LMFDB - Embedded newform 1728.3.q.i.449.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(449,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1728.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.19269881856.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 $ x^8 - 2x^7 + 15x^6 - 2x^5 + 133x^4 - 84x^3 + 276x^2 + 144*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.3
Root			$1.91950 + 3.32468i$ of defining polynomial
Character	$\chi$	$=$	1728.449
Dual form			1728.3.q.i.1601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80902 + 1.04444i) q^{5} +(0.781452 + 1.35351i) q^{7} +O(q^{10})$	$q+(1.80902 + 1.04444i) q^{5} +(0.781452 + 1.35351i) q^{7} +(10.8302 - 6.25280i) q^{11} +(-11.0441 + 19.1289i) q^{13} -12.6991i q^{17} -21.7686 q^{19} +(-28.7989 - 16.6271i) q^{23} +(-10.3183 - 17.8718i) q^{25} +(-25.7787 + 14.8833i) q^{29} +(-6.91549 + 11.9780i) q^{31} +3.26472i q^{35} +8.26807 q^{37} +(-43.8453 - 25.3141i) q^{41} +(35.5364 + 61.5508i) q^{43} +(57.2470 - 33.0516i) q^{47} +(23.2787 - 40.3198i) q^{49} -6.04384i q^{53} +26.1227 q^{55} +(8.01575 + 4.62789i) q^{59} +(-51.9009 - 89.8950i) q^{61} +(-39.9580 + 23.0698i) q^{65} +(-19.8853 + 34.4424i) q^{67} -18.3599i q^{71} -68.5777 q^{73} +(16.9265 + 9.77252i) q^{77} +(-13.3130 - 23.0587i) q^{79} +(-21.0376 + 12.1461i) q^{83} +(13.2634 - 22.9729i) q^{85} +111.730i q^{89} -34.5217 q^{91} +(-39.3800 - 22.7360i) q^{95} +(-2.51182 - 4.35061i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{5} - 6 q^{7}+O(q^{10}) $ 8 * q - 6 * q^5 - 6 * q^7	$ 8 q - 6 q^{5} - 6 q^{7} - 36 q^{11} - 14 q^{13} + 4 q^{19} - 102 q^{23} + 10 q^{25} - 114 q^{29} + 50 q^{31} - 120 q^{37} - 264 q^{41} - 28 q^{43} + 150 q^{47} + 94 q^{49} + 244 q^{55} + 108 q^{59} - 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} + 66 q^{77} - 26 q^{79} - 246 q^{83} + 224 q^{85} + 108 q^{91} - 456 q^{95} - 236 q^{97}+O(q^{100}) $ 8 * q - 6 * q^5 - 6 * q^7 - 36 * q^11 - 14 * q^13 + 4 * q^19 - 102 * q^23 + 10 * q^25 - 114 * q^29 + 50 * q^31 - 120 * q^37 - 264 * q^41 - 28 * q^43 + 150 * q^47 + 94 * q^49 + 244 * q^55 + 108 * q^59 - 14 * q^61 + 198 * q^65 - 20 * q^67 - 76 * q^73 + 66 * q^77 - 26 * q^79 - 246 * q^83 + 224 * q^85 + 108 * q^91 - 456 * q^95 - 236 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.80902	+	1.04444i	0.361805	+	0.208888i	0.669872	−	0.742476i	$-0.266349\pi$
$5$	1.80902	+	1.04444i	0.361805	+	0.208888i	−0.308067	+	0.951365i	$0.599682\pi$
$6$		0			0
$7$	0.781452	+	1.35351i	0.111636	+	0.193359i	0.916430	−	0.400195i	$-0.131058\pi$
$7$	0.781452	+	1.35351i	0.111636	+	0.193359i	−0.804794	+	0.593554i	$0.797724\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	10.8302	−	6.25280i	0.984560	−	0.568436i	0.0809165	−	0.996721i	$-0.474215\pi$
$11$	10.8302	−	6.25280i	0.984560	−	0.568436i	0.903644	+	0.428285i	$0.140882\pi$
$12$		0			0
$13$	−11.0441	+	19.1289i	−0.849545	+	1.47145i	0.0320708	+	0.999486i	$0.489790\pi$
$13$	−11.0441	+	19.1289i	−0.849545	+	1.47145i	−0.881615	+	0.471969i	$0.843544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	12.6991i		−	0.747005i	−0.927629	−	0.373503i	$-0.878157\pi$
$17$		−	12.6991i		−	0.747005i	0.927629	−	0.373503i	$-0.121843\pi$
$18$		0			0
$19$	−21.7686			−1.14572			−0.572859	−	0.819654i	$-0.694166\pi$
$19$	−21.7686			−1.14572			−0.572859	+	0.819654i	$0.694166\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−28.7989	−	16.6271i	−1.25213	−	0.722916i	−0.280596	−	0.959826i	$-0.590532\pi$
$23$	−28.7989	−	16.6271i	−1.25213	−	0.722916i	−0.971532	+	0.236909i	$0.923866\pi$
$24$		0			0
$25$	−10.3183	−	17.8718i	−0.412732	−	0.714872i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−25.7787	+	14.8833i	−0.888920	+	0.513218i	−0.873589	−	0.486665i	$-0.838213\pi$
$29$	−25.7787	+	14.8833i	−0.888920	+	0.513218i	−0.0153306	+	0.999882i	$0.504880\pi$
$30$		0			0
$31$	−6.91549	+	11.9780i	−0.223080	+	0.386386i	−0.955742	−	0.294207i	$-0.904945\pi$
$31$	−6.91549	+	11.9780i	−0.223080	+	0.386386i	0.732662	+	0.680593i	$0.238278\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			3.26472i			0.0932777i
$36$		0			0
$37$	8.26807			0.223461			0.111731	−	0.993739i	$-0.464361\pi$
$37$	8.26807			0.223461			0.111731	+	0.993739i	$0.464361\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−43.8453	−	25.3141i	−1.06940	−	0.617418i	−0.141382	−	0.989955i	$-0.545154\pi$
$41$	−43.8453	−	25.3141i	−1.06940	−	0.617418i	−0.928017	+	0.372538i	$0.878488\pi$
$42$		0			0
$43$	35.5364	+	61.5508i	0.826427	+	1.43141i	0.900824	+	0.434185i	$0.142964\pi$
$43$	35.5364	+	61.5508i	0.826427	+	1.43141i	−0.0743965	+	0.997229i	$0.523703\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	57.2470	−	33.0516i	1.21802	−	0.703225i	0.253527	−	0.967328i	$-0.418409\pi$
$47$	57.2470	−	33.0516i	1.21802	−	0.703225i	0.964495	+	0.264103i	$0.0850759\pi$
$48$		0			0
$49$	23.2787	−	40.3198i	0.475075	−	0.822854i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	6.04384i		−	0.114035i	−0.998373	−	0.0570174i	$-0.981841\pi$
$53$		−	6.04384i		−	0.114035i	0.998373	−	0.0570174i	$-0.0181590\pi$
$54$		0			0
$55$	26.1227			0.474958
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.01575	+	4.62789i	0.135860	+	0.0784389i	0.566390	−	0.824138i	$-0.308340\pi$
$59$	8.01575	+	4.62789i	0.135860	+	0.0784389i	−0.430529	+	0.902577i	$0.641673\pi$
$60$		0			0
$61$	−51.9009	−	89.8950i	−0.850834	−	1.47369i	−0.880457	−	0.474127i	$-0.842764\pi$
$61$	−51.9009	−	89.8950i	−0.850834	−	1.47369i	0.0296226	−	0.999561i	$-0.490569\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−39.9580	+	23.0698i	−0.614738	+	0.354919i
$66$		0			0
$67$	−19.8853	+	34.4424i	−0.296796	+	0.514065i	−0.975401	−	0.220438i	$-0.929251\pi$
$67$	−19.8853	+	34.4424i	−0.296796	+	0.514065i	0.678605	+	0.734503i	$0.262585\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	18.3599i		−	0.258590i	−0.991606	−	0.129295i	$-0.958729\pi$
$71$		−	18.3599i		−	0.258590i	0.991606	−	0.129295i	$-0.0412714\pi$
$72$		0			0
