i	−0.938940	−	0.344081i	$-0.888190\pi$
$673$		−	463.133i		−	0.688163i	0.938940	−	0.344081i	$-0.111810\pi$
$674$		−	639.420i		−	0.948694i
$675$		0			0
$676$	268.558			0.397276
$677$	311.064			0.459474			0.229737	−	0.973253i	$-0.426213\pi$
$677$	311.064			0.459474			0.229737	+	0.973253i	$0.426213\pi$
$678$		0			0
$679$	73.7342			0.108592
$680$	57.8579	+	173.008i	0.0850851	+	0.254424i
$681$		0			0
$682$		−	91.6169i		−	0.134336i
$683$	232.009			0.339691			0.169846	−	0.985471i	$-0.445673\pi$
$683$	232.009			0.339691			0.169846	+	0.985471i	$0.445673\pi$
$684$		0			0
$685$	−259.940	−	777.281i	−0.379475	−	1.13472i
$686$			111.994i			0.163257i
$687$		0			0
$688$			164.199i			0.238661i
$689$		−	375.513i		−	0.545011i
$690$		0			0
$691$	−552.904			−0.800150			−0.400075	−	0.916482i	$-0.631016\pi$
$691$	−552.904			−0.800150			−0.400075	+	0.916482i	$0.631016\pi$
$692$	220.024			0.317954
$693$		0			0
$694$	−267.868			−0.385977
$695$	289.009	+	864.204i	0.415841	+	1.24346i
$696$		0			0
$697$		−	90.8512i		−	0.130346i
$698$	220.326			0.315653
$699$		0			0
$700$	24.4710	+	32.4951i	0.0349586	+	0.0464216i
$701$		−	250.274i		−	0.357024i	−0.983938	−	0.178512i	$-0.942872\pi$
$701$		−	250.274i		−	0.357024i	0.983938	−	0.178512i	$-0.0571284\pi$
$702$		0			0
$703$			87.3755i			0.124290i
$704$			123.009i			0.174729i
$705$		0			0
$706$	−372.485			−0.527600
$707$	−40.4508			−0.0572147
$708$		0			0
$709$	1170.57			1.65102			0.825510	−	0.564388i	$-0.190888\pi$
$709$	1170.57			1.65102			0.825510	+	0.564388i	$0.190888\pi$
$710$	−467.397	+	156.308i	−0.658306	+	0.220152i
$711$		0			0
$712$			388.949i			0.546276i
$713$	−20.2191			−0.0283578
$714$		0			0
$715$	143.677	+	429.627i	0.200947	+	0.600877i
$716$			236.814i			0.330746i
$717$		0			0
$718$		−	112.620i		−	0.156853i
$719$			168.127i			0.233834i	0.993142	+	0.116917i	$0.0373012\pi$
$719$			168.127i			0.233834i	−0.993142	+	0.116917i	$0.962699\pi$
$720$		0			0
$721$	−104.824			−0.145387
$722$	508.347			0.704082
$723$		0			0
$724$	344.794			0.476235
$725$	−641.823	−	852.279i	−0.885274	−	1.17556i
$726$		0			0
$727$		−	382.835i		−	0.526595i	−0.964715	−	0.263298i	$-0.915190\pi$
$727$		−	382.835i		−	0.526595i	0.964715	−	0.263298i	$-0.0848101\pi$
$728$	13.5593			0.0186254
$729$		0			0
$730$	600.985	−	200.983i	0.823267	−	0.275319i
$731$		−	529.520i		−	0.724377i
$732$		0			0
$733$		−	1403.08i		−	1.91416i	−0.289819	−	0.957082i	$-0.593595\pi$
$733$		−	1403.08i		−	1.91416i	0.289819	−	0.957082i	$-0.406405\pi$
$734$		−	673.099i		−	0.917029i
$735$		0			0
$736$	27.1472			0.0368848
$737$	1368.52			1.85688
$738$		0			0
$739$	899.125			1.21668			0.608339	−	0.793677i	$-0.291836\pi$
$739$	899.125			1.21668			0.608339	+	0.793677i	$0.291836\pi$
$740$	−666.843	+	223.007i	−0.901139	+	0.301361i
$741$		0			0
