LMFDB - Embedded newform 1728.3.o.e.127.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1728,3,Mod(127,1728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1728.127"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4])) N = Newforms(chi, 3, names="a")

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

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,3,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$-0.385731i$ of defining polynomial
Character	$\chi$	$=$	1728.127
Dual form			1728.3.o.e.1279.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.454613 - 0.787412i) q^{5} +(6.10709 + 3.52593i) q^{7} +(6.96661 + 4.02218i) q^{11} +(-3.35952 - 5.81886i) q^{13} +26.3462 q^{17} -20.5603i q^{19} +(-21.8305 + 12.6038i) q^{23} +(12.0867 - 20.9347i) q^{25} +(15.1693 - 26.2741i) q^{29} +(0.120040 - 0.0693050i) q^{31} -6.41173i q^{35} -69.7588 q^{37} +(29.3794 + 50.8866i) q^{41} +(2.45853 + 1.41943i) q^{43} +(70.7583 + 40.8523i) q^{47} +(0.364383 + 0.631130i) q^{49} -30.0259 q^{53} -7.31413i q^{55} +(77.1442 - 44.5392i) q^{59} +(-24.0688 + 41.6885i) q^{61} +(-3.05456 + 5.29066i) q^{65} +(44.0829 - 25.4513i) q^{67} -68.4355i q^{71} -22.1474 q^{73} +(28.3638 + 49.1276i) q^{77} +(34.4343 + 19.8807i) q^{79} +(23.0801 + 13.3253i) q^{83} +(-11.9773 - 20.7453i) q^{85} +25.7926 q^{89} -47.3818i q^{91} +(-16.1894 + 9.34695i) q^{95} +(-52.3697 + 90.7070i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} - 3 q^{7} - 18 q^{11} - 5 q^{13} - 6 q^{17} - 81 q^{23} - 23 q^{25} + 69 q^{29} - 45 q^{31} + 20 q^{37} - 54 q^{41} + 207 q^{47} + 41 q^{49} - 252 q^{53} + 306 q^{59} - 7 q^{61} - 93 q^{65}+ \cdots - 10 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 - 3 * q^7 - 18 * q^11 - 5 * q^13 - 6 * q^17 - 81 * q^23 - 23 * q^25 + 69 * q^29 - 45 * q^31 + 20 * q^37 - 54 * q^41 + 207 * q^47 + 41 * q^49 - 252 * q^53 + 306 * q^59 - 7 * q^61 - 93 * q^65 + 12 * q^67 + 74 * q^73 + 207 * q^77 - 33 * q^79 - 549 * q^83 + 30 * q^85 + 168 * q^89 - 684 * q^95 - 10 * q^97

Character values

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

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.454613	−	0.787412i	−0.0909226	−	0.157482i	0.816977	−	0.576670i	$-0.195648\pi$
$5$	−0.454613	−	0.787412i	−0.0909226	−	0.157482i	−0.907900	+	0.419188i	$0.862315\pi$
$6$		0			0
$7$	6.10709	+	3.52593i	0.872442	+	0.503704i	0.868159	−	0.496286i	$-0.165303\pi$
$7$	6.10709	+	3.52593i	0.872442	+	0.503704i	0.00428285	+	0.999991i	$0.498637\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	6.96661	+	4.02218i	0.633329	+	0.365652i	0.782040	−	0.623228i	$-0.214179\pi$
$11$	6.96661	+	4.02218i	0.633329	+	0.365652i	−0.148711	+	0.988881i	$0.547513\pi$
$12$		0			0
$13$	−3.35952	−	5.81886i	−0.258425	−	0.447605i	0.707395	−	0.706818i	$-0.249870\pi$
$13$	−3.35952	−	5.81886i	−0.258425	−	0.447605i	−0.965820	+	0.259213i	$0.916537\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	26.3462			1.54978			0.774889	−	0.632097i	$-0.217806\pi$
$17$	26.3462			1.54978			0.774889	+	0.632097i	$0.217806\pi$
$18$		0			0
$19$		−	20.5603i		−	1.08212i	−0.840984	−	0.541059i	$-0.818023\pi$
$19$		−	20.5603i		−	1.08212i	0.840984	−	0.541059i	$-0.181977\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−21.8305	+	12.6038i	−0.949150	+	0.547992i	−0.892817	−	0.450420i	$-0.851274\pi$
$23$	−21.8305	+	12.6038i	−0.949150	+	0.547992i	−0.0563333	+	0.998412i	$0.517941\pi$
$24$		0			0
$25$	12.0867	−	20.9347i	0.483466	−	0.837388i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	15.1693	−	26.2741i	0.523081	−	0.906002i	−0.476558	−	0.879143i	$-0.658116\pi$
$29$	15.1693	−	26.2741i	0.523081	−	0.906002i	0.999639	−	0.0268597i	$-0.00855072\pi$
$30$		0			0
$31$	0.120040	−	0.0693050i	0.00387225	−	0.00223565i	−0.498063	−	0.867141i	$-0.665955\pi$
$31$	0.120040	−	0.0693050i	0.00387225	−	0.00223565i	0.501935	+	0.864905i	$0.332622\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	6.41173i		−	0.183192i
$36$		0			0
$37$	−69.7588			−1.88537			−0.942687	−	0.333679i	$-0.891710\pi$
$37$	−69.7588			−1.88537			−0.942687	+	0.333679i	$0.891710\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	29.3794	+	50.8866i	0.716571	+	1.24114i	0.962351	+	0.271811i	$0.0876227\pi$
$41$	29.3794	+	50.8866i	0.716571	+	1.24114i	−0.245780	+	0.969326i	$0.579044\pi$
$42$		0			0
$43$	2.45853	+	1.41943i	0.0571751	+	0.0330100i	0.528315	−	0.849048i	$-0.322824\pi$
$43$	2.45853	+	1.41943i	0.0571751	+	0.0330100i	−0.471140	+	0.882058i	$0.656157\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	70.7583	+	40.8523i	1.50550	+	0.869198i	0.999980	+	0.00638063i	$0.00203103\pi$
$47$	70.7583	+	40.8523i	1.50550	+	0.869198i	0.505516	+	0.862817i	$0.331302\pi$
$48$		0			0
$49$	0.364383	+	0.631130i	0.00743639	+	0.0128802i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−30.0259			−0.566526			−0.283263	−	0.959042i	$-0.591417\pi$
$53$	−30.0259			−0.566526			−0.283263	+	0.959042i	$0.591417\pi$
$54$		0			0
$55$		−	7.31413i		−	0.132984i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	77.1442	−	44.5392i	1.30753	−	0.754902i	0.325846	−	0.945423i	$-0.394351\pi$
$59$	77.1442	−	44.5392i	1.30753	−	0.754902i	0.981683	+	0.190520i	$0.0610175\pi$
$60$		0			0
$61$	−24.0688	+	41.6885i	−0.394571	+	0.683417i	−0.993046	−	0.117724i	$-0.962440\pi$
$61$	−24.0688	+	41.6885i	−0.394571	+	0.683417i	0.598475	+	0.801141i	$0.295774\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.05456	+	5.29066i	−0.0469933	+	0.0813948i
$66$		0			0
$67$	44.0829	−	25.4513i	0.657953	−	0.379870i	−0.133543	−	0.991043i	$-0.542636\pi$
$67$	44.0829	−	25.4513i	0.657953	−	0.379870i	0.791497	+	0.611173i	$0.209302\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	68.4355i		−	0.963881i	−0.876204	−	0.481940i	$-0.839932\pi$
$71$		−	68.4355i		−	0.963881i	0.876204	−	0.481940i	$-0.160068\pi$
$72$		0			0
$73$	−22.1474			−0.303389			−0.151695	−	0.988427i	$-0.548473\pi$
