LMFDB - Embedded newform 1728.3.o.g.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(127,1728)]

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([3, 0, 4]))

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

//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);

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: 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.5
Root			$-1.26364 - 1.55023i$ of defining polynomial
Character	$\chi$	$=$	1728.127
Dual form			1728.3.o.g.1279.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35609 + 2.34881i) q^{5} +(-10.0431 - 5.79837i) q^{7} +O(q^{10})$	$q+(1.35609 + 2.34881i) q^{5} +(-10.0431 - 5.79837i) q^{7} +(8.54822 + 4.93532i) q^{11} +(-0.296185 - 0.513008i) q^{13} +8.87968 q^{17} +14.0989i q^{19} +(-18.2754 + 10.5513i) q^{23} +(8.82205 - 15.2802i) q^{25} +(10.1764 - 17.6260i) q^{29} +(-14.3357 + 8.27670i) q^{31} -31.4524i q^{35} +40.6557 q^{37} +(-21.2177 - 36.7502i) q^{41} +(-32.2385 - 18.6129i) q^{43} +(1.57134 + 0.907211i) q^{47} +(42.7423 + 74.0318i) q^{49} -21.1005 q^{53} +26.7709i q^{55} +(-76.6879 + 44.2758i) q^{59} +(-36.4925 + 63.2069i) q^{61} +(0.803307 - 1.39137i) q^{65} +(-38.3110 + 22.1189i) q^{67} -111.798i q^{71} -76.2003 q^{73} +(-57.2337 - 99.1316i) q^{77} +(8.30434 + 4.79451i) q^{79} +(-73.6244 - 42.5070i) q^{83} +(12.0416 + 20.8567i) q^{85} -64.7845 q^{89} +6.86958i q^{91} +(-33.1157 + 19.1193i) q^{95} +(-3.59139 + 6.22047i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5}+O(q^{10}) $ 16 * q + 6 * q^5	$ 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) $ 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.35609	+	2.34881i	0.271218	+	0.469763i	0.969174	−	0.246378i	$-0.0792403\pi$
$5$	1.35609	+	2.34881i	0.271218	+	0.469763i	−0.697956	+	0.716140i	$0.745907\pi$
$6$		0			0
$7$	−10.0431	−	5.79837i	−1.43473	−	0.828339i	−0.437249	−	0.899340i	$-0.644047\pi$
$7$	−10.0431	−	5.79837i	−1.43473	−	0.828339i	−0.997476	+	0.0710013i	$0.977381\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	8.54822	+	4.93532i	0.777111	+	0.448665i	0.835406	−	0.549634i	$-0.185233\pi$
$11$	8.54822	+	4.93532i	0.777111	+	0.448665i	−0.0582943	+	0.998299i	$0.518566\pi$
$12$		0			0
$13$	−0.296185	−	0.513008i	−0.0227835	−	0.0394622i	0.854409	−	0.519601i	$-0.173920\pi$
$13$	−0.296185	−	0.513008i	−0.0227835	−	0.0394622i	−0.877192	+	0.480139i	$0.840586\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	8.87968			0.522334			0.261167	−	0.965294i	$-0.415893\pi$
$17$	8.87968			0.522334			0.261167	+	0.965294i	$0.415893\pi$
$18$		0			0
$19$			14.0989i			0.742046i	0.928624	+	0.371023i	$0.120993\pi$
$19$			14.0989i			0.742046i	−0.928624	+	0.371023i	$0.879007\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−18.2754	+	10.5513i	−0.794583	+	0.458753i	−0.841574	−	0.540142i	$-0.818370\pi$
$23$	−18.2754	+	10.5513i	−0.794583	+	0.458753i	0.0469902	+	0.998895i	$0.485037\pi$
$24$		0			0
$25$	8.82205	−	15.2802i	0.352882	−	0.611209i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	10.1764	−	17.6260i	0.350910	−	0.607793i	−0.635499	−	0.772101i	$-0.719206\pi$
$29$	10.1764	−	17.6260i	0.350910	−	0.607793i	0.986409	+	0.164308i	$0.0525391\pi$
$30$		0			0
$31$	−14.3357	+	8.27670i	−0.462441	+	0.266990i	−0.713070	−	0.701093i	$-0.752696\pi$
$31$	−14.3357	+	8.27670i	−0.462441	+	0.266990i	0.250629	+	0.968083i	$0.419362\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	31.4524i		−	0.898641i
$36$		0			0
$37$	40.6557			1.09880			0.549401	−	0.835559i	$-0.314856\pi$
$37$	40.6557			1.09880			0.549401	+	0.835559i	$0.314856\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−21.2177	−	36.7502i	−0.517506	−	0.896346i	−0.999793	−	0.0203330i	$-0.993527\pi$
$41$	−21.2177	−	36.7502i	−0.517506	−	0.896346i	0.482288	−	0.876013i	$-0.339806\pi$
$42$		0			0
$43$	−32.2385	−	18.6129i	−0.749732	−	0.432858i	0.0758649	−	0.997118i	$-0.475828\pi$
$43$	−32.2385	−	18.6129i	−0.749732	−	0.432858i	−0.825597	+	0.564260i	$0.809162\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.57134	+	0.907211i	0.0334327	+	0.0193024i	0.516623	−	0.856213i	$-0.327189\pi$
$47$	1.57134	+	0.907211i	0.0334327	+	0.0193024i	−0.483191	+	0.875515i	$0.660522\pi$
$48$		0			0
$49$	42.7423	+	74.0318i	0.872291	+	1.51085i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−21.1005			−0.398122			−0.199061	−	0.979987i	$-0.563789\pi$
$53$	−21.1005			−0.398122			−0.199061	+	0.979987i	$0.563789\pi$
$54$		0			0
$55$			26.7709i			0.486744i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−76.6879	+	44.2758i	−1.29980	+	0.750437i	−0.980369	−	0.197174i	$-0.936824\pi$
$59$	−76.6879	+	44.2758i	−1.29980	+	0.750437i	−0.319427	+	0.947611i	$0.603490\pi$
$60$		0			0
$61$	−36.4925	+	63.2069i	−0.598238	+	1.03618i	0.394843	+	0.918749i	$0.370799\pi$
$61$	−36.4925	+	63.2069i	−0.598238	+	1.03618i	−0.993081	+	0.117431i	$0.962534\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.803307	−	1.39137i	0.0123586	−	0.0214057i
$66$		0			0
$67$	−38.3110	+	22.1189i	−0.571807	+	0.330133i	−0.757871	−	0.652405i	$-0.773760\pi$
$67$	−38.3110	+	22.1189i	−0.571807	+	0.330133i	0.186064	+	0.982538i	$0.440427\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	111.798i		−	1.57462i	−0.616557	−	0.787310i	$-0.711473\pi$
$71$		−	111.798i		−	1.57462i	0.616557	−	0.787310i	$-0.288527\pi$
$72$		0			0
$73$	−76.2003			−1.04384			−0.521920	−	0.852995i	$-0.674784\pi$
$73$	−76.2003			−1.04384			−0.521920	+	0.852995i	$0.674784\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−57.2337	−	99.1316i	−0.743294	−	1.28742i
$78$		0			0
$79$	8.30434	+	4.79451i	0.105118	+	0.0606901i	0.551637	−	0.834084i	$-0.314003\pi$
$79$	8.30434	+	4.79451i	0.105118	+	0.0606901i	−0.446519	+	0.894774i	$0.647337\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−73.6244	−	42.5070i	−0.887041	−	0.512133i	−0.0140672	−	0.999901i	$-0.504478\pi$