$73$	−68.5777			−0.939421			−0.469711	−	0.882820i	$-0.655642\pi$
$73$	−68.5777			−0.939421			−0.469711	+	0.882820i	$0.655642\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	16.9265	+	9.77252i	0.219825	+	0.126916i
$78$		0			0
$79$	−13.3130	−	23.0587i	−0.168518	−	0.291883i	0.769381	−	0.638791i	$-0.220565\pi$
$79$	−13.3130	−	23.0587i	−0.168518	−	0.291883i	−0.937899	+	0.346908i	$0.887232\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−21.0376	+	12.1461i	−0.253465	+	0.146338i	−0.621350	−	0.783533i	$-0.713415\pi$
$83$	−21.0376	+	12.1461i	−0.253465	+	0.146338i	0.367885	+	0.929871i	$0.380082\pi$
$84$		0			0
$85$	13.2634	−	22.9729i	0.156040	−	0.270270i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			111.730i			1.25539i	0.778459	+	0.627695i	$0.216001\pi$
$89$			111.730i			1.25539i	−0.778459	+	0.627695i	$0.783999\pi$
$90$		0			0
$91$	−34.5217			−0.379359
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−39.3800	−	22.7360i	−0.414526	−	0.239327i
$96$		0			0
$97$	−2.51182	−	4.35061i	−0.0258951	−	0.0448516i	0.852787	−	0.522258i	$-0.174910\pi$
$97$	−2.51182	−	4.35061i	−0.0258951	−	0.0448516i	−0.878683	+	0.477407i	$0.841577\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−86.1052	+	49.7129i	−0.852527	+	0.492207i	−0.861503	−	0.507753i	$-0.830476\pi$
$101$	−86.1052	+	49.7129i	−0.852527	+	0.492207i	0.00897555	+	0.999960i	$0.497143\pi$
$102$		0			0
$103$	−13.6160	+	23.5836i	−0.132194	+	0.228967i	−0.924522	−	0.381128i	$-0.875536\pi$
$103$	−13.6160	+	23.5836i	−0.132194	+	0.228967i	0.792328	+	0.610096i	$0.208869\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	127.242i		−	1.18918i	−0.804030	−	0.594588i	$-0.797315\pi$
$107$		−	127.242i		−	1.18918i	0.804030	−	0.594588i	$-0.202685\pi$
$108$		0			0
$109$	−55.3100			−0.507431			−0.253716	−	0.967279i	$-0.581653\pi$
$109$	−55.3100			−0.507431			−0.253716	+	0.967279i	$0.581653\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−102.845	−	59.3775i	−0.910131	−	0.525464i	−0.0296577	−	0.999560i	$-0.509442\pi$
$113$	−102.845	−	59.3775i	−0.910131	−	0.525464i	−0.880473	+	0.474096i	$0.842775\pi$
$114$		0			0
$115$	−34.7320	−	60.1576i	−0.302017	−	0.523109i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	17.1884	−	9.92372i	0.144440	−	0.0833926i
$120$		0			0
$121$	17.6950	−	30.6486i	0.146239	−	0.253294i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	95.3294i		−	0.762635i
$126$		0			0
$127$	−74.4516			−0.586233			−0.293116	−	0.956077i	$-0.594692\pi$
$127$	−74.4516			−0.586233			−0.293116	+	0.956077i	$0.594692\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.08499	+	4.09052i	0.0540839	+	0.0312254i	0.526798	−	0.849990i	$-0.323392\pi$
$131$	7.08499	+	4.09052i	0.0540839	+	0.0312254i	−0.472714	+	0.881216i	$0.656726\pi$
$132$		0			0
$133$	−17.0111	−	29.4642i	−0.127903	−	0.221535i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	41.7273	−	24.0913i	0.304579	−	0.175849i	−0.339919	−	0.940455i	$-0.610400\pi$
$137$	41.7273	−	24.0913i	0.304579	−	0.175849i	0.644498	+	0.764606i	$0.277066\pi$
$138$		0			0
$139$	119.023	−	206.155i	0.856284	−	1.48313i	−0.0191645	−	0.999816i	$-0.506101\pi$
$139$	119.023	−	206.155i	0.856284	−	1.48313i	0.875449	−	0.483311i	$-0.160566\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			276.226i			1.93165i
$144$		0			0
$145$	−62.1789			−0.428820
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−246.854	−	142.521i	−1.65674	−	0.956517i	−0.974207	−	0.225658i	$-0.927547\pi$
$149$	−246.854	−	142.521i	−1.65674	−	0.956517i	−0.682529	−	0.730859i	$-0.739120\pi$
$150$		0			0
$151$	77.2434	+	133.790i	0.511546	+	0.886024i	0.999910	+	0.0133838i	$0.00426032\pi$
$151$	77.2434	+	133.790i	0.511546	+	0.886024i	−0.488365	+	0.872640i	$0.662406\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−25.0206	+	14.4456i	−0.161423	+	0.0931976i
$156$		0			0
$157$	119.947	−	207.754i	0.763993	−	1.32328i	−0.176784	−	0.984250i	$-0.556569\pi$
$157$	119.947	−	207.754i	0.763993	−	1.32328i	0.940777	−	0.339026i	$-0.110097\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	51.9730i		−	0.322814i
$162$		0			0
$163$	111.245			0.682483			0.341241	−	0.939976i	$-0.389153\pi$
$163$	111.245			0.682483			0.341241	+	0.939976i	$0.389153\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	37.9116	+	21.8883i	0.227016	+	0.131068i	0.609195	−	0.793021i	$-0.291493\pi$
$167$	37.9116	+	21.8883i	0.227016	+	0.131068i	−0.382179	+	0.924088i	$0.624826\pi$
$168$		0			0
$169$	−159.443	−	276.164i	−0.943452	−	1.63411i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−253.383	+	146.291i	−1.46464	+	0.845611i	−0.999220	−	0.0394795i	$-0.987430\pi$
$173$	−253.383	+	146.291i	−1.46464	+	0.845611i	−0.465420	+	0.885090i	$0.654097\pi$
$174$		0			0
$175$	16.1265	−	27.9319i	0.0921514	−	0.159611i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			194.612i			1.08722i	0.839338	+	0.543610i	$0.182943\pi$
$179$			194.612i			1.08722i	−0.839338	+	0.543610i	$0.817057\pi$
$180$		0			0
$181$	−89.3906			−0.493871			−0.246935	−	0.969032i	$-0.579424\pi$
$181$	−89.3906			−0.493871			−0.246935	+	0.969032i	$0.579424\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	14.9571	+	8.63550i	0.0808494	+	0.0466784i
$186$		0			0
$187$	−79.4048	−	137.533i	−0.424625	−	0.735472i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−44.9085	+	25.9279i	−0.235123	+	0.135748i	−0.612933	−	0.790135i	$-0.710011\pi$
$191$	−44.9085	+	25.9279i	−0.235123	+	0.135748i	0.377810	+	0.925883i	$0.376677\pi$
$192$		0			0
$193$	−29.7763	+	51.5741i	−0.154281	+	0.267223i	−0.932797	−	0.360402i	$-0.882640\pi$
$193$	−29.7763	+	51.5741i	−0.154281	+	0.267223i	0.778516	+	0.627625i	$0.215973\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	47.4968i		−	0.241100i	−0.992707	−	0.120550i	$-0.961534\pi$
$197$		−	47.4968i		−	0.241100i	0.992707	−	0.120550i	$-0.0384659\pi$
$198$		0			0
$199$	−29.5239			−0.148361			−0.0741805	−	0.997245i	$-0.523634\pi$
$199$	−29.5239			−0.148361			−0.0741805	+	0.997245i	$0.523634\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−40.2896	−	23.2612i	−0.198471	−	0.114587i