$73$	−22.1474			−0.303389			−0.151695	+	0.988427i	$0.548473\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	28.3638	+	49.1276i	0.368362	+	0.638021i
$78$		0			0
$79$	34.4343	+	19.8807i	0.435877	+	0.251654i	0.701847	−	0.712327i	$-0.252359\pi$
$79$	34.4343	+	19.8807i	0.435877	+	0.251654i	−0.265970	+	0.963981i	$0.585692\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	23.0801	+	13.3253i	0.278073	+	0.160546i	0.632551	−	0.774519i	$-0.282008\pi$
$83$	23.0801	+	13.3253i	0.278073	+	0.160546i	−0.354478	+	0.935065i	$0.615341\pi$
$84$		0			0
$85$	−11.9773	−	20.7453i	−0.140910	−	0.244063i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	25.7926			0.289804			0.144902	−	0.989446i	$-0.453713\pi$
$89$	25.7926			0.289804			0.144902	+	0.989446i	$0.453713\pi$
$90$		0			0
$91$		−	47.3818i		−	0.520679i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−16.1894	+	9.34695i	−0.170415	+	0.0983890i
$96$		0			0
$97$	−52.3697	+	90.7070i	−0.539894	+	0.935123i	0.459016	+	0.888428i	$0.348202\pi$
$97$	−52.3697	+	90.7070i	−0.539894	+	0.935123i	−0.998909	+	0.0466950i	$0.985131\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	20.4790	−	35.4707i	0.202763	−	0.351195i	−0.746655	−	0.665212i	$-0.768341\pi$
$101$	20.4790	−	35.4707i	0.202763	−	0.351195i	0.949418	+	0.314016i	$0.101675\pi$
$102$		0			0
$103$	125.278	−	72.3293i	1.21629	−	0.702227i	0.252169	−	0.967683i	$-0.418856\pi$
$103$	125.278	−	72.3293i	1.21629	−	0.702227i	0.964123	+	0.265456i	$0.0855227\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			177.858i			1.66222i	0.556105	+	0.831112i	$0.312295\pi$
$107$			177.858i			1.66222i	−0.556105	+	0.831112i	$0.687705\pi$
$108$		0			0
$109$	142.616			1.30840			0.654200	−	0.756322i	$-0.273006\pi$
$109$	142.616			1.30840			0.654200	+	0.756322i	$0.273006\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−100.147	−	173.459i	−0.886254	−	1.53504i	−0.844270	−	0.535918i	$-0.819966\pi$
$113$	−100.147	−	173.459i	−0.886254	−	1.53504i	−0.0419835	−	0.999118i	$-0.513368\pi$
$114$		0			0
$115$	19.8488	+	11.4597i	0.172598	+	0.0996497i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	160.899	+	92.8950i	1.35209	+	0.780630i
$120$		0			0
$121$	−28.1442	−	48.7472i	−0.232597	−	0.402869i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−44.7096			−0.357677
$126$		0			0
$127$		−	181.723i		−	1.43089i	−0.698670	−	0.715445i	$-0.746224\pi$
$127$		−	181.723i		−	1.43089i	0.698670	−	0.715445i	$-0.253776\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	52.9361	−	30.5627i	0.404092	−	0.233303i	−0.284156	−	0.958778i	$-0.591713\pi$
$131$	52.9361	−	30.5627i	0.404092	−	0.233303i	0.688248	+	0.725475i	$0.258380\pi$
$132$		0			0
$133$	72.4940	−	125.563i	0.545068	−	0.944085i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−18.1131	+	31.3729i	−0.132213	+	0.228999i	−0.924529	−	0.381111i	$-0.875542\pi$
$137$	−18.1131	+	31.3729i	−0.132213	+	0.228999i	0.792317	+	0.610110i	$0.208875\pi$
$138$		0			0
$139$	154.652	−	89.2885i	1.11261	−	0.642363i	0.173103	−	0.984904i	$-0.444621\pi$
$139$	154.652	−	89.2885i	1.11261	−	0.642363i	0.939503	+	0.342541i	$0.111287\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	54.0504i		−	0.377975i
$144$		0			0
$145$	−27.5847			−0.190239
$146$		0			0
$147$		0			0
$148$		0			0
$149$	120.043	+	207.921i	0.805660	+	1.39544i	0.915845	+	0.401533i	$0.131522\pi$
$149$	120.043	+	207.921i	0.805660	+	1.39544i	−0.110185	+	0.993911i	$0.535144\pi$
$150$		0			0
$151$	−98.1393	−	56.6607i	−0.649929	−	0.375237i	0.138500	−	0.990362i	$-0.455772\pi$
$151$	−98.1393	−	56.6607i	−0.649929	−	0.375237i	−0.788429	+	0.615126i	$0.789105\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.109143	−	0.0630139i	−0.000704150	−	0.000406541i
$156$		0			0
$157$	60.3604	+	104.547i	0.384461	+	0.665907i	0.991694	−	0.128617i	$-0.0410538\pi$
$157$	60.3604	+	104.547i	0.384461	+	0.665907i	−0.607233	+	0.794524i	$0.707720\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−177.761			−1.10410
$162$		0			0
$163$		−	20.3498i		−	0.124845i	−0.998050	−	0.0624226i	$-0.980117\pi$
$163$		−	20.3498i		−	0.124845i	0.998050	−	0.0624226i	$-0.0198827\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	151.530	−	87.4858i	0.907365	−	0.523867i	0.0277823	−	0.999614i	$-0.491155\pi$
$167$	151.530	−	87.4858i	0.907365	−	0.523867i	0.879582	+	0.475747i	$0.157822\pi$
$168$		0			0
$169$	61.9272	−	107.261i	0.366433	−	0.634681i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	55.9175	−	96.8520i	0.323223	−	0.559838i	−0.657928	−	0.753080i	$-0.728567\pi$
$173$	55.9175	−	96.8520i	0.323223	−	0.559838i	0.981151	+	0.193243i	$0.0619004\pi$
$174$		0			0
$175$	147.629	−	85.2334i	0.843592	−	0.487048i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			18.6939i			0.104435i	0.998636	+	0.0522176i	$0.0166289\pi$
$179$			18.6939i			0.104435i	−0.998636	+	0.0522176i	$0.983371\pi$
$180$		0			0
$181$	98.0536			0.541733			0.270866	−	0.962617i	$-0.412690\pi$
$181$	98.0536			0.541733			0.270866	+	0.962617i	$0.412690\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	31.7132	+	54.9290i	0.171423	+	0.296913i
$186$		0			0
$187$	183.544	+	105.969i	0.981519	+	0.566680i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	240.713	+	138.976i	1.26028	+	0.727621i	0.973128	−	0.230265i	$-0.0739592\pi$
$191$	240.713	+	138.976i	1.26028	+	0.727621i	0.287149	+	0.957886i	$0.407293\pi$
$192$		0			0
$193$	81.1285	+	140.519i	0.420355	+	0.728076i	0.995974	−	0.0896419i	$-0.0285722\pi$
$193$	81.1285	+	140.519i	0.420355	+	0.728076i	−0.575619	+	0.817718i	$0.695239\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−106.182			−0.538993			−0.269496	−	0.963001i	$-0.586857\pi$
$197$	−106.182			−0.538993			−0.269496	+	0.963001i	$0.586857\pi$
$198$		0			0
$199$		−	63.3880i		−	0.318532i	−0.987236	−	0.159266i	$-0.949087\pi$
$199$		−	63.3880i		−	0.318532i	0.987236	−	0.159266i	$-0.0509128\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	185.281	−	106.972i	0.912715	−	0.526956i
$204$		0			0