$83$	−73.6244	−	42.5070i	−0.887041	−	0.512133i	−0.872973	+	0.487768i	$0.837811\pi$
$84$		0			0
$85$	12.0416	+	20.8567i	0.141666	+	0.245373i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−64.7845			−0.727916			−0.363958	−	0.931415i	$-0.618575\pi$
$89$	−64.7845			−0.727916			−0.363958	+	0.931415i	$0.618575\pi$
$90$		0			0
$91$			6.86958i			0.0754898i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−33.1157	+	19.1193i	−0.348586	+	0.201256i
$96$		0			0
$97$	−3.59139	+	6.22047i	−0.0370246	+	0.0641285i	−0.883944	−	0.467593i	$-0.845121\pi$
$97$	−3.59139	+	6.22047i	−0.0370246	+	0.0641285i	0.846919	+	0.531721i	$0.178455\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−55.5037	+	96.1353i	−0.549542	+	0.951834i	0.448764	+	0.893650i	$0.351864\pi$
$101$	−55.5037	+	96.1353i	−0.549542	+	0.951834i	−0.998306	+	0.0581840i	$0.981469\pi$
$102$		0			0
$103$	−79.6133	+	45.9648i	−0.772945	+	0.446260i	−0.833924	−	0.551879i	$-0.813911\pi$
$103$	−79.6133	+	45.9648i	−0.772945	+	0.446260i	0.0609793	+	0.998139i	$0.480578\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	107.741i		−	1.00693i	−0.864016	−	0.503465i	$-0.832058\pi$
$107$		−	107.741i		−	1.00693i	0.864016	−	0.503465i	$-0.167942\pi$
$108$		0			0
$109$	−86.5562			−0.794093			−0.397047	−	0.917798i	$-0.629965\pi$
$109$	−86.5562			−0.794093			−0.397047	+	0.917798i	$0.629965\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.35198	+	4.07376i	0.0208140	+	0.0360509i	0.876245	−	0.481866i	$-0.160041\pi$
$113$	2.35198	+	4.07376i	0.0208140	+	0.0360509i	−0.855431	+	0.517917i	$0.826708\pi$
$114$		0			0
$115$	−49.5662	−	28.6170i	−0.431010	−	0.248844i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−89.1793	−	51.4877i	−0.749406	−	0.432670i
$120$		0			0
$121$	−11.7852	−	20.4126i	−0.0973987	−	0.168700i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	115.658			0.925267
$126$		0			0
$127$		−	8.37118i		−	0.0659148i	−0.999457	−	0.0329574i	$-0.989507\pi$
$127$		−	8.37118i		−	0.0659148i	0.999457	−	0.0329574i	$-0.0104926\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	115.067	−	66.4338i	0.878372	−	0.507129i	0.00825098	−	0.999966i	$-0.497374\pi$
$131$	115.067	−	66.4338i	0.878372	−	0.507129i	0.870121	+	0.492837i	$0.164040\pi$
$132$		0			0
$133$	81.7506	−	141.596i	0.614666	−	1.06463i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−22.5579	+	39.0715i	−0.164656	+	0.285193i	−0.936533	−	0.350579i	$-0.885985\pi$
$137$	−22.5579	+	39.0715i	−0.164656	+	0.285193i	0.771877	+	0.635772i	$0.219318\pi$
$138$		0			0
$139$	−130.744	+	75.4848i	−0.940601	+	0.543056i	−0.890149	−	0.455670i	$-0.849400\pi$
$139$	−130.744	+	75.4848i	−0.940601	+	0.543056i	−0.0504522	+	0.998726i	$0.516066\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	5.84708i		−	0.0408887i
$144$		0			0
$145$	55.2003			0.380692
$146$		0			0
$147$		0			0
$148$		0			0
$149$	71.3914	+	123.653i	0.479137	+	0.829889i	0.999714	−	0.0239255i	$-0.00761646\pi$
$149$	71.3914	+	123.653i	0.479137	+	0.829889i	−0.520577	+	0.853815i	$0.674283\pi$
$150$		0			0
$151$	−220.027	−	127.033i	−1.45713	−	0.841276i	−0.458263	−	0.888817i	$-0.651528\pi$
$151$	−220.027	−	127.033i	−1.45713	−	0.841276i	−0.998869	+	0.0475407i	$0.984862\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−38.8808	−	22.4479i	−0.250844	−	0.144825i
$156$		0			0
$157$	−2.65361	−	4.59618i	−0.0169020	−	0.0292751i	0.857451	−	0.514566i	$-0.172047\pi$
$157$	−2.65361	−	4.59618i	−0.0169020	−	0.0292751i	−0.874353	+	0.485291i	$0.838714\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	244.722			1.52001
$162$		0			0
$163$			59.5534i			0.365359i	0.983173	+	0.182679i	$0.0584770\pi$
$163$			59.5534i			0.365359i	−0.983173	+	0.182679i	$0.941523\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−85.7434	+	49.5040i	−0.513434	+	0.296431i	−0.734244	−	0.678886i	$-0.762463\pi$
$167$	−85.7434	+	49.5040i	−0.513434	+	0.296431i	0.220810	+	0.975317i	$0.429130\pi$
$168$		0			0
$169$	84.3245	−	146.054i	0.498962	−	0.864227i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	19.2965	−	33.4225i	0.111540	−	0.193193i	−0.804851	−	0.593477i	$-0.797755\pi$
$173$	19.2965	−	33.4225i	0.111540	−	0.193193i	0.916391	+	0.400283i	$0.131088\pi$
$174$		0			0
$175$	−177.201	+	102.307i	−1.01258	+	0.584612i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	36.4264i		−	0.203499i	−0.994810	−	0.101750i	$-0.967556\pi$
$179$		−	36.4264i		−	0.203499i	0.994810	−	0.101750i	$-0.0324441\pi$
$180$		0			0
$181$	18.5921			0.102719			0.0513594	−	0.998680i	$-0.483645\pi$
$181$	18.5921			0.102719			0.0513594	+	0.998680i	$0.483645\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	55.1327	+	95.4927i	0.298015	+	0.516177i
$186$		0			0
$187$	75.9055	+	43.8240i	0.405912	+	0.234353i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−244.973	−	141.435i	−1.28258	−	0.740497i	−0.305260	−	0.952269i	$-0.598743\pi$
$191$	−244.973	−	141.435i	−1.28258	−	0.740497i	−0.977319	+	0.211772i	$0.932077\pi$
$192$		0			0
$193$	−151.542	−	262.479i	−0.785193	−	1.35999i	−0.928884	−	0.370372i	$-0.879230\pi$
$193$	−151.542	−	262.479i	−0.785193	−	1.35999i	0.143691	−	0.989623i	$-0.454103\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	139.184			0.706520			0.353260	−	0.935525i	$-0.385073\pi$
$197$	139.184			0.706520			0.353260	+	0.935525i	$0.385073\pi$
$198$		0			0
$199$		−	11.2337i		−	0.0564505i	−0.999602	−	0.0282253i	$-0.991014\pi$
$199$		−	11.2337i		−	0.0564505i	0.999602	−	0.0282253i	$-0.00898558\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−204.404	+	118.013i	−1.00692	+	0.581344i
$204$		0			0
$205$	57.5462	−	99.6730i	0.280713	−	0.486210i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−69.5825	+	120.520i	−0.332931	+	0.576653i
$210$		0			0
$211$	−112.017	+	64.6728i	−0.530884	+	0.306506i	−0.741376	−	0.671090i	$-0.765827\pi$
$211$	−112.017	+	64.6728i	−0.530884	+	0.306506i	0.210492	+	0.977595i	$0.432493\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	100.963i		−	0.469595i