$742$			73.3234i			0.0988186i
$743$	−316.587			−0.426093			−0.213046	−	0.977042i	$-0.568339\pi$
$743$	−316.587			−0.426093			−0.213046	+	0.977042i	$0.568339\pi$
$744$		0			0
$745$	−898.749	+	300.562i	−1.20637	+	0.403439i
$746$		−	87.3755i		−	0.117125i
$747$		0			0
$748$		−	396.689i		−	0.530334i
$749$		−	5.22837i		−	0.00698046i
$750$		0			0
$751$	−286.433			−0.381402			−0.190701	−	0.981648i	$-0.561076\pi$
$751$	−286.433			−0.381402			−0.190701	+	0.981648i	$0.561076\pi$
$752$	−319.196			−0.424463
$753$		0			0
$754$	−355.632			−0.471661
$755$	−179.730	−	537.434i	−0.238053	−	0.711833i
$756$		0			0
$757$		−	783.221i		−	1.03464i	−0.855793	−	0.517319i	$-0.826930\pi$
$757$		−	783.221i		−	1.03464i	0.855793	−	0.517319i	$-0.173070\pi$
$758$	201.307			0.265576
$759$		0			0
$760$	−5.57359	−	16.6663i	−0.00733368	−	0.0219294i
$761$			1031.91i			1.35599i	0.735064	+	0.677997i	$0.237152\pi$
$761$			1031.91i			1.35599i	−0.735064	+	0.677997i	$0.762848\pi$
$762$		0			0
$763$		−	88.0933i		−	0.115456i
$764$			578.787i			0.757574i
$765$		0			0
$766$	−505.609			−0.660064
$767$	−215.927			−0.281521
$768$		0			0
$769$	−831.250			−1.08095			−0.540475	−	0.841360i	$-0.681755\pi$
$769$	−831.250			−1.08095			−0.540475	+	0.841360i	$0.681755\pi$
$770$	−28.0547	−	83.8900i	−0.0364347	−	0.108948i
$771$		0			0
$772$			255.666i			0.331173i
$773$	−395.360			−0.511462			−0.255731	−	0.966748i	$-0.582316\pi$
$773$	−395.360			−0.511462			−0.255731	+	0.966748i	$0.582316\pi$
$774$		0			0
$775$	−84.1400	+	63.3631i	−0.108568	+	0.0817588i
$776$		−	256.340i		−	0.330335i
$777$		0			0
$778$			581.353i			0.747240i
$779$			8.75192i			0.0112348i
$780$		0			0
$781$	1071.69			1.37220
$782$	−87.5462			−0.111952
$783$		0			0
$784$	193.352			0.246623
$785$	−536.725	+	179.493i	−0.683726	+	0.228653i
$786$		0			0
$787$			573.929i			0.729262i	0.931152	+	0.364631i	$0.118805\pi$
$787$			573.929i			0.729262i	−0.931152	+	0.364631i	$0.881195\pi$
$788$	560.828			0.711711
$789$		0			0
$790$	−300.728	−	899.245i	−0.380668	−	1.13829i
$791$			24.7542i			0.0312948i
$792$		0			0
$793$			488.725i			0.616299i
$794$			646.949i			0.814798i
$795$		0			0
$796$	312.853			0.393031
$797$	1408.39			1.76712			0.883560	−	0.468319i	$-0.155140\pi$
$797$	1408.39			1.76712			0.883560	+	0.468319i	$0.155140\pi$
$798$		0			0
$799$	1029.37			1.28832
$800$	112.971	−	85.0744i	0.141213	−	0.106343i
$801$		0			0
$802$		−	660.838i		−	0.823988i
$803$	−1377.99			−1.71606
$804$		0			0
$805$	−18.5139	+	6.19145i	−0.0229986	+	0.00769124i
$806$			35.1093i			0.0435599i
$807$		0			0
$808$			140.629i			0.174046i
$809$			105.645i			0.130587i	0.997866	+	0.0652936i	$0.0207984\pi$
$809$			105.645i			0.130587i	−0.997866	+	0.0652936i	$0.979202\pi$
$810$		0			0
$811$	−1090.81			−1.34502			−0.672508	−	0.740090i	$-0.734783\pi$