$205$	26.7125	−	46.2674i	0.130305	−	0.225695i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	82.6970	−	143.235i	0.395679	−	0.685337i
$210$		0			0
$211$	−4.98019	+	2.87531i	−0.0236028	+	0.0136271i	−0.511755	−	0.859131i	$-0.671004\pi$
$211$	−4.98019	+	2.87531i	−0.0236028	+	0.0136271i	0.488152	+	0.872759i	$0.337671\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	2.58117i		−	0.0120054i
$216$		0			0
$217$	0.977459			0.00450442
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−88.5107	−	153.305i	−0.400501	−	0.693688i
$222$		0			0
$223$	179.786	+	103.799i	0.806215	+	0.465469i	0.845640	−	0.533754i	$-0.179219\pi$
$223$	179.786	+	103.799i	0.806215	+	0.465469i	−0.0394246	+	0.999223i	$0.512552\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	78.8889	+	45.5465i	0.347528	+	0.200646i	0.663596	−	0.748091i	$-0.269029\pi$
$227$	78.8889	+	45.5465i	0.347528	+	0.200646i	−0.316068	+	0.948737i	$0.602363\pi$
$228$		0			0
$229$	−2.04945	−	3.54974i	−0.00894954	−	0.0155011i	0.861516	−	0.507731i	$-0.169515\pi$
$229$	−2.04945	−	3.54974i	−0.00894954	−	0.0155011i	−0.870465	+	0.492229i	$0.836182\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−171.761			−0.737170			−0.368585	−	0.929594i	$-0.620158\pi$
$233$	−171.761			−0.737170			−0.368585	+	0.929594i	$0.620158\pi$
$234$		0			0
$235$		−	74.2879i		−	0.316119i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−78.9068	+	45.5569i	−0.330154	+	0.190614i	−0.655909	−	0.754840i	$-0.727715\pi$
$239$	−78.9068	+	45.5569i	−0.330154	+	0.190614i	0.325755	+	0.945454i	$0.394381\pi$
$240$		0			0
$241$	37.2352	−	64.4933i	0.154503	−	0.267607i	−0.778375	−	0.627800i	$-0.783956\pi$
$241$	37.2352	−	64.4933i	0.154503	−	0.267607i	0.932878	+	0.360193i	$0.117289\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.331306	−	0.573840i	0.00135227	−	0.00234220i
$246$		0			0
$247$	−119.637	+	69.0726i	−0.484362	+	0.279646i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			216.868i			0.864014i	0.901870	+	0.432007i	$0.142194\pi$
$251$			216.868i			0.864014i	−0.901870	+	0.432007i	$0.857806\pi$
$252$		0			0
$253$	−202.779			−0.801499
$254$		0			0
$255$		0			0
$256$		0			0
$257$	143.577	+	248.682i	0.558665	+	0.967636i	0.997608	+	0.0691212i	$0.0220195\pi$
$257$	143.577	+	248.682i	0.558665	+	0.967636i	−0.438943	+	0.898515i	$0.644647\pi$
$258$		0			0
$259$	−426.023	−	245.965i	−1.64488	−	0.949671i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−361.740	−	208.851i	−1.37544	−	0.794108i	−0.383830	−	0.923404i	$-0.625395\pi$
$263$	−361.740	−	208.851i	−1.37544	−	0.794108i	−0.991606	+	0.129295i	$0.958728\pi$
$264$		0			0
$265$	13.6502	+	23.6428i	0.0515100	+	0.0892180i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−489.868			−1.82107			−0.910535	−	0.413433i	$-0.864330\pi$
$269$	−489.868			−1.82107			−0.910535	+	0.413433i	$0.864330\pi$
$270$		0			0
$271$			325.133i			1.19975i	0.800093	+	0.599876i	$0.204784\pi$
$271$			325.133i			1.19975i	−0.800093	+	0.599876i	$0.795216\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	168.406	−	97.2293i	0.612386	−	0.353561i
$276$		0			0
$277$	−86.0882	+	149.109i	−0.310788	+	0.538300i	−0.978533	−	0.206089i	$-0.933926\pi$
$277$	−86.0882	+	149.109i	−0.310788	+	0.538300i	0.667745	+	0.744390i	$0.267260\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	60.1019	−	104.100i	0.213886	−	0.370461i	−0.739042	−	0.673660i	$-0.764721\pi$
$281$	60.1019	−	104.100i	0.213886	−	0.370461i	0.952927	+	0.303199i	$0.0980546\pi$
$282$		0			0
$283$	95.8910	−	55.3627i	0.338837	−	0.195628i	−0.320920	−	0.947106i	$-0.603992\pi$
$283$	95.8910	−	55.3627i	0.338837	−	0.195628i	0.659758	+	0.751478i	$0.270659\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			414.359i			1.44376i
$288$		0			0
$289$	405.124			1.40181
$290$		0			0
$291$		0			0
$292$		0			0
$293$	42.3365	+	73.3289i	0.144493	+	0.250269i	0.929184	−	0.369618i	$-0.120512\pi$
$293$	42.3365	+	73.3289i	0.144493	+	0.250269i	−0.784691	+	0.619888i	$0.787178\pi$
$294$		0			0
$295$	−70.1415	−	40.4962i	−0.237768	−	0.137275i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	146.680	+	84.6856i	0.490568	+	0.283229i
$300$		0			0
$301$	10.0096	+	17.3372i	0.0332546	+	0.0575987i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	43.7680			0.143502
$306$		0			0
$307$		−	220.477i		−	0.718167i	−0.933306	−	0.359083i	$-0.883089\pi$
$307$		−	220.477i		−	0.718167i	0.933306	−	0.359083i	$-0.116911\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	268.968	−	155.289i	0.864849	−	0.499321i	−0.000784168	−	1.00000i	$-0.500250\pi$
$311$	268.968	−	155.289i	0.864849	−	0.499321i	0.865633	+	0.500679i	$0.166916\pi$
$312$		0			0
$313$	−65.5787	+	113.586i	−0.209516	+	0.362893i	−0.951562	−	0.307456i	$-0.900522\pi$
$313$	−65.5787	+	113.586i	−0.209516	+	0.362893i	0.742046	+	0.670349i	$0.233856\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	169.980	−	294.414i	0.536214	−	0.928750i	−0.462889	−	0.886416i	$-0.653187\pi$
$317$	169.980	−	294.414i	0.536214	−	0.928750i	0.999104	−	0.0423342i	$-0.0134794\pi$
$318$		0			0
$319$	211.358	−	122.028i	0.662564	−	0.382532i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	541.685i		−	1.67704i
$324$		0			0
$325$	−162.422			−0.499759
$326$		0			0
$327$		0			0
$328$		0			0
$329$	288.085	+	498.978i	0.875638	+	1.51665i
$330$		0			0
$331$	394.447	+	227.734i	1.19168	+	0.688018i	0.958688	−	0.284460i	$-0.0918143\pi$
$331$	394.447	+	227.734i	1.19168	+	0.688018i	0.232994	+	0.972478i	$0.425148\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−40.0813	−	23.1409i	−0.119646	−	0.0690774i
$336$		0			0
$337$	−21.9543	−	38.0259i	−0.0651462	−	0.112837i	0.831613	−	0.555356i	$-0.187418\pi$
$337$	−21.9543	−	38.0259i	−0.0651462	−	0.112837i	−0.896759	+	0.442520i	$0.854085\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.11503			0.00326988
$342$		0			0
$343$		−	340.402i		−	0.992426i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−340.283	+	196.462i	−0.980642	+	0.566174i	−0.902464	−	0.430766i	$-0.858244\pi$
$347$	−340.283	+	196.462i	−0.980642	+	0.566174i	−0.0781781	+	0.996939i	$0.524910\pi$