$216$		0			0
$217$	191.966			0.884634
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.63003	−	4.55535i	−0.0119006	−	0.0206124i
$222$		0			0
$223$	209.210	+	120.787i	0.938159	+	0.541647i	0.889383	−	0.457163i	$-0.151134\pi$
$223$	209.210	+	120.787i	0.938159	+	0.541647i	0.0487765	+	0.998810i	$0.484468\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−330.710	−	190.936i	−1.45687	−	0.841126i	−0.458016	−	0.888944i	$-0.651440\pi$
$227$	−330.710	−	190.936i	−1.45687	−	0.841126i	−0.998856	+	0.0478181i	$0.984773\pi$
$228$		0			0
$229$	−74.6642	−	129.322i	−0.326044	−	0.564725i	0.655679	−	0.755040i	$-0.272383\pi$
$229$	−74.6642	−	129.322i	−0.326044	−	0.564725i	−0.981723	+	0.190315i	$0.939049\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	218.934			0.939631			0.469816	−	0.882765i	$-0.344320\pi$
$233$	218.934			0.939631			0.469816	+	0.882765i	$0.344320\pi$
$234$		0			0
$235$			4.92103i			0.0209406i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	218.254	−	126.009i	0.913197	−	0.527235i	0.0317388	−	0.999496i	$-0.489896\pi$
$239$	218.254	−	126.009i	0.913197	−	0.527235i	0.881458	+	0.472262i	$0.156562\pi$
$240$		0			0
$241$	−226.014	+	391.467i	−0.937816	+	1.62435i	−0.168282	+	0.985739i	$0.553822\pi$
$241$	−226.014	+	391.467i	−0.937816	+	1.62435i	−0.769534	+	0.638606i	$0.779511\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−115.925	+	200.787i	−0.473162	+	0.819540i
$246$		0			0
$247$	7.23284	−	4.17588i	0.0292828	−	0.0169064i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			139.429i			0.555492i	0.960655	+	0.277746i	$0.0895874\pi$
$251$			139.429i			0.555492i	−0.960655	+	0.277746i	$0.910413\pi$
$252$		0			0
$253$	−208.297			−0.823306
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−235.308	−	407.565i	−0.915594	−	1.58586i	−0.806029	−	0.591875i	$-0.798388\pi$
$257$	−235.308	−	407.565i	−0.915594	−	1.58586i	−0.109564	−	0.993980i	$-0.534946\pi$
$258$		0			0
$259$	−408.308	−	235.737i	−1.57648	−	0.910181i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	22.2028	+	12.8188i	0.0844214	+	0.0487407i	0.541616	−	0.840626i	$-0.317813\pi$
$263$	22.2028	+	12.8188i	0.0844214	+	0.0487407i	−0.457195	+	0.889366i	$0.651146\pi$
$264$		0			0
$265$	−28.6141	−	49.5610i	−0.107978	−	0.187023i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.15075			0.0303002			0.0151501	−	0.999885i	$-0.495177\pi$
$269$	8.15075			0.0303002			0.0151501	+	0.999885i	$0.495177\pi$
$270$		0			0
$271$			401.979i			1.48332i	0.670777	+	0.741659i	$0.265961\pi$
$271$			401.979i			1.48332i	−0.670777	+	0.741659i	$0.734039\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	150.826	−	87.0792i	0.548457	−	0.316652i
$276$		0			0
$277$	−56.2021	+	97.3449i	−0.202896	+	0.351426i	−0.949460	−	0.313887i	$-0.898369\pi$
$277$	−56.2021	+	97.3449i	−0.202896	+	0.351426i	0.746565	+	0.665313i	$0.231702\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−268.867	+	465.692i	−0.956823	+	1.65727i	−0.226681	+	0.973969i	$0.572788\pi$
$281$	−268.867	+	465.692i	−0.956823	+	1.65727i	−0.730141	+	0.683296i	$0.760546\pi$
$282$		0			0
$283$	−122.303	+	70.6114i	−0.432164	+	0.249510i	−0.700268	−	0.713880i	$-0.746936\pi$
$283$	−122.303	+	70.6114i	−0.432164	+	0.249510i	0.268104	+	0.963390i	$0.413603\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			492.113i			1.71468i
$288$		0			0
$289$	−210.151			−0.727167
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−230.291	−	398.875i	−0.785975	−	1.36135i	−0.928415	−	0.371545i	$-0.878828\pi$
$293$	−230.291	−	398.875i	−0.785975	−	1.36135i	0.142440	−	0.989803i	$-0.454505\pi$
$294$		0			0
$295$	−207.991	−	120.084i	−0.705055	−	0.407064i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.8258	+	6.25029i	0.0362068	+	0.0209040i
$300$		0			0
$301$	215.849	+	373.862i	0.717107	+	1.24206i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−197.948			−0.649011
$306$		0			0
$307$		−	210.322i		−	0.685089i	−0.939502	−	0.342545i	$-0.888711\pi$
$307$		−	210.322i		−	0.685089i	0.939502	−	0.342545i	$-0.111289\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	110.993	−	64.0821i	0.356892	−	0.206052i	−0.310824	−	0.950467i	$-0.600605\pi$
$311$	110.993	−	64.0821i	0.356892	−	0.206052i	0.667717	+	0.744416i	$0.267272\pi$
$312$		0			0
$313$	−3.62140	+	6.27245i	−0.0115700	+	0.0200398i	−0.871752	−	0.489947i	$-0.837016\pi$
$313$	−3.62140	+	6.27245i	−0.0115700	+	0.0200398i	0.860182	+	0.509986i	$0.170350\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−120.145	+	208.098i	−0.379007	+	0.656460i	−0.990918	−	0.134467i	$-0.957068\pi$
$317$	−120.145	+	208.098i	−0.379007	+	0.656460i	0.611911	+	0.790927i	$0.290401\pi$
$318$		0			0
$319$	173.980	−	100.447i	0.545392	−	0.314882i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			125.194i			0.387596i
$324$		0			0
$325$	−10.4518			−0.0321595
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.5207	−	18.2224i	−0.0319778	−	0.0553872i
$330$		0			0
$331$	370.385	+	213.842i	1.11899	+	0.646048i	0.941142	−	0.338011i	$-0.109754\pi$
$331$	370.385	+	213.842i	1.11899	+	0.646048i	0.177845	+	0.984058i	$0.443087\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−103.906	−	59.9904i	−0.310168	−	0.179076i
$336$		0			0
$337$	152.442	+	264.037i	0.452349	+	0.783492i	0.998531	−	0.0541746i	$-0.0172528\pi$
$337$	152.442	+	264.037i	0.452349	+	0.783492i	−0.546182	+	0.837666i	$0.683919\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−163.393			−0.479157
$342$		0			0
$343$		−	423.102i		−	1.23353i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	146.406	−	84.5276i	0.421919	−	0.243595i	−0.273979	−	0.961736i	$-0.588340\pi$
$347$	146.406	−	84.5276i	0.421919	−	0.243595i	0.695898	+	0.718140i	$0.255006\pi$
$348$		0			0
$349$	−107.298	+	185.846i	−0.307444	+	0.532509i	−0.977802	−	0.209529i	$-0.932807\pi$