$204$		0			0
$205$	−52.8782	−	91.5877i	−0.257942	−	0.446769i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−235.758	+	136.115i	−1.12803	+	0.651268i
$210$		0			0
$211$	−81.0561	+	140.393i	−0.384152	+	0.665371i	−0.991651	−	0.128949i	$-0.958840\pi$
$211$	−81.0561	+	140.393i	−0.384152	+	0.665371i	0.607499	+	0.794320i	$0.292173\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			148.462i			0.690523i
$216$		0			0
$217$	−21.6165			−0.0996151
$218$		0			0
$219$		0			0
$220$		0			0
$221$	242.920	+	140.250i	1.09918	+	0.634614i
$222$		0			0
$223$	−102.706	−	177.891i	−0.460564	−	0.797719i	0.538426	−	0.842673i	$-0.319019\pi$
$223$	−102.706	−	177.891i	−0.460564	−	0.797719i	−0.998989	+	0.0449536i	$0.985686\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−54.0416	+	31.2009i	−0.238069	+	0.137449i	−0.614289	−	0.789081i	$-0.710557\pi$
$227$	−54.0416	+	31.2009i	−0.238069	+	0.137449i	0.376220	+	0.926530i	$0.377224\pi$
$228$		0			0
$229$	5.73790	−	9.93834i	0.0250563	−	0.0433989i	−0.853225	−	0.521542i	$-0.825357\pi$
$229$	5.73790	−	9.93834i	0.0250563	−	0.0433989i	0.878282	+	0.478144i	$0.158690\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			177.096i			0.760069i	0.924972	+	0.380035i	$0.124088\pi$
$233$			177.096i			0.760069i	−0.924972	+	0.380035i	$0.875912\pi$
$234$		0			0
$235$	138.082			0.587581
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−231.234	−	133.503i	−0.967505	−	0.558589i	−0.0690305	−	0.997615i	$-0.521991\pi$
$239$	−231.234	−	133.503i	−0.967505	−	0.558589i	−0.898475	+	0.439025i	$0.855324\pi$
$240$		0			0
$241$	40.7178	+	70.5252i	0.168953	+	0.292636i	0.938052	−	0.346494i	$-0.112628\pi$
$241$	40.7178	+	70.5252i	0.168953	+	0.292636i	−0.769099	+	0.639130i	$0.779295\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	84.2233	−	48.6263i	0.343769	−	0.198475i
$246$		0			0
$247$	240.415	−	416.410i	0.973338	−	1.68587i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			311.819i			1.24231i	0.783689	+	0.621153i	$0.213336\pi$
$251$			311.819i			1.24231i	−0.783689	+	0.621153i	$0.786664\pi$
$252$		0			0
$253$	−415.863			−1.64373
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−335.121	−	193.482i	−1.30397	−	0.752849i	−0.322889	−	0.946437i	$-0.604654\pi$
$257$	−335.121	−	193.482i	−1.30397	−	0.752849i	−0.981083	+	0.193588i	$0.937988\pi$
$258$		0			0
$259$	6.46110	+	11.1909i	0.0249463	+	0.0432083i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	417.095	−	240.810i	1.58591	−	0.915627i	0.591942	−	0.805981i	$-0.298362\pi$
$263$	417.095	−	240.810i	1.58591	−	0.915627i	0.993971	−	0.109646i	$-0.0349718\pi$
$264$		0			0
$265$	6.31243	−	10.9334i	0.0238205	−	0.0412583i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			225.818i			0.839474i	0.907646	+	0.419737i	$0.137878\pi$
$269$			225.818i			0.839474i	−0.907646	+	0.419737i	$0.862122\pi$
$270$		0			0
$271$	23.6619			0.0873135			0.0436567	−	0.999047i	$-0.486099\pi$
$271$	23.6619			0.0873135			0.0436567	+	0.999047i	$0.486099\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−223.498	−	129.036i	−0.812718	−	0.469223i
$276$		0			0
$277$	27.9969	+	48.4920i	0.101072	+	0.175061i	0.912126	−	0.409909i	$-0.134440\pi$
$277$	27.9969	+	48.4920i	0.101072	+	0.175061i	−0.811055	+	0.584970i	$0.801106\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−122.023	+	70.4498i	−0.434244	+	0.250711i	−0.701153	−	0.713011i	$-0.747331\pi$
$281$	−122.023	+	70.4498i	−0.434244	+	0.250711i	0.266909	+	0.963722i	$0.413998\pi$
$282$		0			0
$283$	−155.690	+	269.663i	−0.550141	+	0.952872i	0.448123	+	0.893972i	$0.352093\pi$
$283$	−155.690	+	269.663i	−0.550141	+	0.952872i	−0.998264	+	0.0589002i	$0.981241\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	79.1271i		−	0.275704i
$288$		0			0
$289$	127.733			0.441983
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−273.621	−	157.975i	−0.933859	−	0.539164i	−0.0458290	−	0.998949i	$-0.514593\pi$
$293$	−273.621	−	157.975i	−0.933859	−	0.539164i	−0.888030	+	0.459786i	$0.847926\pi$
$294$		0			0
$295$	9.66712	+	16.7439i	0.0327699	+	0.0567591i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	636.116	−	367.262i	2.12748	−	1.22830i
$300$		0			0
$301$	−55.5399	+	96.1980i	−0.184518	+	0.319595i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	216.829i		−	0.710916i
$306$		0			0
$307$	−379.819			−1.23720			−0.618598	−	0.785707i	$-0.712299\pi$
$307$	−379.819			−1.23720			−0.618598	+	0.785707i	$0.712299\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−335.497	−	193.699i	−1.07877	−	0.622827i	−0.148204	−	0.988957i	$-0.547349\pi$
$311$	−335.497	−	193.699i	−1.07877	−	0.622827i	−0.930564	+	0.366130i	$0.880683\pi$
$312$		0			0
$313$	−100.742	−	174.491i	−0.321860	−	0.557479i	0.659011	−	0.752133i	$-0.270975\pi$
$313$	−100.742	−	174.491i	−0.321860	−	0.557479i	−0.980872	+	0.194654i	$0.937642\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	319.046	−	184.201i	1.00645	−	0.581077i	0.0963027	−	0.995352i	$-0.469298\pi$
$317$	319.046	−	184.201i	1.00645	−	0.581077i	0.910152	+	0.414275i	$0.135965\pi$
$318$		0			0
$319$	−186.125	+	322.378i	−0.583463	+	1.01059i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			276.442i			0.855857i
$324$		0			0
$325$	455.824			1.40254
$326$		0			0
$327$		0			0
$328$		0			0
$329$	89.4716	+	51.6564i	0.271950	+	0.157010i
$330$		0			0
$331$	150.832	+	261.248i	0.455684	+	0.789268i	0.998727	−	0.0504365i	$-0.0160613\pi$
$331$	150.832	+	261.248i	0.455684	+	0.789268i	−0.543043	+	0.839705i	$0.682728\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−71.9460	+	41.5380i	−0.214764	+	0.123994i
$336$		0			0
$337$	85.5075	−	148.103i	0.253732	−	0.439476i	−0.710819	−	0.703375i	$-0.751675\pi$
$337$	85.5075	−	148.103i	0.253732	−	0.439476i	0.964550	+	0.263899i	$0.0850087\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			172.965i			0.507227i
$342$		0			0
$343$	149.347			0.435414
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−264.744	−	152.850i	−0.762950	−	0.440489i	0.0674041	−	0.997726i	$-0.478528\pi$