$348$		0			0
$349$	−271.979	+	471.082i	−0.779310	+	1.34981i	0.153029	+	0.988222i	$0.451097\pi$
$349$	−271.979	+	471.082i	−0.779310	+	1.34981i	−0.932340	+	0.361584i	$0.882236\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	63.7961	−	110.498i	0.180725	−	0.313026i	−0.761402	−	0.648280i	$-0.775489\pi$
$353$	63.7961	−	110.498i	0.180725	−	0.313026i	0.942128	+	0.335254i	$0.108822\pi$
$354$		0			0
$355$	−53.8870	+	31.1117i	−0.151794	+	0.0876385i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			285.077i			0.794085i	0.917800	+	0.397043i	$0.129963\pi$
$359$			285.077i			0.794085i	−0.917800	+	0.397043i	$0.870037\pi$
$360$		0			0
$361$	−61.7239			−0.170980
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.0685	+	17.4391i	0.0275849	+	0.0477785i
$366$		0			0
$367$	280.084	+	161.706i	0.763171	+	0.440617i	0.830433	−	0.557119i	$-0.188093\pi$
$367$	280.084	+	161.706i	0.763171	+	0.440617i	−0.0672623	+	0.997735i	$0.521426\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−183.371	−	105.869i	−0.494261	−	0.285362i
$372$		0			0
$373$	−257.740	−	446.419i	−0.690993	−	1.19683i	−0.971513	−	0.236987i	$-0.923840\pi$
$373$	−257.740	−	446.419i	−0.690993	−	1.19683i	0.280520	−	0.959848i	$-0.409493\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−203.847			−0.540708
$378$		0			0
$379$			21.2535i			0.0560779i	0.999607	+	0.0280389i	$0.00892624\pi$
$379$			21.2535i			0.0560779i	−0.999607	+	0.0280389i	$0.991074\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−93.4125	+	53.9317i	−0.243897	+	0.140814i	−0.616966	−	0.786989i	$-0.711639\pi$
$383$	−93.4125	+	53.9317i	−0.243897	+	0.140814i	0.373070	+	0.927803i	$0.378305\pi$
$384$		0			0
$385$	25.7891	−	44.6681i	0.0669847	−	0.116021i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	75.1474	−	130.159i	0.193181	−	0.334599i	−0.753122	−	0.657881i	$-0.771453\pi$
$389$	75.1474	−	130.159i	0.193181	−	0.334599i	0.946303	+	0.323282i	$0.104786\pi$
$390$		0			0
$391$	−575.150	+	332.063i	−1.47097	+	0.849266i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	36.1520i		−	0.0915241i
$396$		0			0
$397$	−137.203			−0.345600			−0.172800	−	0.984957i	$-0.555281\pi$
$397$	−137.203			−0.345600			−0.172800	+	0.984957i	$0.555281\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	133.366	+	230.996i	0.332583	+	0.576050i	0.983017	−	0.183512i	$-0.0587466\pi$
$401$	133.366	+	230.996i	0.332583	+	0.576050i	−0.650435	+	0.759562i	$0.725413\pi$
$402$		0			0
$403$	−0.806553	−	0.465664i	−0.00200137	−	0.00115549i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−485.983	−	280.582i	−1.19406	−	0.689391i
$408$		0			0
$409$	−341.404	−	591.329i	−0.834729	−	1.44579i	−0.894251	−	0.447565i	$-0.852291\pi$
$409$	−341.404	−	591.329i	−0.834729	−	1.44579i	0.0595226	−	0.998227i	$-0.481042\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	628.169			1.52099
$414$		0			0
$415$		−	24.2314i		−	0.0583889i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−449.030	+	259.248i	−1.07167	+	0.618730i	−0.928638	−	0.370988i	$-0.879019\pi$
$419$	−449.030	+	259.248i	−1.07167	+	0.618730i	−0.143034	+	0.989718i	$0.545686\pi$
$420$		0			0
$421$	170.758	−	295.761i	0.405601	−	0.702521i	−0.588790	−	0.808286i	$-0.700396\pi$
$421$	170.758	−	295.761i	0.405601	−	0.702521i	0.994391	+	0.105765i	$0.0337290\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	318.438	−	551.550i	0.749265	−	1.29777i
$426$		0			0
$427$	−293.981	+	169.730i	−0.688481	+	0.397495i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	166.603i		−	0.386550i	−0.981145	−	0.193275i	$-0.938089\pi$
$431$		−	166.603i		−	0.386550i	0.981145	−	0.193275i	$-0.0619110\pi$
$432$		0			0
$433$	−677.766			−1.56528			−0.782640	−	0.622475i	$-0.786127\pi$
$433$	−677.766			−1.56528			−0.782640	+	0.622475i	$0.786127\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	259.138	+	448.840i	0.592992	+	1.02709i
$438$		0			0
$439$	−427.032	−	246.547i	−0.972738	−	0.561610i	−0.0726678	−	0.997356i	$-0.523151\pi$
$439$	−427.032	−	246.547i	−0.972738	−	0.561610i	−0.900070	+	0.435746i	$0.856485\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	284.084	+	164.016i	0.641273	+	0.370239i	0.785105	−	0.619363i	$-0.212609\pi$
$443$	284.084	+	164.016i	0.641273	+	0.370239i	−0.143832	+	0.989602i	$0.545942\pi$
$444$		0			0
$445$	−11.7256	−	20.3094i	−0.0263497	−	0.0456391i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−19.0862			−0.0425082			−0.0212541	−	0.999774i	$-0.506766\pi$
$449$	−19.0862			−0.0425082			−0.0212541	+	0.999774i	$0.506766\pi$
$450$		0			0
$451$			472.677i			1.04806i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−37.3090	+	21.5404i	−0.0819978	+	0.0473415i
$456$		0			0
$457$	−137.806	+	238.686i	−0.301544	+	0.522289i	−0.976486	−	0.215581i	$-0.930835\pi$
$457$	−137.806	+	238.686i	−0.301544	+	0.522289i	0.674942	+	0.737871i	$0.264169\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−199.467	+	345.486i	−0.432683	+	0.749428i	−0.997103	−	0.0760589i	$-0.975766\pi$
$461$	−199.467	+	345.486i	−0.432683	+	0.749428i	0.564421	+	0.825487i	$0.309100\pi$
$462$		0			0
$463$	−15.7881	+	9.11524i	−0.0340995	+	0.0196873i	−0.516953	−	0.856014i	$-0.672934\pi$
$463$	−15.7881	+	9.11524i	−0.0340995	+	0.0196873i	0.482853	+	0.875701i	$0.339600\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	499.275i		−	1.06911i	−0.845133	−	0.534555i	$-0.820479\pi$
$467$		−	499.275i		−	1.06911i	0.845133	−	0.534555i	$-0.179521\pi$
$468$		0			0
$469$	358.958			0.765368
$470$		0			0
$471$		0			0
$472$		0			0
$473$	11.4184	+	19.7773i	0.0241404	+	0.0418124i
$474$		0			0
$475$	−430.423	−	248.505i	−0.906153	−	0.523168i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	52.4473	+	30.2805i	0.109493	+	0.0632160i	0.553747	−	0.832685i	$-0.313198\pi$
$479$	52.4473	+	30.2805i	0.109493	+	0.0632160i	−0.444253	+	0.895901i	$0.646531\pi$
$480$		0			0
$481$	234.356	+	405.917i	0.487227	+	0.843902i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	95.2317			0.196354