$349$	−107.298	+	185.846i	−0.307444	+	0.532509i	0.670358	+	0.742037i	$0.266140\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	275.895	−	477.865i	0.781574	−	1.35373i	−0.149451	−	0.988769i	$-0.547751\pi$
$353$	275.895	−	477.865i	0.781574	−	1.35373i	0.931025	−	0.364956i	$-0.118916\pi$
$354$		0			0
$355$	262.593	−	151.608i	0.739698	−	0.427065i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	554.828i		−	1.54548i	−0.634721	−	0.772741i	$-0.718885\pi$
$359$		−	554.828i		−	1.54548i	0.634721	−	0.772741i	$-0.281115\pi$
$360$		0			0
$361$	162.222			0.449367
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−103.334	−	178.980i	−0.283108	−	0.490357i
$366$		0			0
$367$	−145.642	−	84.0864i	−0.396845	−	0.229118i	0.288277	−	0.957547i	$-0.406918\pi$
$367$	−145.642	−	84.0864i	−0.396845	−	0.229118i	−0.685122	+	0.728429i	$0.740251\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	211.913	+	122.348i	0.571195	+	0.329780i
$372$		0			0
$373$	−171.699	−	297.391i	−0.460318	−	0.797295i	0.538658	−	0.842524i	$-0.318931\pi$
$373$	−171.699	−	297.391i	−0.460318	−	0.797295i	−0.998977	+	0.0452296i	$0.985598\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.0564			−0.0319798
$378$		0			0
$379$			602.392i			1.58943i	0.606986	+	0.794713i	$0.292379\pi$
$379$			602.392i			1.58943i	−0.606986	+	0.794713i	$0.707621\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−315.762	+	182.305i	−0.824443	+	0.475992i	−0.851946	−	0.523630i	$-0.824578\pi$
$383$	−315.762	+	182.305i	−0.824443	+	0.475992i	0.0275035	+	0.999622i	$0.491244\pi$
$384$		0			0
$385$	155.228	−	268.862i	0.403189	−	0.698344i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	107.326	−	185.893i	0.275901	−	0.477875i	−0.694461	−	0.719530i	$-0.744357\pi$
$389$	107.326	−	185.893i	0.275901	−	0.477875i	0.970362	+	0.241656i	$0.0776904\pi$
$390$		0			0
$391$	−162.280	+	93.6923i	−0.415038	+	0.239622i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			26.0071i			0.0658409i
$396$		0			0
$397$	684.628			1.72450			0.862251	−	0.506480i	$-0.169054\pi$
$397$	684.628			1.72450			0.862251	+	0.506480i	$0.169054\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−95.1918	−	164.877i	−0.237386	−	0.411164i	0.722577	−	0.691290i	$-0.242957\pi$
$401$	−95.1918	−	164.877i	−0.237386	−	0.411164i	−0.959963	+	0.280125i	$0.909624\pi$
$402$		0			0
$403$	8.49203	+	4.90287i	0.0210720	+	0.0121659i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	347.534	+	200.649i	0.853892	+	0.492995i
$408$		0			0
$409$	188.978	+	327.320i	0.462049	+	0.800293i	0.999063	−	0.0432806i	$-0.0137809\pi$
$409$	188.978	+	327.320i	0.462049	+	0.800293i	−0.537014	+	0.843574i	$0.680448\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1026.91			2.48647
$414$		0			0
$415$		−	230.573i		−	0.555598i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	267.326	−	154.341i	0.638009	−	0.368355i	−0.145838	−	0.989308i	$-0.546588\pi$
$419$	267.326	−	154.341i	0.638009	−	0.368355i	0.783847	+	0.620954i	$0.213255\pi$
$420$		0			0
$421$	−176.834	+	306.286i	−0.420034	+	0.727521i	−0.995942	−	0.0899938i	$-0.971315\pi$
$421$	−176.834	+	306.286i	−0.420034	+	0.727521i	0.575908	+	0.817514i	$0.304649\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	78.3369	−	135.684i	0.184322	−	0.319255i
$426$		0			0
$427$	732.995	−	423.195i	1.71662	−	0.991088i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			472.777i			1.09693i	0.836174	+	0.548465i	$0.184787\pi$
$431$			472.777i			1.09693i	−0.836174	+	0.548465i	$0.815213\pi$
$432$		0			0
$433$	61.4188			0.141845			0.0709224	−	0.997482i	$-0.477406\pi$
$433$	61.4188			0.141845			0.0709224	+	0.997482i	$0.477406\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−148.762	−	257.663i	−0.340416	−	0.589618i
$438$		0			0
$439$	354.347	+	204.582i	0.807169	+	0.466019i	0.845972	−	0.533228i	$-0.179021\pi$
$439$	354.347	+	204.582i	0.807169	+	0.466019i	−0.0388030	+	0.999247i	$0.512354\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	668.806	+	386.136i	1.50972	+	0.871638i	0.999936	+	0.0113360i	$0.00360844\pi$
$443$	668.806	+	386.136i	1.50972	+	0.871638i	0.509785	+	0.860302i	$0.329725\pi$
$444$		0			0
$445$	−87.8536	−	152.167i	−0.197424	−	0.341948i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	789.037			1.75732			0.878660	−	0.477448i	$-0.158438\pi$
$449$	789.037			1.75732			0.878660	+	0.477448i	$0.158438\pi$
$450$		0			0
$451$		−	418.865i		−	0.928747i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−16.1354	+	9.31575i	−0.0354623	+	0.0204742i
$456$		0			0
$457$	138.165	−	239.309i	0.302331	−	0.523653i	−0.674332	−	0.738428i	$-0.735568\pi$
$457$	138.165	−	239.309i	0.302331	−	0.523653i	0.976664	+	0.214775i	$0.0689018\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−294.041	+	509.295i	−0.637834	+	1.10476i	0.348073	+	0.937467i	$0.386836\pi$
$461$	−294.041	+	509.295i	−0.637834	+	1.10476i	−0.985907	+	0.167293i	$0.946497\pi$
$462$		0			0
$463$	677.285	−	391.031i	1.46282	−	0.844558i	0.463677	−	0.886004i	$-0.346530\pi$
$463$	677.285	−	391.031i	1.46282	−	0.844558i	0.999141	+	0.0414459i	$0.0131964\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	663.203i		−	1.42014i	−0.704133	−	0.710068i	$-0.748664\pi$
$467$		−	663.203i		−	1.42014i	0.704133	−	0.710068i	$-0.251336\pi$
$468$		0			0
$469$	513.014			1.09385
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−183.721	−	318.214i	−0.388417	−	0.672758i
$474$		0			0
$475$	215.434	+	124.381i	0.453546	+	0.261855i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	562.018	+	324.481i	1.17331	+	0.677414i	0.954459	−	0.298344i	$-0.0964341\pi$
$479$	562.018	+	324.481i	1.17331	+	0.677414i	0.218856	+	0.975757i	$0.429767\pi$
$480$		0			0
$481$	−12.0416	−	20.8567i	−0.0250346	−	0.0433611i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.4810			−0.0401669
$486$		0			0
$487$			282.104i			0.579269i	0.957137	+	0.289635i	$0.0935338\pi$