$347$	−264.744	−	152.850i	−0.762950	−	0.440489i	−0.830354	+	0.557237i	$0.811862\pi$
$348$		0			0
$349$	11.1944	+	19.3893i	0.0320756	+	0.0555566i	0.881618	−	0.471964i	$-0.156455\pi$
$349$	11.1944	+	19.3893i	0.0320756	+	0.0555566i	−0.849542	+	0.527521i	$0.823122\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	462.657	−	267.115i	1.31064	−	0.756700i	0.328440	−	0.944525i	$-0.393477\pi$
$353$	462.657	−	267.115i	1.31064	−	0.756700i	0.982203	+	0.187825i	$0.0601437\pi$
$354$		0			0
$355$	19.1758	−	33.2134i	0.0540163	−	0.0935590i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	217.172i		−	0.604936i	−0.953159	−	0.302468i	$-0.902189\pi$
$359$		−	217.172i		−	0.604936i	0.953159	−	0.302468i	$-0.0978106\pi$
$360$		0			0
$361$	112.874			0.312669
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−124.059	−	71.6253i	−0.339887	−	0.196234i
$366$		0			0
$367$	51.1847	+	88.6546i	0.139468	+	0.241566i	0.927295	−	0.374330i	$-0.122127\pi$
$367$	51.1847	+	88.6546i	0.139468	+	0.241566i	−0.787827	+	0.615896i	$0.788794\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.18042	−	4.72297i	0.0220497	−	0.0127304i
$372$		0			0
$373$	−243.458	+	421.682i	−0.652702	+	1.13051i	0.329762	+	0.944064i	$0.393031\pi$
$373$	−243.458	+	421.682i	−0.652702	+	1.13051i	−0.982464	+	0.186450i	$0.940302\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	657.490i		−	1.74401i
$378$		0			0
$379$	553.727			1.46102			0.730510	−	0.682901i	$-0.239282\pi$
$379$	553.727			1.46102			0.730510	+	0.682901i	$0.239282\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	184.612	+	106.586i	0.482016	+	0.278292i	0.721256	−	0.692668i	$-0.243565\pi$
$383$	184.612	+	106.586i	0.482016	+	0.278292i	−0.239240	+	0.970960i	$0.576898\pi$
$384$		0			0
$385$	20.4136	+	35.3574i	0.0530224	+	0.0918375i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−82.4958	+	47.6290i	−0.212071	+	0.122439i	−0.602274	−	0.798290i	$-0.705738\pi$
$389$	−82.4958	+	47.6290i	−0.212071	+	0.122439i	0.390202	+	0.920729i	$0.372405\pi$
$390$		0			0
$391$	−211.149	+	365.720i	−0.540022	+	0.935346i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	55.6184i		−	0.140806i
$396$		0			0
$397$	481.407			1.21261			0.606306	−	0.795231i	$-0.292651\pi$
$397$	481.407			1.21261			0.606306	+	0.795231i	$0.292651\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	517.354	+	298.694i	1.29016	+	0.744874i	0.978682	−	0.205380i	$-0.0658430\pi$
$401$	517.354	+	298.694i	1.29016	+	0.744874i	0.311477	+	0.950254i	$0.399176\pi$
$402$		0			0
$403$	−152.750	−	264.571i	−0.379033	−	0.656505i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	89.5446	−	51.6986i	0.220011	−	0.127024i
$408$		0			0
$409$	−53.7260	+	93.0562i	−0.131359	+	0.227521i	−0.924201	−	0.381907i	$-0.875268\pi$
$409$	−53.7260	+	93.0562i	−0.131359	+	0.227521i	0.792841	+	0.609428i	$0.208601\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			14.4659i			0.0350264i
$414$		0			0
$415$	−50.7433			−0.122273
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−39.6993	−	22.9204i	−0.0947477	−	0.0547026i	0.451878	−	0.892080i	$-0.350754\pi$
$419$	−39.6993	−	22.9204i	−0.0947477	−	0.0547026i	−0.546625	+	0.837377i	$0.684088\pi$
$420$		0			0
$421$	5.53062	+	9.57932i	0.0131369	+	0.0227537i	0.872519	−	0.488580i	$-0.162485\pi$
$421$	5.53062	+	9.57932i	0.0131369	+	0.0227537i	−0.859382	+	0.511334i	$0.829152\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−226.956	+	131.033i	−0.534013	+	0.308313i
$426$		0			0
$427$	81.1161	−	140.497i	0.189967	−	0.329033i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			590.788i			1.37074i	0.728196	+	0.685369i	$0.240359\pi$
$431$			590.788i			1.37074i	−0.728196	+	0.685369i	$0.759641\pi$
$432$		0			0
$433$	−13.9683			−0.0322594			−0.0161297	−	0.999870i	$-0.505134\pi$
$433$	−13.9683			−0.0322594			−0.0161297	+	0.999870i	$0.505134\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	626.914	+	361.949i	1.43459	+	0.828258i
$438$		0			0
$439$	−35.9051	−	62.1894i	−0.0817883	−	0.141662i	0.822230	−	0.569156i	$-0.192730\pi$
$439$	−35.9051	−	62.1894i	−0.0817883	−	0.141662i	−0.904018	+	0.427494i	$0.859396\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	581.028	−	335.457i	1.31158	−	0.757239i	0.329219	−	0.944254i	$-0.393214\pi$
$443$	581.028	−	335.457i	1.31158	−	0.757239i	0.982357	+	0.187015i	$0.0598812\pi$
$444$		0			0
$445$	−116.695	+	202.122i	−0.262236	+	0.454206i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			830.401i			1.84945i	0.380642	+	0.924723i	$0.375703\pi$
$449$			830.401i			1.84945i	−0.380642	+	0.924723i	$0.624297\pi$
$450$		0			0
$451$	−633.136			−1.40385
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−62.4505	−	36.0558i	−0.137254	−	0.0792435i
$456$		0			0
$457$	423.113	+	732.854i	0.925850	+	1.60362i	0.790188	+	0.612864i	$0.209983\pi$
$457$	423.113	+	732.854i	0.925850	+	1.60362i	0.135661	+	0.990755i	$0.456684\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	109.019	−	62.9423i	0.236484	−	0.136534i	−0.377076	−	0.926182i	$-0.623070\pi$
$461$	109.019	−	62.9423i	0.236484	−	0.136534i	0.613560	+	0.789648i	$0.289737\pi$
$462$		0			0
$463$	−307.121	+	531.950i	−0.663329	+	1.14892i	0.316407	+	0.948624i	$0.397524\pi$
$463$	−307.121	+	531.950i	−0.663329	+	1.14892i	−0.979735	+	0.200296i	$0.935810\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			172.270i			0.368887i	0.982843	+	0.184444i	$0.0590484\pi$
$467$			172.270i			0.368887i	−0.982843	+	0.184444i	$0.940952\pi$
$468$		0			0
$469$	−62.1576			−0.132532
$470$		0			0
$471$		0			0
$472$		0			0
$473$	769.729	+	444.403i	1.62733	+	0.939542i
$474$		0			0
$475$	224.615	+	389.045i	0.472874	+	0.819042i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−174.532	+	100.766i	−0.364367	+	0.210367i	−0.670995	−	0.741462i	$-0.734133\pi$
$479$	−174.532	+	100.766i	−0.364367	+	0.210367i	0.306628	+	0.951829i	$0.400799\pi$
$480$		0			0
$481$	−91.3132	+	158.159i	−0.189840	+	0.328813i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	10.4938i		−	0.0216367i