$811$	−1090.81			−1.34502			−0.672508	+	0.740090i	$0.734783\pi$
$812$	69.4416			0.0855192
$813$		0			0
$814$	1529.00			1.87838
$815$	722.725	−	241.696i	0.886779	−	0.296559i
$816$		0			0
$817$			51.0099i			0.0624357i
$818$	634.379			0.775524
$819$		0			0
$820$	−66.7939	+	22.3374i	−0.0814560	+	0.0272407i
$821$			851.302i			1.03691i	0.855105	+	0.518454i	$0.173492\pi$
$821$			851.302i			1.03691i	−0.855105	+	0.518454i	$0.826508\pi$
$822$		0			0
$823$			1120.12i			1.36103i	0.732736	+	0.680513i	$0.238243\pi$
$823$			1120.12i			1.36103i	−0.732736	+	0.680513i	$0.761757\pi$
$824$			364.426i			0.442264i
$825$		0			0
$826$	42.1623			0.0510440
$827$	−1214.63			−1.46871			−0.734357	−	0.678763i	$-0.762516\pi$
$827$	−1214.63			−1.46871			−0.734357	+	0.678763i	$0.762516\pi$
$828$		0			0
$829$	1495.22			1.80364			0.901821	−	0.432111i	$-0.142231\pi$
$829$	1495.22			1.80364			0.901821	+	0.432111i	$0.142231\pi$
$830$	−244.503	−	731.119i	−0.294581	−	0.880866i
$831$		0			0
$832$		−	47.1395i		−	0.0566580i
$833$	−623.537			−0.748544
$834$		0			0
$835$	167.860	+	501.940i	0.201030	+	0.601125i
$836$			38.2141i			0.0457106i
$837$		0			0
$838$			510.297i			0.608946i
$839$			463.865i			0.552879i	0.961031	+	0.276439i	$0.0891545\pi$
$839$			463.865i			0.552879i	−0.961031	+	0.276439i	$0.910846\pi$
$840$		0			0
$841$	−980.308			−1.16565
$842$	−504.958			−0.599712
$843$		0			0
$844$	45.0152			0.0533355
$845$	212.938	+	636.734i	0.251998	+	0.753531i
$846$		0			0
$847$			93.9081i			0.110871i
$848$	254.912			0.300603
$849$		0			0
$850$	−364.316	+	274.354i	−0.428607	+	0.322770i
$851$		−	337.438i		−	0.396519i
$852$		0			0
$853$		−	495.850i		−	0.581301i	−0.956829	−	0.290651i	$-0.906128\pi$
$853$		−	495.850i		−	0.581301i	0.956829	−	0.290651i	$-0.0938717\pi$
$854$		−	95.4295i		−	0.111744i
$855$		0			0
$856$	−18.1766			−0.0212344
$857$	1704.43			1.98884			0.994418	−	0.105511i	$-0.0336478\pi$
$857$	1704.43			1.98884			0.994418	+	0.105511i	$0.0336478\pi$
$858$		0			0
$859$	−207.523			−0.241586			−0.120793	−	0.992678i	$-0.538544\pi$
$859$	−207.523			−0.241586			−0.120793	+	0.992678i	$0.538544\pi$
$860$	−389.304	+	130.192i	−0.452679	+	0.151386i
$861$		0			0
$862$		−	927.649i		−	1.07616i
$863$	117.426			0.136068			0.0680338	−	0.997683i	$-0.478327\pi$
$863$	117.426			0.136068			0.0680338	+	0.997683i	$0.478327\pi$
$864$		0			0
$865$	174.456	+	521.663i	0.201683	+	0.603079i
$866$		−	232.457i		−	0.268426i
$867$		0			0
$868$		−	6.85552i		−	0.00789806i
$869$			2061.87i			2.37270i
$870$		0			0
$871$	−524.442			−0.602115
$872$	−306.260			−0.351215
$873$		0			0
$874$	8.43355			0.00964937
$875$	−57.6408	+	83.7842i	−0.0658752	+	0.0957534i
$876$		0			0
$877$			908.637i			1.03607i	0.855358	+	0.518037i	$0.173337\pi$
$877$			908.637i			1.03607i	−0.855358	+	0.518037i	$0.826663\pi$