$487$			282.104i			0.579269i	−0.957137	+	0.289635i	$0.906466\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−652.933	+	376.971i	−1.32980	+	0.767762i	−0.985269	−	0.171012i	$-0.945296\pi$
$491$	−652.933	+	376.971i	−1.32980	+	0.767762i	−0.344534	+	0.938774i	$0.611963\pi$
$492$		0			0
$493$	90.3630	−	156.513i	0.183292	−	0.317471i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−648.247	+	1122.80i	−1.30432	+	2.25915i
$498$		0			0
$499$	−446.169	+	257.596i	−0.894126	+	0.516224i	−0.875290	−	0.483599i	$-0.839329\pi$
$499$	−446.169	+	257.596i	−0.894126	+	0.516224i	−0.0188362	+	0.999823i	$0.505996\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	523.660i		−	1.04107i	−0.853839	−	0.520537i	$-0.825732\pi$
$503$		−	523.660i		−	1.04107i	0.853839	−	0.520537i	$-0.174268\pi$
$504$		0			0
$505$	−301.072			−0.596182
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−267.685	−	463.645i	−0.525905	−	0.910893i	−0.999545	−	0.0301749i	$-0.990394\pi$
$509$	−267.685	−	463.645i	−0.525905	−	0.910893i	0.473640	−	0.880719i	$-0.342940\pi$
$510$		0			0
$511$	765.285	+	441.838i	1.49762	+	0.864653i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−215.925	−	124.665i	−0.419273	−	0.242067i
$516$		0			0
$517$	8.95475	+	15.5101i	0.0173206	+	0.0300002i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−177.268			−0.340246			−0.170123	−	0.985423i	$-0.554416\pi$
$521$	−177.268			−0.340246			−0.170123	+	0.985423i	$0.554416\pi$
$522$		0			0
$523$		−	444.206i		−	0.849343i	−0.905347	−	0.424672i	$-0.860390\pi$
$523$		−	444.206i		−	0.849343i	0.905347	−	0.424672i	$-0.139610\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−127.296	+	73.4944i	−0.241548	+	0.139458i
$528$		0			0
$529$	−41.8394	+	72.4679i	−0.0790914	+	0.136990i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.5688	+	21.7697i	−0.0235812	+	0.0408438i
$534$		0			0
$535$	253.065	−	146.107i	0.473018	−	0.273097i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			843.787i			1.56547i
$540$		0			0
$541$	−571.163			−1.05575			−0.527877	−	0.849321i	$-0.677012\pi$
$541$	−571.163			−1.05575			−0.527877	+	0.849321i	$0.677012\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−117.378	−	203.304i	−0.215372	−	0.373036i
$546$		0			0
$547$	139.875	+	80.7569i	0.255713	+	0.147636i	0.622377	−	0.782717i	$-0.286167\pi$
$547$	139.875	+	80.7569i	0.255713	+	0.147636i	−0.366664	+	0.930353i	$0.619500\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	248.507	+	143.476i	0.451011	+	0.260391i
$552$		0			0
$553$	−55.6008	−	96.3034i	−0.100544	−	0.174147i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−568.917			−1.02139			−0.510697	−	0.859761i	$-0.670613\pi$
$557$	−568.917			−1.02139			−0.510697	+	0.859761i	$0.670613\pi$
$558$		0			0
$559$			22.0515i			0.0394481i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−250.527	+	144.642i	−0.444985	+	0.256912i	−0.705710	−	0.708501i	$-0.749372\pi$
$563$	−250.527	+	144.642i	−0.444985	+	0.256912i	0.260725	+	0.965413i	$0.416038\pi$
$564$		0			0
$565$	−6.37900	+	11.0487i	−0.0112903	+	0.0195553i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	223.117	−	386.450i	0.392121	−	0.679174i	−0.600608	−	0.799544i	$-0.705075\pi$
$569$	223.117	−	386.450i	0.392121	−	0.679174i	0.992729	+	0.120370i	$0.0384079\pi$
$570$		0			0
$571$	372.386	−	214.997i	0.652164	−	0.376527i	−0.137121	−	0.990554i	$-0.543785\pi$
$571$	372.386	−	214.997i	0.652164	−	0.376527i	0.789285	+	0.614027i	$0.210451\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			372.337i			0.647542i
$576$		0			0
$577$	50.9694			0.0883353			0.0441676	−	0.999024i	$-0.485936\pi$
$577$	50.9694			0.0883353			0.0441676	+	0.999024i	$0.485936\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	492.943	+	853.803i	0.848440	+	1.46954i
$582$		0			0
$583$	−180.371	−	104.137i	−0.309385	−	0.178623i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	643.771	+	371.681i	1.09671	+	0.633188i	0.935356	−	0.353708i	$-0.115079\pi$
$587$	643.771	+	371.681i	1.09671	+	0.633188i	0.161358	+	0.986896i	$0.448413\pi$
$588$		0			0
$589$	−116.692	−	202.117i	−0.198119	−	0.343152i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	382.547			0.645104			0.322552	−	0.946552i	$-0.395459\pi$
$593$	382.547			0.645104			0.322552	+	0.946552i	$0.395459\pi$
$594$		0			0
$595$		−	279.287i		−	0.469391i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	856.248	−	494.355i	1.42946	−	0.825301i	0.432384	−	0.901689i	$-0.357672\pi$
$599$	856.248	−	494.355i	1.42946	−	0.825301i	0.997078	+	0.0763888i	$0.0243390\pi$
$600$		0			0
$601$	−263.280	+	456.015i	−0.438070	+	0.758760i	−0.997541	−	0.0700905i	$-0.977671\pi$
$601$	−263.280	+	456.015i	−0.438070	+	0.758760i	0.559470	+	0.828850i	$0.311005\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	31.9637	−	55.3627i	0.0528325	−	0.0915086i
$606$		0			0
$607$	−447.631	+	258.440i	−0.737448	+	0.425766i	−0.821141	−	0.570726i	$-0.806662\pi$
$607$	−447.631	+	258.440i	−0.737448	+	0.425766i	0.0836928	+	0.996492i	$0.473329\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	1.07481i		−	0.00175910i
$612$		0			0
$613$	−762.957			−1.24463			−0.622314	−	0.782768i	$-0.713807\pi$
$613$	−762.957			−1.24463			−0.622314	+	0.782768i	$0.713807\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−60.9168	−	105.511i	−0.0987307	−	0.171007i	0.812429	−	0.583060i	$-0.198145\pi$
$617$	−60.9168	−	105.511i	−0.0987307	−	0.171007i	−0.911160	+	0.412054i	$0.864812\pi$
$618$		0			0
$619$	265.675	+	153.388i	0.429200	+	0.247799i	0.699006	−	0.715116i	$-0.253626\pi$
$619$	265.675	+	153.388i	0.429200	+	0.247799i	−0.269806	+	0.962915i	$0.586959\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	650.636	+	375.645i	1.04436	+	0.602961i
$624$		0			0
$625$	−63.7082	−	110.346i	−0.101933	−	0.176553i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	361.010			0.573942
$630$		0			0
$631$		−	1071.11i		−	1.69749i	−0.528805	−	0.848744i	$-0.677360\pi$