$486$		0			0
$487$			852.354i			1.75021i	0.483931	+	0.875106i	$0.339209\pi$
$487$			852.354i			1.75021i	−0.483931	+	0.875106i	$0.660791\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−585.457	+	338.014i	−1.19238	+	0.688419i	−0.958845	−	0.283930i	$-0.908362\pi$
$491$	−585.457	+	338.014i	−1.19238	+	0.688419i	−0.233532	+	0.972349i	$0.575028\pi$
$492$		0			0
$493$	399.655	−	692.223i	0.810659	−	1.40410i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	241.299	−	417.942i	0.485511	−	0.840930i
$498$		0			0
$499$	−736.084	+	424.978i	−1.47512	+	0.851660i	−0.999607	−	0.0280487i	$-0.991071\pi$
$499$	−736.084	+	424.978i	−1.47512	+	0.851660i	−0.475512	+	0.879709i	$0.657737\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	945.179i		−	1.87908i	−0.342433	−	0.939542i	$-0.611251\pi$
$503$		−	945.179i		−	1.87908i	0.342433	−	0.939542i	$-0.388749\pi$
$504$		0			0
$505$	−37.2401			−0.0737428
$506$		0			0
$507$		0			0
$508$		0			0
$509$	125.931	+	218.119i	0.247409	+	0.428524i	0.962806	−	0.270194i	$-0.0870877\pi$
$509$	125.931	+	218.119i	0.247409	+	0.428524i	−0.715397	+	0.698718i	$0.753754\pi$
$510$		0			0
$511$	−135.256	−	78.0903i	−0.264689	−	0.152819i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−113.906	−	65.7637i	−0.221177	−	0.127696i
$516$		0			0
$517$	328.630	+	569.205i	0.635649	+	1.10098i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−856.423			−1.64381			−0.821903	−	0.569628i	$-0.807087\pi$
$521$	−856.423			−1.64381			−0.821903	+	0.569628i	$0.807087\pi$
$522$		0			0
$523$			741.634i			1.41804i	0.705189	+	0.709019i	$0.250862\pi$
$523$			741.634i			1.41804i	−0.705189	+	0.709019i	$0.749138\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.16260	−	1.82593i	0.00600113	−	0.00346475i
$528$		0			0
$529$	53.2125	−	92.1667i	0.100591	−	0.174228i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	197.402	−	341.910i	0.370359	−	0.641481i
$534$		0			0
$535$	140.048	−	80.8565i	0.261771	−	0.151134i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			5.86245i			0.0108765i
$540$		0			0
$541$	434.157			0.802509			0.401254	−	0.915967i	$-0.368574\pi$
$541$	434.157			0.802509			0.401254	+	0.915967i	$0.368574\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−64.8349	−	112.297i	−0.118963	−	0.206050i
$546$		0			0
$547$	235.269	+	135.832i	0.430107	+	0.248323i	0.699392	−	0.714738i	$-0.253454\pi$
$547$	235.269	+	135.832i	0.430107	+	0.248323i	−0.269285	+	0.963061i	$0.586787\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−540.201	−	311.885i	−0.980402	−	0.566035i
$552$		0			0
$553$	140.196	+	242.826i	0.253518	+	0.439107i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	41.7759			0.0750016			0.0375008	−	0.999297i	$-0.488060\pi$
$557$	41.7759			0.0750016			0.0375008	+	0.999297i	$0.488060\pi$
$558$		0			0
$559$		−	19.0744i		−	0.0341224i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−388.403	+	224.245i	−0.689882	+	0.398303i	−0.803568	−	0.595213i	$-0.797068\pi$
$563$	−388.403	+	224.245i	−0.689882	+	0.398303i	0.113686	+	0.993517i	$0.463734\pi$
$564$		0			0
$565$	−91.0559	+	157.713i	−0.161161	+	0.279139i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	180.208	−	312.130i	0.316710	−	0.548559i	−0.663089	−	0.748540i	$-0.730755\pi$
$569$	180.208	−	312.130i	0.316710	−	0.548559i	0.979800	+	0.199982i	$0.0640883\pi$
$570$		0			0
$571$	665.784	−	384.391i	1.16600	−	0.673189i	0.213263	−	0.976995i	$-0.431591\pi$
$571$	665.784	−	384.391i	1.16600	−	0.673189i	0.952734	+	0.303806i	$0.0982574\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			609.352i			1.05974i
$576$		0			0
$577$	−413.359			−0.716394			−0.358197	−	0.933646i	$-0.616608\pi$
$577$	−413.359			−0.716394			−0.358197	+	0.933646i	$0.616608\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	93.9682	+	162.758i	0.161735	+	0.280134i
$582$		0			0
$583$	−209.179	−	120.769i	−0.358797	−	0.207152i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.41240	−	0.815451i	−0.00240614	−	0.00138918i	0.498796	−	0.866719i	$-0.333776\pi$
$587$	−1.41240	−	0.815451i	−0.00240614	−	0.00138918i	−0.501203	+	0.865330i	$0.667109\pi$
$588$		0			0
$589$	−1.42493	−	2.46805i	−0.00241923	−	0.00419024i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−652.407			−1.10018			−0.550091	−	0.835105i	$-0.685407\pi$
$593$	−652.407			−1.10018			−0.550091	+	0.835105i	$0.685407\pi$
$594$		0			0
$595$		−	168.925i		−	0.283908i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−148.315	+	85.6298i	−0.247605	+	0.142955i	−0.618667	−	0.785653i	$-0.712327\pi$
$599$	−148.315	+	85.6298i	−0.247605	+	0.142955i	0.371062	+	0.928608i	$0.378994\pi$
$600$		0			0
$601$	−65.9875	+	114.294i	−0.109796	+	0.190173i	−0.915688	−	0.401891i	$-0.868353\pi$
$601$	−65.9875	+	114.294i	−0.109796	+	0.190173i	0.805891	+	0.592063i	$0.201686\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−25.5894	+	44.3222i	−0.0422966	+	0.0732598i
$606$		0			0
$607$	−514.763	+	297.199i	−0.848045	+	0.489619i	−0.859991	−	0.510310i	$-0.829531\pi$
$607$	−514.763	+	297.199i	−0.848045	+	0.489619i	0.0119458	+	0.999929i	$0.496197\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	548.977i		−	0.898489i
$612$		0			0
$613$	−367.632			−0.599727			−0.299863	−	0.953982i	$-0.596941\pi$
$613$	−367.632			−0.599727			−0.299863	+	0.953982i	$0.596941\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.0806	−	36.5126i	−0.0341662	−	0.0591776i	0.848437	−	0.529297i	$-0.177544\pi$
$617$	−21.0806	−	36.5126i	−0.0341662	−	0.0591776i	−0.882603	+	0.470119i	$0.844211\pi$
$618$		0			0
$619$	214.298	+	123.725i	0.346200	+	0.199879i	0.663010	−	0.748610i	$-0.269279\pi$
$619$	214.298	+	123.725i	0.346200	+	0.199879i	−0.316810	+	0.948489i	$0.602612\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	157.518	+	90.9428i	0.252837	+	0.145976i
$624$		0			0
$625$	−281.841	−	488.163i	−0.450945	−	0.781060i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1837.88			−2.92191
$630$		0			0