$878$	187.081			0.213077
$879$		0			0
$880$	−291.647	+	97.5332i	−0.331417	+	0.110833i
$881$		−	1226.54i		−	1.39221i	−0.717941	−	0.696104i	$-0.754915\pi$
$881$		−	1226.54i		−	1.39221i	0.717941	−	0.696104i	$-0.245085\pi$
$882$		0			0
$883$		−	760.022i		−	0.860728i	−0.902656	−	0.430364i	$-0.858385\pi$
$883$		−	760.022i		−	0.860728i	0.902656	−	0.430364i	$-0.141615\pi$
$884$			152.019i			0.171967i
$885$		0			0
$886$	−644.153			−0.727036
$887$	−597.542			−0.673667			−0.336833	−	0.941564i	$-0.609356\pi$
$887$	−597.542			−0.673667			−0.336833	+	0.941564i	$0.609356\pi$
$888$		0			0
$889$	−108.796			−0.122380
$890$	−922.171	+	308.395i	−1.03615	+	0.346511i
$891$		0			0
$892$		−	709.653i		−	0.795575i
$893$	−99.1615			−0.111043
$894$		0			0
$895$	−561.470	+	187.768i	−0.627341	+	0.209797i
$896$			9.20455i			0.0102729i
$897$		0			0
$898$		−	587.957i		−	0.654741i
$899$			179.806i			0.200007i
$900$		0			0
$901$	−822.058			−0.912384
$902$	153.151			0.169791
$903$		0			0
$904$	86.0589			0.0951979
$905$	273.385	+	817.483i	0.302083	+	0.903296i
$906$		0			0
$907$			1708.26i			1.88341i	0.336435	+	0.941707i	$0.390779\pi$
$907$			1708.26i			1.88341i	−0.336435	+	0.941707i	$0.609221\pi$
$908$	−830.195			−0.914312
$909$		0			0
$910$	10.7511	+	32.1482i	0.0118144	+	0.0353277i
$911$			1432.15i			1.57206i	0.618187	+	0.786031i	$0.287868\pi$
$911$			1432.15i			1.57206i	−0.618187	+	0.786031i	$0.712132\pi$
$912$		0			0
$913$			1676.38i			1.83612i
$914$		−	429.416i		−	0.469820i
$915$		0			0
$916$	−440.441			−0.480830
$917$	50.2658			0.0548155
$918$		0			0
$919$	−244.398			−0.265939			−0.132969	−	0.991120i	$-0.542451\pi$
$919$	−244.398			−0.265939			−0.132969	+	0.991120i	$0.542451\pi$
$920$	21.5248	+	64.3641i	0.0233965	+	0.0699610i
$921$		0			0
$922$			606.400i			0.657701i
$923$	−410.692			−0.444954
$924$		0			0
$925$	−1057.47	−	1404.22i	−1.14321	−	1.51807i
$926$			1151.85i			1.24390i
$927$		0			0
$928$		−	241.416i		−	0.260147i
$929$		−	376.003i		−	0.404740i	−0.979309	−	0.202370i	$-0.935136\pi$
$929$		−	376.003i		−	0.404740i	0.979309	−	0.202370i	$-0.0648643\pi$
$930$		0			0
$931$	60.0669			0.0645187
$932$	20.0690			0.0215332
$933$		0			0
$934$	858.594			0.919266
$935$	940.524	−	314.532i	1.00591	−	0.336398i
$936$		0			0
$937$		−	412.076i		−	0.439782i	−0.975524	−	0.219891i	$-0.929430\pi$
$937$		−	412.076i		−	0.439782i	0.975524	−	0.219891i	$-0.0705701\pi$
$938$	102.404			0.109172
$939$		0			0
$940$	−253.088	−	756.792i	−0.269243	−	0.805098i
$941$			334.579i			0.355556i	0.984071	+	0.177778i	$0.0568910\pi$
$941$			334.579i			0.355556i	−0.984071	+	0.177778i	$0.943109\pi$
$942$		0			0
$943$		−	33.7993i		−	0.0358423i
$944$		−	146.579i		−	0.155274i
$945$		0			0
$946$	892.632			0.943585
$947$	611.132			0.645335			0.322667	−	0.946512i	$-0.395420\pi$