$486$		0			0
$487$	801.178			1.64513			0.822565	−	0.568671i	$-0.192542\pi$
$487$	801.178			1.64513			0.822565	+	0.568671i	$0.192542\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−625.711	−	361.255i	−1.27436	−	0.735753i	−0.298555	−	0.954392i	$-0.596505\pi$
$491$	−625.711	−	361.255i	−1.27436	−	0.735753i	−0.975806	+	0.218640i	$0.929838\pi$
$492$		0			0
$493$	189.005	+	327.366i	0.383376	+	0.664028i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.8503	−	14.3474i	0.0500007	−	0.0288679i
$498$		0			0
$499$	−69.4409	+	120.275i	−0.139160	+	0.241032i	−0.927179	−	0.374619i	$-0.877774\pi$
$499$	−69.4409	+	120.275i	−0.139160	+	0.241032i	0.788019	+	0.615651i	$0.211107\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	794.533i		−	1.57959i	−0.613372	−	0.789794i	$-0.710187\pi$
$503$		−	794.533i		−	1.57959i	0.613372	−	0.789794i	$-0.289813\pi$
$504$		0			0
$505$	−207.689			−0.411264
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−179.929	−	103.882i	−0.353495	−	0.204090i	0.312729	−	0.949843i	$-0.398757\pi$
$509$	−179.929	−	103.882i	−0.353495	−	0.204090i	−0.666224	+	0.745752i	$0.732090\pi$
$510$		0			0
$511$	−53.5902	−	92.8209i	−0.104873	−	0.181646i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−49.2634	+	28.4422i	−0.0956571	+	0.0552276i
$516$		0			0
$517$	413.330	−	715.908i	0.799477	−	1.38474i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	248.275i		−	0.476535i	−0.971200	−	0.238267i	$-0.923421\pi$
$521$		−	248.275i		−	0.476535i	0.971200	−	0.238267i	$-0.0765795\pi$
$522$		0			0
$523$	−108.678			−0.207797			−0.103898	−	0.994588i	$-0.533132\pi$
$523$	−108.678			−0.207797			−0.103898	+	0.994588i	$0.533132\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	152.109	+	87.8204i	0.288633	+	0.166642i
$528$		0			0
$529$	288.420	+	499.557i	0.545216	+	0.944343i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	968.463	−	559.142i	1.81700	−	1.04905i
$534$		0			0
$535$	132.896	−	230.183i	0.248405	−	0.430249i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	582.227i		−	1.08020i
$540$		0			0
$541$	20.0646			0.0370880			0.0185440	−	0.999828i	$-0.494097\pi$
$541$	20.0646			0.0370880			0.0185440	+	0.999828i	$0.494097\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−100.057	−	57.7680i	−0.183591	−	0.105996i
$546$		0			0
$547$	86.6937	+	150.158i	0.158489	+	0.274512i	0.934324	−	0.356424i	$-0.116004\pi$
$547$	86.6937	+	150.158i	0.158489	+	0.274512i	−0.775835	+	0.630936i	$0.782671\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	561.167	−	323.990i	1.01845	−	0.588003i
$552$		0			0
$553$	20.8069	−	36.0386i	0.0376254	−	0.0651692i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	434.666i		−	0.780370i	−0.920737	−	0.390185i	$-0.872411\pi$
$557$		−	434.666i		−	0.780370i	0.920737	−	0.390185i	$-0.127589\pi$
$558$		0			0
$559$	−1569.87			−2.80835
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−86.8277	−	50.1300i	−0.154223	−	0.0890409i	0.420902	−	0.907106i	$-0.361714\pi$
$563$	−86.8277	−	50.1300i	−0.154223	−	0.0890409i	−0.575126	+	0.818065i	$0.695047\pi$
$564$		0			0
$565$	−124.032	−	214.830i	−0.219526	−	0.380231i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−44.1556	+	25.4932i	−0.0776020	+	0.0448036i	−0.538299	−	0.842754i	$-0.680933\pi$
$569$	−44.1556	+	25.4932i	−0.0776020	+	0.0448036i	0.460697	+	0.887558i	$0.347600\pi$
$570$		0			0
$571$	430.481	−	745.615i	0.753907	−	1.30581i	−0.192009	−	0.981393i	$-0.561500\pi$
$571$	430.481	−	745.615i	0.753907	−	1.30581i	0.945916	−	0.324412i	$-0.105166\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			686.252i			1.19348i
$576$		0			0
$577$	59.3431			0.102848			0.0514239	−	0.998677i	$-0.483624\pi$
$577$	59.3431			0.102848			0.0514239	+	0.998677i	$0.483624\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−32.8797	−	18.9831i	−0.0565916	−	0.0326732i
$582$		0			0
$583$	−37.7909	−	65.4558i	−0.0648215	−	0.112274i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−534.777	+	308.754i	−0.911034	+	0.525986i	−0.880764	−	0.473556i	$-0.842970\pi$
$587$	−534.777	+	308.754i	−0.911034	+	0.525986i	−0.0302706	+	0.999542i	$0.509637\pi$
$588$		0			0
$589$	150.541	−	260.744i	0.255587	−	0.442690i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	342.310i		−	0.577251i	−0.957442	−	0.288626i	$-0.906802\pi$
$593$		−	342.310i		−	0.577251i	0.957442	−	0.288626i	$-0.0931983\pi$
$594$		0			0
$595$	41.4589			0.0696789
$596$		0			0
$597$		0			0
$598$		0			0
$599$	379.292	+	218.984i	0.633209	+	0.365583i	0.781994	−	0.623286i	$-0.214203\pi$
$599$	379.292	+	218.984i	0.633209	+	0.365583i	−0.148785	+	0.988870i	$0.547536\pi$
$600$		0			0
$601$	304.452	+	527.327i	0.506576	+	0.877416i	0.999971	+	0.00761053i	$0.00242253\pi$
$601$	304.452	+	527.327i	0.506576	+	0.877416i	−0.493395	+	0.869806i	$0.664244\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	64.0212	−	36.9627i	0.105820	−	0.0610953i
$606$		0			0
$607$	540.751	−	936.608i	0.890858	−	1.54301i	0.0520102	−	0.998647i	$-0.483437\pi$
$607$	540.751	−	936.608i	0.890858	−	1.54301i	0.838848	−	0.544365i	$-0.183230\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			1460.10i			2.38968i
$612$		0			0
$613$	222.279			0.362609			0.181304	−	0.983427i	$-0.441968\pi$
$613$	222.279			0.362609			0.181304	+	0.983427i	$0.441968\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	31.0310	+	17.9158i	0.0502934	+	0.0290369i	0.524936	−	0.851142i	$-0.324089\pi$
$617$	31.0310	+	17.9158i	0.0502934	+	0.0290369i	−0.474642	+	0.880179i	$0.657423\pi$
$618$		0			0
$619$	−161.494	−	279.717i	−0.260896	−	0.451885i	0.705584	−	0.708626i	$-0.250685\pi$
$619$	−161.494	−	279.717i	−0.260896	−	0.451885i	−0.966480	+	0.256741i	$0.917351\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−151.228	+	87.3114i	−0.242741	+	0.140147i
$624$		0			0
$625$	−158.391	+	274.342i	−0.253426	+	0.438947i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	104.997i		−	0.166927i
$630$		0			0