$631$		−	725.556i		−	1.14985i	−0.818206	−	0.574926i	$-0.805031\pi$
$631$		−	725.556i		−	1.14985i	0.818206	−	0.574926i	$-0.194969\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−143.091	+	82.6136i	−0.225340	+	0.130100i
$636$		0			0
$637$	2.44831	−	4.24059i	0.00384349	−	0.00665713i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−458.006	+	793.290i	−0.714518	+	1.23758i	0.248626	+	0.968599i	$0.420021\pi$
$641$	−458.006	+	793.290i	−0.714518	+	1.23758i	−0.963145	+	0.268983i	$0.913312\pi$
$642$		0			0
$643$	−686.803	+	396.526i	−1.06812	+	0.616681i	−0.927668	−	0.373406i	$-0.878190\pi$
$643$	−686.803	+	396.526i	−1.06812	+	0.616681i	−0.140455	+	0.990087i	$0.544857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	78.3837i		−	0.121150i	−0.998164	−	0.0605748i	$-0.980707\pi$
$647$		−	78.3837i		−	0.121150i	0.998164	−	0.0605748i	$-0.0192934\pi$
$648$		0			0
$649$	716.579			1.10413
$650$		0			0
$651$		0			0
$652$		0			0
$653$	131.250	+	227.332i	0.200996	+	0.348135i	0.948850	−	0.315728i	$-0.102249\pi$
$653$	131.250	+	227.332i	0.200996	+	0.348135i	−0.747854	+	0.663864i	$0.768915\pi$
$654$		0			0
$655$	−48.1308	−	27.7883i	−0.0734822	−	0.0424250i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1116.03	−	644.339i	−1.69352	−	0.977753i	−0.951638	−	0.307221i	$-0.900601\pi$
$659$	−1116.03	−	644.339i	−1.69352	−	0.977753i	−0.741880	−	0.670533i	$-0.766066\pi$
$660$		0			0
$661$	184.429	+	319.441i	0.279016	+	0.483270i	0.971140	−	0.238508i	$-0.0766585\pi$
$661$	184.429	+	319.441i	0.279016	+	0.483270i	−0.692125	+	0.721778i	$0.743325\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−131.827			−0.198236
$666$		0			0
$667$			764.766i			1.14658i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−335.357	+	193.618i	−0.499787	+	0.288552i
$672$		0			0
$673$	127.862	−	221.463i	0.189988	−	0.329069i	−0.755258	−	0.655428i	$-0.772488\pi$
$673$	127.862	−	221.463i	0.189988	−	0.329069i	0.945246	+	0.326359i	$0.105822\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	566.571	−	981.330i	0.836885	−	1.44953i	−0.0556014	−	0.998453i	$-0.517708\pi$
$677$	566.571	−	981.330i	0.836885	−	1.44953i	0.892486	−	0.451074i	$-0.148959\pi$
$678$		0			0
$679$	−639.653	+	369.304i	−0.942052	+	0.543894i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			941.046i			1.37781i	0.724850	+	0.688907i	$0.241909\pi$
$683$			941.046i			1.37781i	−0.724850	+	0.688907i	$0.758091\pi$
$684$		0			0
$685$	32.9379			0.0480845
$686$		0			0
$687$		0			0
$688$		0			0
$689$	100.873	+	174.717i	0.146404	+	0.253580i
$690$		0			0
$691$	−1163.81	−	671.923i	−1.68423	−	0.972393i	−0.958792	−	0.284109i	$-0.908302\pi$
$691$	−1163.81	−	671.923i	−1.68423	−	0.972393i	−0.725441	−	0.688284i	$-0.758364\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−140.614	−	81.1834i	−0.202322	−	0.116811i
$696$		0			0
$697$	774.036	+	1340.67i	1.11053	+	1.92349i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−28.1783			−0.0401973			−0.0200986	−	0.999798i	$-0.506398\pi$
$701$	−28.1783			−0.0401973			−0.0200986	+	0.999798i	$0.506398\pi$
$702$		0			0
$703$			1434.26i			2.04020i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	250.135	−	144.415i	0.353797	−	0.204265i
$708$		0			0
$709$	−624.660	+	1081.94i	−0.881043	+	1.52601i	−0.0308605	+	0.999524i	$0.509825\pi$
$709$	−624.660	+	1081.94i	−0.881043	+	1.52601i	−0.850183	+	0.526488i	$0.823509\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.74702	+	3.02592i	−0.00245023	+	0.00424393i
$714$		0			0
$715$	−42.5599	+	24.5720i	−0.0595244	+	0.0343664i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			738.132i			1.02661i	0.858206	+	0.513305i	$0.171579\pi$
$719$			738.132i			1.02661i	−0.858206	+	0.513305i	$0.828421\pi$
$720$		0			0
$721$	1020.11			1.41486
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−366.693	−	635.131i	−0.505784	−	0.876043i
$726$		0			0
$727$	−326.676	−	188.606i	−0.449348	−	0.259431i	0.258207	−	0.966090i	$-0.416868\pi$
$727$	−326.676	−	188.606i	−0.449348	−	0.259431i	−0.707555	+	0.706659i	$0.750202\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	64.7729	+	37.3967i	0.0886087	+	0.0511582i
$732$		0			0
$733$	−280.849	−	486.445i	−0.383150	−	0.663635i	0.608361	−	0.793661i	$-0.291827\pi$
$733$	−280.849	−	486.445i	−0.383150	−	0.663635i	−0.991511	+	0.130025i	$0.958494\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	409.478			0.555601
$738$		0			0
$739$		−	912.732i		−	1.23509i	−0.786535	−	0.617545i	$-0.788127\pi$
$739$		−	912.732i		−	1.23509i	0.786535	−	0.617545i	$-0.211873\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−913.005	+	527.123i	−1.22881	+	0.709453i	−0.966781	−	0.255608i	$-0.917725\pi$
$743$	−913.005	+	527.123i	−1.22881	+	0.709453i	−0.262028	+	0.965060i	$0.584391\pi$
$744$		0			0
$745$	109.146	−	189.047i	0.146505	−	0.253755i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−627.115	+	1086.20i	−0.837270	+	1.45019i
$750$		0			0
$751$	916.482	−	529.131i	1.22035	−	0.704569i	0.255357	−	0.966847i	$-0.417807\pi$
$751$	916.482	−	529.131i	1.22035	−	0.704569i	0.964992	+	0.262278i	$0.0844737\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			103.035i			0.136470i
$756$		0			0
$757$	359.804			0.475302			0.237651	−	0.971351i	$-0.423623\pi$
$757$	359.804			0.475302			0.237651	+	0.971351i	$0.423623\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	311.474	+	539.489i	0.409296	+	0.708921i	0.994811	−	0.101740i	$-0.0324411\pi$
$761$	311.474	+	539.489i	0.409296	+	0.708921i	−0.585515	+	0.810661i	$0.699108\pi$
$762$		0			0
$763$	870.966	+	502.853i	1.14150	+	0.659047i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−518.336	−	299.261i	−0.675796	−	0.390171i
$768$		0			0
$769$	−534.453	−	925.699i	−0.694997	−	1.20377i	−0.970182	−	0.242379i	$-0.922072\pi$
$769$	−534.453	−	925.699i	−0.694997	−	1.20377i	0.275185	−	0.961391i	$-0.411261\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−512.261			−0.662692			−0.331346	−	0.943509i	$-0.607503\pi$
$773$	−512.261			−0.662692			−0.331346	+	0.943509i	$0.607503\pi$