$631$		−	1071.11i		−	1.69749i	0.528805	−	0.848744i	$-0.322640\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	19.6623	−	11.3521i	0.0309643	−	0.0178773i
$636$		0			0
$637$	25.3193	−	43.8543i	0.0397477	−	0.0688450i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−527.259	+	913.240i	−0.822557	+	1.42471i	0.0812143	+	0.996697i	$0.474120\pi$
$641$	−527.259	+	913.240i	−0.822557	+	1.42471i	−0.903772	+	0.428015i	$0.859213\pi$
$642$		0			0
$643$	−42.0680	+	24.2880i	−0.0654246	+	0.0377729i	−0.532355	−	0.846521i	$-0.678693\pi$
$643$	−42.0680	+	24.2880i	−0.0654246	+	0.0377729i	0.466931	+	0.884294i	$0.345360\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			539.373i			0.833653i	0.908986	+	0.416826i	$0.136858\pi$
$647$			539.373i			0.833653i	−0.908986	+	0.416826i	$0.863142\pi$
$648$		0			0
$649$	−874.061			−1.34678
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−276.457	−	478.838i	−0.423365	−	0.733290i	0.572901	−	0.819624i	$-0.305818\pi$
$653$	−276.457	−	478.838i	−0.423365	−	0.733290i	−0.996266	+	0.0863348i	$0.972485\pi$
$654$		0			0
$655$	312.081	+	180.180i	0.476460	+	0.275084i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	734.162	+	423.869i	1.11406	+	0.643200i	0.939877	−	0.341514i	$-0.110940\pi$
$659$	734.162	+	423.869i	1.11406	+	0.643200i	0.174178	+	0.984714i	$0.444273\pi$
$660$		0			0
$661$	359.447	+	622.580i	0.543792	+	0.941876i	0.998682	+	0.0513280i	$0.0163454\pi$
$661$	359.447	+	622.580i	0.543792	+	0.941876i	−0.454890	+	0.890548i	$0.650321\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	443.444			0.666833
$666$		0			0
$667$			429.497i			0.643923i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−623.893	+	360.205i	−0.929796	+	0.536818i
$672$		0			0
$673$	288.488	−	499.675i	0.428659	−	0.742460i	−0.568095	−	0.822963i	$-0.692319\pi$
$673$	288.488	−	499.675i	0.428659	−	0.742460i	0.996754	+	0.0805033i	$0.0256528\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−101.021	+	174.974i	−0.149219	+	0.258454i	−0.930939	−	0.365175i	$-0.881009\pi$
$677$	−101.021	+	174.974i	−0.149219	+	0.258454i	0.781720	+	0.623629i	$0.214343\pi$
$678$		0			0
$679$	72.1372	−	41.6484i	0.106240	−	0.0613379i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			568.249i			0.831990i	0.909367	+	0.415995i	$0.136567\pi$
$683$			568.249i			0.831990i	−0.909367	+	0.415995i	$0.863433\pi$
$684$		0			0
$685$	−122.362			−0.178631
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.24965	+	10.8247i	0.00907060	+	0.0157107i
$690$		0			0
$691$	−351.376	−	202.867i	−0.508504	−	0.293585i	0.223714	−	0.974655i	$-0.428182\pi$
$691$	−351.376	−	202.867i	−0.508504	−	0.293585i	−0.732218	+	0.681070i	$0.761515\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−354.600	−	204.728i	−0.510215	−	0.294573i
$696$		0			0
$697$	−188.407	−	326.330i	−0.270311	−	0.468192i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	83.5164			0.119139			0.0595695	−	0.998224i	$-0.481027\pi$
$701$	83.5164			0.119139			0.0595695	+	0.998224i	$0.481027\pi$
$702$		0			0
$703$			573.200i			0.815363i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1114.86	−	643.663i	1.57688	−	0.910414i
$708$		0			0
$709$	173.908	−	301.217i	0.245286	−	0.424848i	−0.716926	−	0.697149i	$-0.754452\pi$
$709$	173.908	−	301.217i	0.245286	−	0.424848i	0.962212	+	0.272302i	$0.0877849\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	174.660	−	302.520i	0.244965	−	0.424292i
$714$		0			0
$715$	13.7337	−	7.92916i	0.0192080	−	0.0110897i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			536.277i			0.745865i	0.927858	+	0.372933i	$0.121648\pi$
$719$			536.277i			0.745865i	−0.927858	+	0.372933i	$0.878352\pi$
$720$		0			0
$721$	1066.08			1.47862
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−179.553	−	310.995i	−0.247659	−	0.428959i
$726$		0			0
$727$	−815.055	−	470.573i	−1.12112	−	0.647280i	−0.179435	−	0.983770i	$-0.557427\pi$
$727$	−815.055	−	470.573i	−1.12112	−	0.647280i	−0.941687	+	0.336490i	$0.890760\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−286.267	−	165.277i	−0.391611	−	0.226096i
$732$		0			0
$733$	−311.063	−	538.777i	−0.424370	−	0.735030i	0.571991	−	0.820260i	$-0.306171\pi$
$733$	−311.063	−	538.777i	−0.424370	−	0.735030i	−0.996361	+	0.0852294i	$0.972838\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−436.655			−0.592477
$738$		0			0
$739$		−	444.439i		−	0.601406i	−0.953718	−	0.300703i	$-0.902779\pi$
$739$		−	444.439i		−	0.601406i	0.953718	−	0.300703i	$-0.0972213\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−66.2270	+	38.2362i	−0.0891346	+	0.0514619i	−0.543905	−	0.839147i	$-0.683055\pi$
$743$	−66.2270	+	38.2362i	−0.0891346	+	0.0514619i	0.454770	+	0.890609i	$0.349721\pi$
$744$		0			0
$745$	−193.626	+	335.370i	−0.259901	+	0.450161i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−624.725	+	1082.06i	−0.834079	+	1.44467i
$750$		0			0
$751$	949.025	−	547.920i	1.26368	−	0.729587i	0.289897	−	0.957058i	$-0.406379\pi$
$751$	949.025	−	547.920i	1.26368	−	0.729587i	0.973785	+	0.227471i	$0.0730457\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	689.070i		−	0.912676i
$756$		0			0
$757$	346.346			0.457525			0.228762	−	0.973482i	$-0.426532\pi$
$757$	346.346			0.457525			0.228762	+	0.973482i	$0.426532\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	106.565	+	184.576i	0.140033	+	0.242544i	0.927509	−	0.373802i	$-0.121946\pi$
$761$	106.565	+	184.576i	0.140033	+	0.242544i	−0.787476	+	0.616345i	$0.788613\pi$
$762$		0			0
$763$	869.291	+	501.885i	1.13931	+	0.657779i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	45.4277	+	26.2277i	0.0592277	+	0.0341952i
$768$		0			0
$769$	−270.786	−	469.015i	−0.352127	−	0.609902i	0.634495	−	0.772927i	$-0.281208\pi$
$769$	−270.786	−	469.015i	−0.352127	−	0.609902i	−0.986622	+	0.163025i	$0.947875\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1255.73			1.62449			0.812245	−	0.583317i	$-0.198245\pi$
$773$	1255.73			1.62449			0.812245	+	0.583317i	$0.198245\pi$