$631$	794.037			1.25838			0.629189	−	0.777252i	$-0.283387\pi$
$631$	794.037			1.25838			0.629189	+	0.777252i	$0.283387\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−134.685	−	77.7602i	−0.212102	−	0.122457i
$636$		0			0
$637$	514.183	+	890.591i	0.807194	+	1.39810i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	753.063	−	434.781i	1.17483	−	0.678286i	0.220013	−	0.975497i	$-0.429390\pi$
$641$	753.063	−	434.781i	1.17483	−	0.678286i	0.954812	+	0.297211i	$0.0960566\pi$
$642$		0			0
$643$	31.2519	−	54.1299i	0.0486033	−	0.0841834i	−0.840700	−	0.541501i	$-0.817856\pi$
$643$	31.2519	−	54.1299i	0.0486033	−	0.0841834i	0.889304	+	0.457317i	$0.151190\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			761.439i			1.17688i	0.808542	+	0.588438i	$0.200257\pi$
$647$			761.439i			1.17688i	−0.808542	+	0.588438i	$0.799743\pi$
$648$		0			0
$649$	115.749			0.178350
$650$		0			0
$651$		0			0
$652$		0			0
$653$	129.622	+	74.8371i	0.198502	+	0.114605i	0.595956	−	0.803017i	$-0.296773\pi$
$653$	129.622	+	74.8371i	0.198502	+	0.114605i	−0.397455	+	0.917622i	$0.630106\pi$
$654$		0			0
$655$	8.54461	+	14.7997i	0.0130452	+	0.0225950i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	564.273	−	325.783i	0.856256	−	0.494360i	−0.00650063	−	0.999979i	$-0.502069\pi$
$659$	564.273	−	325.783i	0.856256	−	0.494360i	0.862757	+	0.505619i	$0.168736\pi$
$660$		0			0
$661$	−596.672	+	1033.47i	−0.902681	+	1.56349i	−0.0786818	+	0.996900i	$0.525071\pi$
$661$	−596.672	+	1033.47i	−0.902681	+	1.56349i	−0.824000	+	0.566590i	$0.808262\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	71.0685i		−	0.106870i
$666$		0			0
$667$	989.865			1.48405
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1124.19	−	649.051i	−1.67539	−	0.967290i
$672$		0			0
$673$	−74.7771	−	129.518i	−0.111110	−	0.192448i	0.805108	−	0.593128i	$-0.202107\pi$
$673$	−74.7771	−	129.518i	−0.111110	−	0.192448i	−0.916218	+	0.400680i	$0.868774\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−607.487	+	350.733i	−0.897322	+	0.518069i	−0.876331	−	0.481710i	$-0.840016\pi$
$677$	−607.487	+	350.733i	−0.897322	+	0.518069i	−0.0209919	+	0.999780i	$0.506682\pi$
$678$		0			0
$679$	3.92574	−	6.79958i	0.00578165	−	0.0100141i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			503.096i			0.736597i	0.929708	+	0.368299i	$0.120060\pi$
$683$			503.096i			0.736597i	−0.929708	+	0.368299i	$0.879940\pi$
$684$		0			0
$685$	100.648			0.146931
$686$		0			0
$687$		0			0
$688$		0			0
$689$	115.612	+	66.7487i	0.167797	+	0.0968776i
$690$		0			0
$691$	−329.413	−	570.561i	−0.476720	−	0.825703i	0.522924	−	0.852379i	$-0.324841\pi$
$691$	−329.413	−	570.561i	−0.476720	−	0.825703i	−0.999644	+	0.0266761i	$0.991508\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	430.633	−	248.626i	0.619615	−	0.357735i
$696$		0			0
$697$	−321.466	+	556.796i	−0.461214	+	0.798846i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			172.963i			0.246738i	0.992361	+	0.123369i	$0.0393698\pi$
$701$			172.963i			0.246738i	−0.992361	+	0.123369i	$0.960630\pi$
$702$		0			0
$703$	−179.985			−0.256024
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−134.574	−	77.6964i	−0.190345	−	0.109896i
$708$		0			0
$709$	527.267	+	913.254i	0.743677	+	1.28809i	0.950810	+	0.309774i	$0.100253\pi$
$709$	527.267	+	913.254i	0.743677	+	1.28809i	−0.207133	+	0.978313i	$0.566413\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	398.317	−	229.969i	0.558650	−	0.322537i
$714$		0			0
$715$	−288.501	+	499.699i	−0.403498	+	0.698879i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			1164.78i			1.62000i	0.586432	+	0.809998i	$0.300532\pi$
$719$			1164.78i			1.62000i	−0.586432	+	0.809998i	$0.699468\pi$
$720$		0			0
$721$	−42.5611			−0.0590306
$722$		0			0
$723$		0			0
$724$		0			0
$725$	531.983	+	307.141i	0.733770	+	0.423642i
$726$		0			0
$727$	492.209	+	852.530i	0.677041	+	1.17267i	0.975868	+	0.218362i	$0.0700712\pi$
$727$	492.209	+	852.530i	0.677041	+	1.17267i	−0.298827	+	0.954307i	$0.596595\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	781.639	−	451.280i	1.06927	−	0.617345i
$732$		0			0
$733$	−246.459	+	426.879i	−0.336233	+	0.582372i	−0.983721	−	0.179703i	$-0.942486\pi$
$733$	−246.459	+	426.879i	−0.336233	+	0.582372i	0.647488	+	0.762076i	$0.275820\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			497.355i			0.674837i
$738$		0			0
$739$	−571.150			−0.772869			−0.386435	−	0.922317i	$-0.626293\pi$
$739$	−571.150			−0.772869			−0.386435	+	0.922317i	$0.626293\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−910.255	−	525.536i	−1.22511	−	0.707316i	−0.259105	−	0.965849i	$-0.583427\pi$
$743$	−910.255	−	525.536i	−1.22511	−	0.707316i	−0.966002	+	0.258533i	$0.916761\pi$
$744$		0			0
$745$	−297.709	−	515.648i	−0.399610	−	0.692144i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	172.224	−	99.4334i	0.229938	−	0.132755i
$750$		0			0
$751$	42.3053	−	73.2749i	0.0563319	−	0.0975698i	−0.836484	−	0.547991i	$-0.815393\pi$
$751$	42.3053	−	73.2749i	0.0563319	−	0.0975698i	0.892816	+	0.450421i	$0.148726\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			322.705i			0.427423i
$756$		0			0
$757$	−1007.63			−1.33109			−0.665543	−	0.746360i	$-0.731800\pi$
$757$	−1007.63			−1.33109			−0.665543	+	0.746360i	$0.731800\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−393.981	−	227.465i	−0.517715	−	0.298903i	0.218285	−	0.975885i	$-0.429954\pi$
$761$	−393.981	−	227.465i	−0.517715	−	0.298903i	−0.735999	+	0.676983i	$0.763287\pi$
$762$		0			0
$763$	−43.2221	−	74.8629i	−0.0566476	−	0.0981165i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−177.053	+	102.222i	−0.230838	+	0.133275i
$768$		0			0
$769$	352.232	−	610.084i	0.458039	−	0.793347i	−0.540818	−	0.841139i	$-0.681885\pi$
$769$	352.232	−	610.084i	0.458039	−	0.793347i	0.998857	+	0.0477927i	$0.0152187\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			1021.43i			1.32138i	0.750658	+	0.660691i	$0.229737\pi$
$773$			1021.43i			1.32138i	−0.750658	+	0.660691i	$0.770263\pi$
$774$		0			0