$774$		0			0
$775$		−	3.35066i		−	0.00432344i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1046.24	−	604.048i	1.34306	−	0.775415i
$780$		0			0
$781$	275.260	−	476.764i	0.352445	−	0.610453i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	54.8813	−	95.0571i	0.0699124	−	0.121092i
$786$		0			0
$787$	153.809	−	88.8019i	0.195438	−	0.112836i	−0.399088	−	0.916913i	$-0.630673\pi$
$787$	153.809	−	88.8019i	0.195438	−	0.112836i	0.594526	+	0.804077i	$0.297340\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	1412.44i		−	1.78564i
$792$		0			0
$793$	323.439			0.407868
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−190.381	−	329.750i	−0.238872	−	0.413739i	0.721519	−	0.692395i	$-0.243444\pi$
$797$	−190.381	−	329.750i	−0.238872	−	0.413739i	−0.960391	+	0.278656i	$0.910111\pi$
$798$		0			0
$799$	1864.21	+	1076.30i	2.33318	+	1.34706i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−154.292	−	89.0808i	−0.192145	−	0.110935i
$804$		0			0
$805$	80.8123	+	139.971i	0.100388	+	0.173877i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	720.850			0.891039			0.445519	−	0.895272i	$-0.353019\pi$
$809$	720.850			0.891039			0.445519	+	0.895272i	$0.353019\pi$
$810$		0			0
$811$		−	1048.82i		−	1.29324i	−0.762813	−	0.646619i	$-0.776182\pi$
$811$		−	1048.82i		−	1.29324i	0.762813	−	0.646619i	$-0.223818\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16.0237	+	9.25127i	−0.0196609	+	0.0113512i
$816$		0			0
$817$	29.1839	−	50.5479i	0.0357208	−	0.0618702i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	361.666	−	626.424i	0.440519	−	0.763001i	−0.557209	−	0.830372i	$-0.688128\pi$
$821$	361.666	−	626.424i	0.440519	−	0.763001i	0.997728	+	0.0673712i	$0.0214612\pi$
$822$		0			0
$823$	−1074.90	+	620.596i	−1.30608	+	0.754066i	−0.981440	−	0.191772i	$-0.938577\pi$
$823$	−1074.90	+	620.596i	−1.30608	+	0.754066i	−0.324640	+	0.945838i	$0.605243\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			348.111i			0.420932i	0.977601	+	0.210466i	$0.0674981\pi$
$827$			348.111i			0.420932i	−0.977601	+	0.210466i	$0.932502\pi$
$828$		0			0
$829$	−731.151			−0.881968			−0.440984	−	0.897515i	$-0.645370\pi$
$829$	−731.151			−0.881968			−0.440984	+	0.897515i	$0.645370\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.60012	+	16.6279i	0.0115248	+	0.0199615i
$834$		0			0
$835$	−137.775	−	79.5443i	−0.165000	−	0.0952627i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	563.141	+	325.130i	0.671205	+	0.387520i	0.796533	−	0.604595i	$-0.206665\pi$
$839$	563.141	+	325.130i	0.671205	+	0.387520i	−0.125328	+	0.992115i	$0.539998\pi$
$840$		0			0
$841$	−39.7179	−	68.7934i	−0.0472269	−	0.0817995i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−112.612			−0.133268
$846$		0			0
$847$		−	396.938i		−	0.468640i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1522.87	−	879.227i	1.78950	−	1.03317i
$852$		0			0
$853$	664.274	−	1150.56i	0.778750	−	1.34884i	−0.153912	−	0.988085i	$-0.549187\pi$
$853$	664.274	−	1150.56i	0.778750	−	1.34884i	0.932662	−	0.360751i	$-0.117479\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	323.338	−	560.038i	0.377290	−	0.653486i	−0.613377	−	0.789791i	$-0.710189\pi$
$857$	323.338	−	560.038i	0.377290	−	0.653486i	0.990667	+	0.136304i	$0.0435225\pi$
$858$		0			0
$859$	−527.482	+	304.542i	−0.614065	+	0.354530i	−0.774555	−	0.632507i	$-0.782026\pi$
$859$	−527.482	+	304.542i	−0.614065	+	0.354530i	0.160490	+	0.987037i	$0.448693\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	93.0849i		−	0.107862i	−0.998545	−	0.0539310i	$-0.982825\pi$
$863$		−	93.0849i		−	0.107862i	0.998545	−	0.0539310i	$-0.0171751\pi$
$864$		0			0
$865$	−101.683			−0.117553
$866$		0			0
$867$		0			0
$868$		0			0
$869$	159.927	+	277.002i	0.184036	+	0.318759i
$870$		0			0
$871$	−296.195	−	171.008i	−0.340063	−	0.196335i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−273.046	−	157.643i	−0.312052	−	0.180164i
$876$		0			0
$877$	−330.684	−	572.762i	−0.377063	−	0.653092i	0.613571	−	0.789640i	$-0.289733\pi$
$877$	−330.684	−	572.762i	−0.377063	−	0.653092i	−0.990633	+	0.136548i	$0.956399\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	659.388			0.748455			0.374227	−	0.927337i	$-0.377908\pi$
$881$	659.388			0.748455			0.374227	+	0.927337i	$0.377908\pi$
$882$		0			0
$883$			776.943i			0.879890i	0.898025	+	0.439945i	$0.145002\pi$
$883$			776.943i			0.879890i	−0.898025	+	0.439945i	$0.854998\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	598.849	−	345.745i	0.675139	−	0.389792i	−0.122882	−	0.992421i	$-0.539214\pi$
$887$	598.849	−	345.745i	0.675139	−	0.389792i	0.798021	+	0.602629i	$0.205880\pi$
$888$		0			0
$889$	640.743	−	1109.80i	0.720745	−	1.24837i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	839.934	−	1454.81i	0.940575	−	1.62912i
$894$		0			0
$895$	14.7198	−	8.49849i	0.0164467	−	0.00949552i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	4.20525i		−	0.00467769i
$900$		0			0
$901$	−791.069			−0.877990
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−44.5764	−	77.2087i	−0.0492557	−	0.0853134i
$906$		0			0
$907$	−81.4675	−	47.0353i	−0.0898209	−	0.0518581i	0.454417	−	0.890789i	$-0.349848\pi$
$907$	−81.4675	−	47.0353i	−0.0898209	−	0.0518581i	−0.544238	+	0.838931i	$0.683181\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	818.478	+	472.549i	0.898440	+	0.518714i	0.876694	−	0.481049i	$-0.159744\pi$
$911$	818.478	+	472.549i	0.898440	+	0.518714i	0.0217460	+	0.999764i	$0.493077\pi$
$912$		0			0
$913$	107.193	+	185.664i	0.117408	+	0.203356i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	431.047			0.470062
$918$		0			0
$919$		−	29.1099i		−	0.0316757i	−0.999875	−	0.0158378i	$-0.994958\pi$
$919$		−	29.1099i		−	0.0316757i	0.999875	−	0.0158378i	$-0.00504155\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−398.217	+	229.911i	−0.431438	+	0.249091i
$924$		0			0
$925$	−843.151	+	1460.38i	−0.911514	+	1.57879i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−383.769	+	664.707i	−0.413099	+	0.715508i	−0.995227	−	0.0975893i	$-0.968887\pi$