$774$		0			0
$775$			292.070i			0.376864i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	518.136	−	299.146i	0.665130	−	0.384013i
$780$		0			0
$781$	551.759	−	955.675i	0.706478	−	1.22366i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.19706	−	12.4657i	0.00916822	−	0.0158798i
$786$		0			0
$787$	859.448	−	496.202i	1.09206	−	0.630499i	0.157933	−	0.987450i	$-0.449517\pi$
$787$	859.448	−	496.202i	1.09206	−	0.630499i	0.934123	+	0.356951i	$0.116184\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	54.5507i		−	0.0689643i
$792$		0			0
$793$	43.2342			0.0545198
$794$		0			0
$795$		0			0
$796$		0			0
$797$	319.262	+	552.978i	0.400580	+	0.693824i	0.993796	−	0.111219i	$-0.0354754\pi$
$797$	319.262	+	552.978i	0.400580	+	0.693824i	−0.593216	+	0.805043i	$0.702142\pi$
$798$		0			0
$799$	13.9530	+	8.05574i	0.0174630	+	0.0100823i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−651.377	−	376.073i	−0.811179	−	0.468335i
$804$		0			0
$805$	331.865	+	574.806i	0.412254	+	0.714045i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	174.260			0.215401			0.107701	−	0.994183i	$-0.465651\pi$
$809$	174.260			0.215401			0.107701	+	0.994183i	$0.465651\pi$
$810$		0			0
$811$			1182.19i			1.45770i	0.684675	+	0.728849i	$0.259944\pi$
$811$			1182.19i			1.45770i	−0.684675	+	0.728849i	$0.740056\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−139.880	+	80.7597i	−0.171632	+	0.0990917i
$816$		0			0
$817$	262.421	−	454.527i	0.321201	−	0.556336i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	293.955	−	509.144i	0.358045	−	0.620151i	−0.629590	−	0.776928i	$-0.716777\pi$
$821$	293.955	−	509.144i	0.358045	−	0.620151i	0.987634	+	0.156777i	$0.0501103\pi$
$822$		0			0
$823$	−98.0750	+	56.6236i	−0.119168	+	0.0688015i	−0.558399	−	0.829573i	$-0.688584\pi$
$823$	−98.0750	+	56.6236i	−0.119168	+	0.0688015i	0.439231	+	0.898374i	$0.355251\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			800.560i			0.968030i	0.875060	+	0.484015i	$0.160822\pi$
$827$			800.560i			0.968030i	−0.875060	+	0.484015i	$0.839178\pi$
$828$		0			0
$829$	−1162.87			−1.40274			−0.701369	−	0.712798i	$-0.747427\pi$
$829$	−1162.87			−1.40274			−0.701369	+	0.712798i	$0.747427\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	379.538	+	657.378i	0.455627	+	0.789170i
$834$		0			0
$835$	−232.551	−	134.264i	−0.278505	−	0.160795i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1355.92	−	782.842i	−1.61612	−	0.933065i	−0.987912	−	0.155017i	$-0.950457\pi$
$839$	−1355.92	−	782.842i	−1.61612	−	0.933065i	−0.628205	−	0.778048i	$-0.716210\pi$
$840$		0			0
$841$	213.383	+	369.590i	0.253725	+	0.439464i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	457.406			0.541309
$846$		0			0
$847$			273.341i			0.322717i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−743.000	+	428.971i	−0.873091	+	0.504079i
$852$		0			0
$853$	68.8088	−	119.180i	0.0806668	−	0.139719i	−0.822870	−	0.568230i	$-0.807628\pi$
$853$	68.8088	−	119.180i	0.0806668	−	0.139719i	0.903537	+	0.428511i	$0.140962\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	384.489	−	665.955i	0.448646	−	0.777077i	−0.549653	−	0.835393i	$-0.685240\pi$
$857$	384.489	−	665.955i	0.448646	−	0.777077i	0.998298	+	0.0583164i	$0.0185732\pi$
$858$		0			0
$859$	178.353	−	102.972i	0.207629	−	0.119875i	−0.392580	−	0.919718i	$-0.628417\pi$
$859$	178.353	−	102.972i	0.207629	−	0.119875i	0.600209	+	0.799843i	$0.295084\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	772.757i		−	0.895431i	−0.894176	−	0.447716i	$-0.852238\pi$
$863$		−	772.757i		−	0.895431i	0.894176	−	0.447716i	$-0.147762\pi$
$864$		0			0
$865$	104.671			0.121007
$866$		0			0
$867$		0			0
$868$		0			0
$869$	47.3249	+	81.9692i	0.0544591	+	0.0943258i
$870$		0			0
$871$	22.6943	+	13.1026i	0.0260555	+	0.0150432i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1161.57	−	670.630i	−1.32750	−	0.766435i
$876$		0			0
$877$	200.096	+	346.577i	0.228160	+	0.395185i	0.957263	−	0.289219i	$-0.0933957\pi$
$877$	200.096	+	346.577i	0.228160	+	0.395185i	−0.729103	+	0.684404i	$0.760062\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	728.323			0.826700			0.413350	−	0.910572i	$-0.364359\pi$
$881$	728.323			0.826700			0.413350	+	0.910572i	$0.364359\pi$
$882$		0			0
$883$		−	383.413i		−	0.434216i	−0.976148	−	0.217108i	$-0.930338\pi$
$883$		−	383.413i		−	0.434216i	0.976148	−	0.217108i	$-0.0696625\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1255.91	−	725.098i	1.41590	−	0.817473i	0.419968	−	0.907539i	$-0.362041\pi$
$887$	1255.91	−	725.098i	1.41590	−	0.817473i	0.995936	+	0.0900662i	$0.0287079\pi$
$888$		0			0
$889$	−48.5392	+	84.0724i	−0.0545998	+	0.0945696i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−12.7907	+	22.1541i	−0.0143232	+	0.0248086i
$894$		0			0
$895$	85.5589	−	49.3974i	0.0955965	−	0.0551927i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			336.907i			0.374758i
$900$		0			0
$901$	−187.365			−0.207952
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.2125	+	43.6694i	0.0278592	+	0.0482535i
$906$		0			0
$907$	−533.290	−	307.895i	−0.587971	−	0.339465i	0.176324	−	0.984332i	$-0.443580\pi$
$907$	−533.290	−	307.895i	−0.587971	−	0.339465i	−0.764295	+	0.644867i	$0.776913\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	227.031	+	131.076i	0.249211	+	0.143882i	0.619403	−	0.785073i	$-0.287375\pi$
$911$	227.031	+	131.076i	0.249211	+	0.143882i	−0.370192	+	0.928955i	$0.620708\pi$
$912$		0			0
$913$	−419.572	−	726.720i	−0.459553	−	0.795969i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1540.83			−1.68030
$918$		0			0
$919$		−	566.458i		−	0.616385i	−0.951324	−	0.308193i	$-0.900276\pi$
$919$		−	566.458i		−	0.616385i	0.951324	−	0.308193i	$-0.0997241\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−57.3533	+	33.1130i	−0.0621379	+	0.0358754i
$924$		0			0