$775$	285.424			0.368289
$776$		0			0
$777$		0			0
$778$		0			0
$779$	954.453	+	551.054i	1.22523	+	0.707386i
$780$		0			0
$781$	−114.801	−	198.840i	−0.146992	−	0.254597i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	433.974	−	250.555i	0.552833	−	0.319178i
$786$		0			0
$787$	−202.007	+	349.886i	−0.256680	+	0.444582i	−0.965350	−	0.260957i	$-0.915962\pi$
$787$	−202.007	+	349.886i	−0.256680	+	0.444582i	0.708671	+	0.705539i	$0.249295\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	185.603i		−	0.234643i
$792$		0			0
$793$	2292.79			2.89129
$794$		0			0
$795$		0			0
$796$		0			0
$797$	765.042	+	441.697i	0.959902	+	0.554200i	0.896143	−	0.443766i	$-0.146358\pi$
$797$	765.042	+	441.697i	0.959902	+	0.554200i	0.0637592	+	0.997965i	$0.479691\pi$
$798$		0			0
$799$	−419.725	−	726.985i	−0.525313	−	0.909869i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−742.708	+	428.803i	−0.924917	+	0.534001i
$804$		0			0
$805$	54.2827	−	94.0204i	0.0674320	−	0.116796i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	372.575i		−	0.460537i	−0.973127	−	0.230269i	$-0.926040\pi$
$809$		−	372.575i		−	0.460537i	0.973127	−	0.230269i	$-0.0739605\pi$
$810$		0			0
$811$	267.519			0.329863			0.164932	−	0.986305i	$-0.447260\pi$
$811$	267.519			0.329863			0.164932	+	0.986305i	$0.447260\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	201.244	+	116.188i	0.246925	+	0.142562i
$816$		0			0
$817$	−773.578	−	1339.88i	−0.946852	−	1.64000i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	574.911	−	331.925i	0.700257	−	0.404293i	−0.107186	−	0.994239i	$-0.534184\pi$
$821$	574.911	−	331.925i	0.700257	−	0.404293i	0.807443	+	0.589946i	$0.200851\pi$
$822$		0			0
$823$	468.171	−	810.896i	0.568859	−	0.985292i	−0.427820	−	0.903864i	$-0.640718\pi$
$823$	468.171	−	810.896i	0.568859	−	0.985292i	0.996679	−	0.0814286i	$-0.0259483\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	499.832i		−	0.604392i	−0.953246	−	0.302196i	$-0.902280\pi$
$827$		−	499.832i		−	0.604392i	0.953246	−	0.302196i	$-0.0977196\pi$
$828$		0			0
$829$	667.578			0.805280			0.402640	−	0.915358i	$-0.368093\pi$
$829$	667.578			0.805280			0.402640	+	0.915358i	$0.368093\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−512.025	−	295.618i	−0.614676	−	0.354883i
$834$		0			0
$835$	45.7220	+	79.1929i	0.0547569	+	0.0948418i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	64.1295	−	37.0252i	0.0764356	−	0.0441301i	−0.461295	−	0.887247i	$-0.652615\pi$
$839$	64.1295	−	37.0252i	0.0764356	−	0.0441301i	0.537731	+	0.843117i	$0.319282\pi$
$840$		0			0
$841$	22.5264	−	39.0169i	0.0267853	−	0.0463935i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	666.116i		−	0.788303i
$846$		0			0
$847$	55.3110			0.0653023
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−238.112	−	137.474i	−0.279802	−	0.161544i
$852$		0			0
$853$	−553.775	−	959.167i	−0.649209	−	1.12446i	−0.983312	−	0.181927i	$-0.941767\pi$
$853$	−553.775	−	959.167i	−0.649209	−	1.12446i	0.334103	−	0.942537i	$-0.391567\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−687.370	+	396.854i	−0.802066	+	0.463073i	−0.844193	−	0.536039i	$-0.819920\pi$
$857$	−687.370	+	396.854i	−0.802066	+	0.463073i	0.0421271	+	0.999112i	$0.486587\pi$
$858$		0			0
$859$	121.830	−	211.016i	0.141828	−	0.245653i	−0.786357	−	0.617772i	$-0.788035\pi$
$859$	121.830	−	211.016i	0.141828	−	0.245653i	0.928185	+	0.372119i	$0.121369\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	841.279i		−	0.974830i	−0.873170	−	0.487415i	$-0.837940\pi$
$863$		−	841.279i		−	0.974830i	0.873170	−	0.487415i	$-0.162060\pi$
$864$		0			0
$865$	−611.167			−0.706552
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−288.363	−	166.486i	−0.331833	−	0.191584i
$870$		0			0
$871$	−439.230	−	760.768i	−0.504282	−	0.873442i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	129.030	−	74.4953i	0.147462	−	0.0851375i
$876$		0			0
$877$	302.656	−	524.216i	0.345104	−	0.597738i	−0.640269	−	0.768151i	$-0.721177\pi$
$877$	302.656	−	524.216i	0.345104	−	0.597738i	0.985373	+	0.170413i	$0.0545103\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			820.188i			0.930974i	0.885055	+	0.465487i	$0.154121\pi$
$881$			820.188i			0.930974i	−0.885055	+	0.465487i	$0.845879\pi$
$882$		0			0
$883$	−623.820			−0.706478			−0.353239	−	0.935533i	$-0.614920\pi$
$883$	−623.820			−0.706478			−0.353239	+	0.935533i	$0.614920\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−212.242	−	122.538i	−0.239281	−	0.138149i	0.375565	−	0.926796i	$-0.377449\pi$
$887$	−212.242	−	122.538i	−0.239281	−	0.138149i	−0.614846	+	0.788647i	$0.710782\pi$
$888$		0			0
$889$	−58.1803	−	100.771i	−0.0654447	−	0.113353i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1246.19	+	719.488i	−1.39551	+	0.805698i
$894$		0			0
$895$	−203.261	+	352.058i	−0.227107	+	0.393361i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	411.702i		−	0.457955i
$900$		0			0
$901$	−76.7513			−0.0851845
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−161.710	−	93.3632i	−0.178685	−	0.103164i
$906$		0			0
$907$	−109.071	−	188.917i	−0.120255	−	0.208287i	0.799613	−	0.600515i	$-0.205038\pi$
$907$	−109.071	−	188.917i	−0.120255	−	0.208287i	−0.919868	+	0.392228i	$0.871704\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	558.980	−	322.727i	0.613589	−	0.354256i	−0.160780	−	0.986990i	$-0.551401\pi$
$911$	558.980	−	322.727i	0.613589	−	0.354256i	0.774369	+	0.632735i	$0.218068\pi$
$912$		0			0
$913$	−151.894	+	263.088i	−0.166368	+	0.288157i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			12.7862i			0.0139435i
$918$		0			0
$919$	−1567.66			−1.70583			−0.852917	−	0.522047i	$-0.825169\pi$
$919$	−1567.66			−1.70583			−0.852917	+	0.522047i	$0.825169\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	351.204	+	202.768i	0.380503	+	0.219684i
$924$		0			0
$925$	−85.3123	−	147.765i	−0.0922296	−	0.159746i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−78.1550	+	45.1228i	−0.0841281	+	0.0485714i	−0.541474	−	0.840718i	$-0.682133\pi$