$929$	−383.769	+	664.707i	−0.413099	+	0.715508i	0.582128	+	0.813097i	$0.302220\pi$
$930$		0			0
$931$	12.9762	−	7.49181i	0.0139379	−	0.00804705i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	192.700i		−	0.206096i
$936$		0			0
$937$	−736.778			−0.786316			−0.393158	−	0.919471i	$-0.628617\pi$
$937$	−736.778			−0.786316			−0.393158	+	0.919471i	$0.628617\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	531.351	+	920.327i	0.564667	+	0.978031i	0.997081	+	0.0763560i	$0.0243285\pi$
$941$	531.351	+	920.327i	0.564667	+	0.978031i	−0.432414	+	0.901675i	$0.642338\pi$
$942$		0			0
$943$	−1282.73	−	740.585i	−1.36027	−	0.785350i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−499.283	−	288.261i	−0.527226	−	0.304394i	0.212660	−	0.977126i	$-0.431787\pi$
$947$	−499.283	−	288.261i	−0.527226	−	0.304394i	−0.739886	+	0.672732i	$0.765121\pi$
$948$		0			0
$949$	74.4047	+	128.873i	0.0784033	+	0.135799i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−677.961			−0.711397			−0.355698	−	0.934601i	$-0.615757\pi$
$953$	−677.961			−0.711397			−0.355698	+	0.934601i	$0.615757\pi$
$954$		0			0
$955$		−	252.720i		−	0.264629i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−221.237	+	127.731i	−0.230696	+	0.133192i
$960$		0			0
$961$	−480.490	+	832.234i	−0.499990	+	0.866008i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	73.7641	−	127.763i	0.0764395	−	0.132397i
$966$		0			0
$967$	1153.25	−	665.830i	1.19261	−	0.688552i	0.233710	−	0.972306i	$-0.424913\pi$
$967$	1153.25	−	665.830i	1.19261	−	0.688552i	0.958897	+	0.283755i	$0.0915801\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			385.062i			0.396563i	0.980145	+	0.198281i	$0.0635360\pi$
$971$			385.062i			0.396563i	−0.980145	+	0.198281i	$0.936464\pi$
$972$		0			0
$973$	1259.30			1.29424
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−142.550	−	246.905i	−0.145906	−	0.252717i	0.783804	−	0.621008i	$-0.213276\pi$
$977$	−142.550	−	246.905i	−0.145906	−	0.252717i	−0.929711	+	0.368291i	$0.879943\pi$
$978$		0			0
$979$	179.687	+	103.742i	0.183541	+	0.105968i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1164.42	+	672.280i	1.18456	+	0.683907i	0.957065	−	0.289872i	$-0.0936129\pi$
$983$	1164.42	+	672.280i	1.18456	+	0.683907i	0.227496	+	0.973779i	$0.426946\pi$
$984$		0			0
$985$	48.2715	+	83.6087i	0.0490066	+	0.0848819i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−71.5610			−0.0723570
$990$		0			0
$991$		−	1457.00i		−	1.47023i	−0.677944	−	0.735114i	$-0.737129\pi$
$991$		−	1457.00i		−	1.47023i	0.677944	−	0.735114i	$-0.262871\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−49.9125	+	28.8170i	−0.0501633	+	0.0289618i
$996$		0			0
$997$	−160.689	+	278.322i	−0.161173	+	0.279160i	−0.935290	−	0.353883i	$-0.884861\pi$
$997$	−160.689	+	278.322i	−0.161173	+	0.279160i	0.774117	+	0.633043i	$0.218194\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.e.127.2		8
3.2	odd	2		576.3.o.d.511.2		8
4.3	odd	2		1728.3.o.f.127.2		8
8.3	odd	2		432.3.o.b.127.3		8
8.5	even	2		432.3.o.a.127.3		8
9.4	even	3		1728.3.o.f.1279.2		8
9.5	odd	6		576.3.o.f.319.3		8
12.11	even	2		576.3.o.f.511.3		8
24.5	odd	2		144.3.o.c.79.3	yes	8
24.11	even	2		144.3.o.a.79.2	yes	8
36.23	even	6		576.3.o.d.319.2		8
36.31	odd	6	inner	1728.3.o.e.1279.2		8
72.5	odd	6		144.3.o.a.31.2	✓	8
72.11	even	6		1296.3.g.j.1135.6		8
72.13	even	6		432.3.o.b.415.3		8
72.29	odd	6		1296.3.g.j.1135.5		8
72.43	odd	6		1296.3.g.k.1135.4		8
72.59	even	6		144.3.o.c.31.3	yes	8
72.61	even	6		1296.3.g.k.1135.3		8
72.67	odd	6		432.3.o.a.415.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.2	✓	8	72.5	odd	6
144.3.o.a.79.2	yes	8	24.11	even	2
144.3.o.c.31.3	yes	8	72.59	even	6
144.3.o.c.79.3	yes	8	24.5	odd	2
432.3.o.a.127.3		8	8.5	even	2
432.3.o.a.415.3		8	72.67	odd	6
432.3.o.b.127.3		8	8.3	odd	2
432.3.o.b.415.3		8	72.13	even	6
576.3.o.d.319.2		8	36.23	even	6
576.3.o.d.511.2		8	3.2	odd	2
576.3.o.f.319.3		8	9.5	odd	6
576.3.o.f.511.3		8	12.11	even	2
1296.3.g.j.1135.5		8	72.29	odd	6
1296.3.g.j.1135.6		8	72.11	even	6
1296.3.g.k.1135.3		8	72.61	even	6
1296.3.g.k.1135.4		8	72.43	odd	6
1728.3.o.e.127.2		8	1.1	even	1	trivial
1728.3.o.e.1279.2		8	36.31	odd	6	inner
1728.3.o.f.127.2		8	4.3	odd	2
1728.3.o.f.1279.2		8	9.4	even	3

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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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.454613 - 0.787412i) q^{5} +(6.10709 + 3.52593i) q^{7} +(6.96661 + 4.02218i) q^{11} +(-3.35952 - 5.81886i) q^{13} +26.3462 q^{17} -20.5603i q^{19} +(-21.8305 + 12.6038i) q^{23} +(12.0867 - 20.9347i) q^{25} +(15.1693 - 26.2741i) q^{29} +(0.120040 - 0.0693050i) q^{31} -6.41173i q^{35} -69.7588 q^{37} +(29.3794 + 50.8866i) q^{41} +(2.45853 + 1.41943i) q^{43} +(70.7583 + 40.8523i) q^{47} +(0.364383 + 0.631130i) q^{49} -30.0259 q^{53} -7.31413i q^{55} +(77.1442 - 44.5392i) q^{59} +(-24.0688 + 41.6885i) q^{61} +(-3.05456 + 5.29066i) q^{65} +(44.0829 - 25.4513i) q^{67} -68.4355i q^{71} -22.1474 q^{73} +(28.3638 + 49.1276i) q^{77} +(34.4343 + 19.8807i) q^{79} +(23.0801 + 13.3253i) q^{83} +(-11.9773 - 20.7453i) q^{85} +25.7926 q^{89} -47.3818i q^{91} +(-16.1894 + 9.34695i) q^{95} +(-52.3697 + 90.7070i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} - 3 q^{7} - 18 q^{11} - 5 q^{13} - 6 q^{17} - 81 q^{23} - 23 q^{25} + 69 q^{29} - 45 q^{31} + 20 q^{37} - 54 q^{41} + 207 q^{47} + 41 q^{49} - 252 q^{53} + 306 q^{59} - 7 q^{61} - 93 q^{65}+ \cdots - 10 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 - 3 * q^7 - 18 * q^11 - 5 * q^13 - 6 * q^17 - 81 * q^23 - 23 * q^25 + 69 * q^29 - 45 * q^31 + 20 * q^37 - 54 * q^41 + 207 * q^47 + 41 * q^49 - 252 * q^53 + 306 * q^59 - 7 * q^61 - 93 * q^65 + 12 * q^67 + 74 * q^73 + 207 * q^77 - 33 * q^79 - 549 * q^83 + 30 * q^85 + 168 * q^89 - 684 * q^95 - 10 * q^97

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