$925$	358.667	−	621.229i	0.387748	−	0.671599i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−298.745	+	517.442i	−0.321577	+	0.556988i	−0.980814	−	0.194948i	$-0.937546\pi$
$929$	−298.745	+	517.442i	−0.321577	+	0.556988i	0.659236	+	0.751936i	$0.270880\pi$
$930$		0			0
$931$	−1043.77	+	602.618i	−1.12112	+	0.647281i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			237.717i			0.254243i
$936$		0			0
$937$	457.785			0.488564			0.244282	−	0.969704i	$-0.421448\pi$
$937$	457.785			0.488564			0.244282	+	0.969704i	$0.421448\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−677.858	−	1174.09i	−0.720360	−	1.24770i	−0.960856	−	0.277049i	$-0.910643\pi$
$941$	−677.858	−	1174.09i	−0.720360	−	1.24770i	0.240496	−	0.970650i	$-0.422690\pi$
$942$		0			0
$943$	775.526	+	447.750i	0.822403	+	0.474814i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	567.925	+	327.891i	0.599709	+	0.346242i	0.768927	−	0.639336i	$-0.220791\pi$
$947$	567.925	+	327.891i	0.599709	+	0.346242i	−0.169218	+	0.985579i	$0.554124\pi$
$948$		0			0
$949$	22.5694	+	39.0914i	0.0237823	+	0.0411922i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−554.778			−0.582139			−0.291069	−	0.956702i	$-0.594011\pi$
$953$	−554.778			−0.582139			−0.291069	+	0.956702i	$0.594011\pi$
$954$		0			0
$955$		−	767.193i		−	0.803344i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	453.102	−	261.599i	0.472474	−	0.272783i
$960$		0			0
$961$	−343.493	+	594.947i	−0.357432	+	0.619091i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	411.009	−	711.889i	0.425917	−	0.737709i
$966$		0			0
$967$	−502.000	+	289.830i	−0.519131	+	0.299720i	−0.736579	−	0.676351i	$-0.763560\pi$
$967$	−502.000	+	289.830i	−0.519131	+	0.299720i	0.217448	+	0.976072i	$0.430227\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	260.660i		−	0.268445i	−0.990951	−	0.134223i	$-0.957146\pi$
$971$		−	260.660i		−	0.268445i	0.990951	−	0.134223i	$-0.0428537\pi$
$972$		0			0
$973$	1750.76			1.79934
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−638.953	−	1106.70i	−0.653995	−	1.13275i	−0.982145	−	0.188127i	$-0.939758\pi$
$977$	−638.953	−	1106.70i	−0.653995	−	1.13275i	0.328149	−	0.944626i	$-0.393575\pi$
$978$		0			0
$979$	−553.793	−	319.732i	−0.565672	−	0.326591i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	378.325	+	218.426i	0.384868	+	0.222204i	0.679934	−	0.733273i	$-0.262008\pi$
$983$	378.325	+	218.426i	0.384868	+	0.222204i	−0.295066	+	0.955477i	$0.595342\pi$
$984$		0			0
$985$	188.746	+	326.918i	0.191621	+	0.331897i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	785.562			0.794300
$990$		0			0
$991$			1344.50i			1.35671i	0.734734	+	0.678356i	$0.237307\pi$
$991$			1344.50i			1.35671i	−0.734734	+	0.678356i	$0.762693\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	26.3858	−	15.2338i	0.0265184	−	0.0153104i
$996$		0			0
$997$	−942.397	+	1632.28i	−0.945233	+	1.63719i	−0.189949	+	0.981794i	$0.560832\pi$
$997$	−942.397	+	1632.28i	−0.945233	+	1.63719i	−0.755284	+	0.655398i	$0.772501\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.g.127.5		16
3.2	odd	2		576.3.o.g.511.3		16
4.3	odd	2	inner	1728.3.o.g.127.6		16
8.3	odd	2		108.3.f.c.19.2		16
8.5	even	2		108.3.f.c.19.3		16
9.4	even	3	inner	1728.3.o.g.1279.6		16
9.5	odd	6		576.3.o.g.319.6		16
12.11	even	2		576.3.o.g.511.6		16
24.5	odd	2		36.3.f.c.7.6	✓	16
24.11	even	2		36.3.f.c.7.7	yes	16
36.23	even	6		576.3.o.g.319.3		16
36.31	odd	6	inner	1728.3.o.g.1279.5		16
72.5	odd	6		36.3.f.c.31.7	yes	16
72.11	even	6		324.3.d.i.163.1		8
72.13	even	6		108.3.f.c.91.2		16
72.29	odd	6		324.3.d.i.163.2		8
72.43	odd	6		324.3.d.g.163.8		8
72.59	even	6		36.3.f.c.31.6	yes	16
72.61	even	6		324.3.d.g.163.7		8
72.67	odd	6		108.3.f.c.91.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.6	✓	16	24.5	odd	2
36.3.f.c.7.7	yes	16	24.11	even	2
36.3.f.c.31.6	yes	16	72.59	even	6
36.3.f.c.31.7	yes	16	72.5	odd	6
108.3.f.c.19.2		16	8.3	odd	2
108.3.f.c.19.3		16	8.5	even	2
108.3.f.c.91.2		16	72.13	even	6
108.3.f.c.91.3		16	72.67	odd	6
324.3.d.g.163.7		8	72.61	even	6
324.3.d.g.163.8		8	72.43	odd	6
324.3.d.i.163.1		8	72.11	even	6
324.3.d.i.163.2		8	72.29	odd	6
576.3.o.g.319.3		16	36.23	even	6
576.3.o.g.319.6		16	9.5	odd	6
576.3.o.g.511.3		16	3.2	odd	2
576.3.o.g.511.6		16	12.11	even	2
1728.3.o.g.127.5		16	1.1	even	1	trivial
1728.3.o.g.127.6		16	4.3	odd	2	inner
1728.3.o.g.1279.5		16	36.31	odd	6	inner
1728.3.o.g.1279.6		16	9.4	even	3	inner

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35609 + 2.34881i) q^{5} +(-10.0431 - 5.79837i) q^{7} +O(q^{10})\)	\(q+(1.35609 + 2.34881i) q^{5} +(-10.0431 - 5.79837i) q^{7} +(8.54822 + 4.93532i) q^{11} +(-0.296185 - 0.513008i) q^{13} +8.87968 q^{17} +14.0989i q^{19} +(-18.2754 + 10.5513i) q^{23} +(8.82205 - 15.2802i) q^{25} +(10.1764 - 17.6260i) q^{29} +(-14.3357 + 8.27670i) q^{31} -31.4524i q^{35} +40.6557 q^{37} +(-21.2177 - 36.7502i) q^{41} +(-32.2385 - 18.6129i) q^{43} +(1.57134 + 0.907211i) q^{47} +(42.7423 + 74.0318i) q^{49} -21.1005 q^{53} +26.7709i q^{55} +(-76.6879 + 44.2758i) q^{59} +(-36.4925 + 63.2069i) q^{61} +(0.803307 - 1.39137i) q^{65} +(-38.3110 + 22.1189i) q^{67} -111.798i q^{71} -76.2003 q^{73} +(-57.2337 - 99.1316i) q^{77} +(8.30434 + 4.79451i) q^{79} +(-73.6244 - 42.5070i) q^{83} +(12.0416 + 20.8567i) q^{85} -64.7845 q^{89} +6.86958i q^{91} +(-33.1157 + 19.1193i) q^{95} +(-3.59139 + 6.22047i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5}+O(q^{10}) \) 16 * q + 6 * q^5	\( 16 q + 6 q^{5} + 46 q^{13} - 12 q^{17} - 30 q^{25} + 42 q^{29} - 56 q^{37} - 84 q^{41} + 58 q^{49} - 72 q^{53} + 34 q^{61} + 30 q^{65} + 116 q^{73} - 330 q^{77} + 140 q^{85} + 384 q^{89} - 148 q^{97}+O(q^{100}) \) 16 * q + 6 * q^5 + 46 * q^13 - 12 * q^17 - 30 * q^25 + 42 * q^29 - 56 * q^37 - 84 * q^41 + 58 * q^49 - 72 * q^53 + 34 * q^61 + 30 * q^65 + 116 * q^73 - 330 * q^77 + 140 * q^85 + 384 * q^89 - 148 * q^97

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