$947$	611.132			0.645335			0.322667	+	0.946512i	$0.395420\pi$
$948$		0			0
$949$	528.073			0.556452
$950$	35.0955	−	26.4292i	0.0369426	−	0.0278202i
$951$		0			0
$952$		−	29.6835i		−	0.0311802i
$953$	−1445.17			−1.51644			−0.758221	−	0.651997i	$-0.773931\pi$
$953$	−1445.17			−1.51644			−0.758221	+	0.651997i	$0.773931\pi$
$954$		0			0
$955$	−1372.26	+	458.916i	−1.43693	+	0.480540i
$956$		−	228.726i		−	0.239253i
$957$		0			0
$958$		−	486.332i		−	0.507654i
$959$			133.360i			0.139062i
$960$		0			0
$961$	−943.249			−0.981529
$962$	−585.941			−0.609086
$963$		0			0
$964$	−127.442			−0.132201
$965$	−606.167	+	202.716i	−0.628152	+	0.210068i
$966$		0			0
$967$			1183.07i			1.22344i	0.791073	+	0.611721i	$0.209523\pi$
$967$			1183.07i			1.22344i	−0.791073	+	0.611721i	$0.790477\pi$
$968$	326.475			0.337268
$969$		0			0
$970$	607.765	−	203.250i	0.626561	−	0.209536i
$971$			1444.94i			1.48810i	0.668124	+	0.744050i	$0.267097\pi$
$971$			1444.94i			1.48810i	−0.668124	+	0.744050i	$0.732903\pi$
$972$		0			0
$973$		−	148.274i		−	0.152388i
$974$		−	425.338i		−	0.436692i
$975$		0			0
$976$	−331.765			−0.339923
$977$	−1246.51			−1.27586			−0.637929	−	0.770095i	$-0.720209\pi$
$977$	−1246.51			−1.27586			−0.637929	+	0.770095i	$0.720209\pi$
$978$		0			0
$979$	2114.44			2.15979
$980$	153.308	+	458.425i	0.156437	+	0.467781i
$981$		0			0
$982$		−	245.951i		−	0.250459i
$983$	144.005			0.146495			0.0732477	−	0.997314i	$-0.476664\pi$
$983$	144.005			0.146495			0.0732477	+	0.997314i	$0.476664\pi$
$984$		0			0
$985$	444.677	+	1329.69i	0.451449	+	1.34994i
$986$			778.537i			0.789591i
$987$		0			0
$988$		−	14.6444i		−	0.0148222i
$989$		−	196.997i		−	0.199188i
$990$		0			0
$991$	725.742			0.732333			0.366167	−	0.930549i	$-0.380670\pi$
$991$	725.742			0.732333			0.366167	+	0.930549i	$0.380670\pi$
$992$	−23.8335			−0.0240257
$993$		0			0
$994$	80.1926			0.0806767
$995$	248.059	+	741.753i	0.249305	+	0.745480i
$996$		0			0
$997$		−	881.323i		−	0.883975i	−0.897021	−	0.441987i	$-0.854274\pi$
$997$		−	881.323i		−	0.883975i	0.897021	−	0.441987i	$-0.145726\pi$
$998$	1077.08			1.07924
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.b.d.269.2	yes	4
3.2	odd	2		270.3.b.a.269.3	✓	4
4.3	odd	2		2160.3.c.m.1889.2		4
5.2	odd	4		1350.3.d.o.701.3		8
5.3	odd	4		1350.3.d.o.701.6		8
5.4	even	2		270.3.b.a.269.4	yes	4
9.2	odd	6		810.3.j.f.539.2		8
9.4	even	3		810.3.j.a.269.4		8
9.5	odd	6		810.3.j.f.269.1		8
9.7	even	3		810.3.j.a.539.3		8
12.11	even	2		2160.3.c.g.1889.3		4
15.2	even	4		1350.3.d.o.701.7		8
15.8	even	4		1350.3.d.o.701.2		8
15.14	odd	2	inner	270.3.b.d.269.1	yes	4
20.19	odd	2		2160.3.c.g.1889.4		4
45.4	even	6		810.3.j.f.269.2		8
45.14	odd	6		810.3.j.a.269.3		8
45.29	odd	6		810.3.j.a.539.4		8
45.34	even	6		810.3.j.f.539.1		8