$929$	−78.1550	+	45.1228i	−0.0841281	+	0.0485714i	0.457346	+	0.889289i	$0.348800\pi$
$930$		0			0
$931$	−506.745	+	877.708i	−0.544302	+	0.942758i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	331.734i		−	0.354796i
$936$		0			0
$937$	−593.849			−0.633777			−0.316889	−	0.948463i	$-0.602638\pi$
$937$	−593.849			−0.633777			−0.316889	+	0.948463i	$0.602638\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	40.2459	+	23.2360i	0.0427693	+	0.0246928i	0.521232	−	0.853415i	$-0.325473\pi$
$941$	40.2459	+	23.2360i	0.0427693	+	0.0246928i	−0.478463	+	0.878108i	$0.658806\pi$
$942$		0			0
$943$	841.800	+	1458.04i	0.892683	+	1.54617i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1614.20	+	931.957i	−1.70454	+	0.984115i	−0.763502	+	0.645806i	$0.776522\pi$
$947$	−1614.20	+	931.957i	−1.70454	+	0.984115i	−0.941035	+	0.338309i	$0.890145\pi$
$948$		0			0
$949$	757.378	−	1311.82i	0.798080	−	1.38232i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	293.678i		−	0.308162i	−0.988058	−	0.154081i	$-0.950758\pi$
$953$		−	293.678i		−	0.308162i	0.988058	−	0.154081i	$-0.0492416\pi$
$954$		0			0
$955$	−108.321			−0.113425
$956$		0			0
$957$		0			0
$958$		0			0
$959$	65.2158	+	37.6523i	0.0680039	+	0.0392621i
$960$		0			0
$961$	384.852	+	666.583i	0.400470	+	0.693635i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−107.732	+	62.1991i	−0.111639	+	0.0644550i
$966$		0			0
$967$	56.1241	−	97.2098i	0.0580394	−	0.100527i	−0.835546	−	0.549421i	$-0.814848\pi$
$967$	56.1241	−	97.2098i	0.0580394	−	0.100527i	0.893585	+	0.448894i	$0.148182\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1539.13i		−	1.58510i	−0.609807	−	0.792550i	$-0.708753\pi$
$971$		−	1539.13i		−	1.58510i	0.609807	−	0.792550i	$-0.291247\pi$
$972$		0			0
$973$	372.044			0.382368
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−294.065	−	169.778i	−0.300987	−	0.173775i	0.341899	−	0.939737i	$-0.388930\pi$
$977$	−294.065	−	169.778i	−0.300987	−	0.173775i	−0.642886	+	0.765962i	$0.722263\pi$
$978$		0			0
$979$	698.623	+	1210.05i	0.713609	+	1.23601i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	892.130	−	515.072i	0.907559	−	0.523979i	0.0279139	−	0.999610i	$-0.491114\pi$
$983$	892.130	−	515.072i	0.907559	−	0.523979i	0.879645	+	0.475631i	$0.157780\pi$
$984$		0			0
$985$	49.6075	−	85.9228i	0.0503630	−	0.0872312i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	2363.46i		−	2.38975i
$990$		0			0
$991$	439.103			0.443091			0.221546	−	0.975150i	$-0.428890\pi$
$991$	439.103			0.443091			0.221546	+	0.975150i	$0.428890\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−53.4094	−	30.8359i	−0.0536777	−	0.0309909i
$996$		0			0
$997$	−381.047	−	659.993i	−0.382194	−	0.661979i	0.609182	−	0.793031i	$-0.291498\pi$
$997$	−381.047	−	659.993i	−0.382194	−	0.661979i	−0.991376	+	0.131051i	$0.958165\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.q.i.449.3		8
3.2	odd	2		576.3.q.j.257.4		8
4.3	odd	2		1728.3.q.j.449.3		8
8.3	odd	2		216.3.m.b.17.2		8
8.5	even	2		432.3.q.e.17.2		8
9.2	odd	6	inner	1728.3.q.i.1601.3		8
9.7	even	3		576.3.q.j.65.4		8
12.11	even	2		576.3.q.i.257.1		8
24.5	odd	2		144.3.q.e.113.1		8
24.11	even	2		72.3.m.b.41.4	✓	8
36.7	odd	6		576.3.q.i.65.1		8
36.11	even	6		1728.3.q.j.1601.3		8
72.5	odd	6		1296.3.e.i.161.3		8
72.11	even	6		216.3.m.b.89.2		8
72.13	even	6		1296.3.e.i.161.6		8
72.29	odd	6		432.3.q.e.305.2		8
72.43	odd	6		72.3.m.b.65.4	yes	8
72.59	even	6		648.3.e.c.161.3		8
72.61	even	6		144.3.q.e.65.1		8
72.67	odd	6		648.3.e.c.161.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.b.41.4	✓	8	24.11	even	2
72.3.m.b.65.4	yes	8	72.43	odd	6
144.3.q.e.65.1		8	72.61	even	6
144.3.q.e.113.1		8	24.5	odd	2
216.3.m.b.17.2		8	8.3	odd	2
216.3.m.b.89.2		8	72.11	even	6
432.3.q.e.17.2		8	8.5	even	2
432.3.q.e.305.2		8	72.29	odd	6
576.3.q.i.65.1		8	36.7	odd	6
576.3.q.i.257.1		8	12.11	even	2
576.3.q.j.65.4		8	9.7	even	3
576.3.q.j.257.4		8	3.2	odd	2
648.3.e.c.161.3		8	72.59	even	6
648.3.e.c.161.6		8	72.67	odd	6
1296.3.e.i.161.3		8	72.5	odd	6
1296.3.e.i.161.6		8	72.13	even	6
1728.3.q.i.449.3		8	1.1	even	1	trivial
1728.3.q.i.1601.3		8	9.2	odd	6	inner
1728.3.q.j.449.3		8	4.3	odd	2
1728.3.q.j.1601.3		8	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 + 1.04444i) q^{5} +(0.781452 + 1.35351i) q^{7} +O(q^{10})\)	\(q+(1.80902 + 1.04444i) q^{5} +(0.781452 + 1.35351i) q^{7} +(10.8302 - 6.25280i) q^{11} +(-11.0441 + 19.1289i) q^{13} -12.6991i q^{17} -21.7686 q^{19} +(-28.7989 - 16.6271i) q^{23} +(-10.3183 - 17.8718i) q^{25} +(-25.7787 + 14.8833i) q^{29} +(-6.91549 + 11.9780i) q^{31} +3.26472i q^{35} +8.26807 q^{37} +(-43.8453 - 25.3141i) q^{41} +(35.5364 + 61.5508i) q^{43} +(57.2470 - 33.0516i) q^{47} +(23.2787 - 40.3198i) q^{49} -6.04384i q^{53} +26.1227 q^{55} +(8.01575 + 4.62789i) q^{59} +(-51.9009 - 89.8950i) q^{61} +(-39.9580 + 23.0698i) q^{65} +(-19.8853 + 34.4424i) q^{67} -18.3599i q^{71} -68.5777 q^{73} +(16.9265 + 9.77252i) q^{77} +(-13.3130 - 23.0587i) q^{79} +(-21.0376 + 12.1461i) q^{83} +(13.2634 - 22.9729i) q^{85} +111.730i q^{89} -34.5217 q^{91} +(-39.3800 - 22.7360i) q^{95} +(-2.51182 - 4.35061i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{5} - 6 q^{7}+O(q^{10}) \) 8 * q - 6 * q^5 - 6 * q^7	\( 8 q - 6 q^{5} - 6 q^{7} - 36 q^{11} - 14 q^{13} + 4 q^{19} - 102 q^{23} + 10 q^{25} - 114 q^{29} + 50 q^{31} - 120 q^{37} - 264 q^{41} - 28 q^{43} + 150 q^{47} + 94 q^{49} + 244 q^{55} + 108 q^{59} - 14 q^{61} + 198 q^{65} - 20 q^{67} - 76 q^{73} + 66 q^{77} - 26 q^{79} - 246 q^{83} + 224 q^{85} + 108 q^{91} - 456 q^{95} - 236 q^{97}+O(q^{100}) \) 8 * q - 6 * q^5 - 6 * q^7 - 36 * q^11 - 14 * q^13 + 4 * q^19 - 102 * q^23 + 10 * q^25 - 114 * q^29 + 50 * q^31 - 120 * q^37 - 264 * q^41 - 28 * q^43 + 150 * q^47 + 94 * q^49 + 244 * q^55 + 108 * q^59 - 14 * q^61 + 198 * q^65 - 20 * q^67 - 76 * q^73 + 66 * q^77 - 26 * q^79 - 246 * q^83 + 224 * q^85 + 108 * q^91 - 456 * q^95 - 236 * q^97

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