60.59	even	2		2160.3.c.m.1889.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.b.a.269.3	✓	4	3.2	odd	2
270.3.b.a.269.4	yes	4	5.4	even	2
270.3.b.d.269.1	yes	4	15.14	odd	2	inner
270.3.b.d.269.2	yes	4	1.1	even	1	trivial
810.3.j.a.269.3		8	45.14	odd	6
810.3.j.a.269.4		8	9.4	even	3
810.3.j.a.539.3		8	9.7	even	3
810.3.j.a.539.4		8	45.29	odd	6
810.3.j.f.269.1		8	9.5	odd	6
810.3.j.f.269.2		8	45.4	even	6
810.3.j.f.539.1		8	45.34	even	6
810.3.j.f.539.2		8	9.2	odd	6
1350.3.d.o.701.2		8	15.8	even	4
1350.3.d.o.701.3		8	5.2	odd	4
1350.3.d.o.701.6		8	5.3	odd	4
1350.3.d.o.701.7		8	15.2	even	4
2160.3.c.g.1889.3		4	12.11	even	2
2160.3.c.g.1889.4		4	20.19	odd	2
2160.3.c.m.1889.1		4	60.59	even	2
2160.3.c.m.1889.2		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.00000 q^{4} +(1.58579 + 4.74186i) q^{5} -0.813575i q^{7} -2.82843 q^{8} +(-2.24264 - 6.70601i) q^{10} +15.3762i q^{11} -5.89243i q^{13} +1.15057i q^{14} +4.00000 q^{16} -12.8995 q^{17} +1.24264 q^{19} +(3.17157 + 9.48373i) q^{20} -21.7452i q^{22} -4.79899 q^{23} +(-19.9706 + 15.0392i) q^{25} +8.33316i q^{26} -1.62715i q^{28} +42.6768i q^{29} +4.21320 q^{31} -5.65685 q^{32} +18.2426 q^{34} +(3.85786 - 1.29016i) q^{35} +70.3144i q^{37} -1.75736 q^{38} +(-4.48528 - 13.4120i) q^{40} +7.04300i q^{41} +41.0496i q^{43} +30.7523i q^{44} +6.78680 q^{46} -79.7990 q^{47} +48.3381 q^{49} +(28.2426 - 21.2686i) q^{50} -11.7849i q^{52} +63.7279 q^{53} +(-72.9117 + 24.3833i) q^{55} +2.30114i q^{56} -60.3541i q^{58} -36.6448i q^{59} -82.9411 q^{61} -5.95837 q^{62} +8.00000 q^{64} +(27.9411 - 9.34414i) q^{65} -89.0027i q^{67} -25.7990 q^{68} +(-5.45584 + 1.82456i) q^{70} -69.6982i q^{71} +89.6188i q^{73} -99.4396i q^{74} +2.48528 q^{76} +12.5097 q^{77} +134.095 q^{79} +(6.34315 + 18.9675i) q^{80} -9.96031i q^{82} +109.024 q^{83} +(-20.4558 - 61.1677i) q^{85} -58.0529i q^{86} -43.4904i q^{88} -137.514i q^{89} -4.79394 q^{91} -9.59798 q^{92} +112.853 q^{94} +(1.97056 + 5.89243i) q^{95} +90.6298i q^{97} -68.3604 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 12 q^{5} + 8 q^{10} + 16 q^{16} - 12 q^{17} - 12 q^{19} + 24 q^{20} + 60 q^{23} - 12 q^{25} - 68 q^{31} + 56 q^{34} + 72 q^{35} - 24 q^{38} + 16 q^{40} + 112 q^{46} - 240 q^{47} - 180 q^{49}+ \cdots - 528 q^{98}+O(q^{100}) \) 4 * q + 8 * q^4 + 12 * q^5 + 8 * q^10 + 16 * q^16 - 12 * q^17 - 12 * q^19 + 24 * q^20 + 60 * q^23 - 12 * q^25 - 68 * q^31 + 56 * q^34 + 72 * q^35 - 24 * q^38 + 16 * q^40 + 112 * q^46 - 240 * q^47 - 180 * q^49 + 96 * q^50 + 204 * q^53 - 88 * q^55 - 196 * q^61 - 120 * q^62 + 32 * q^64 - 24 * q^65 - 24 * q^68 + 80 * q^70 - 24 * q^76 - 312 * q^77 + 180 * q^79 + 48 * q^80 + 108 * q^83 + 20 * q^85 + 456 * q^91 + 120 * q^92 + 112 * q^94 - 60 * q^95 - 528 * q^98

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