LMFDB - Embedded newform 1728.3.o.a.1279.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1279.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1728.1279
Dual form			1728.3.o.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{5} +(-3.00000 + 1.73205i) q^{7} +O(q^{10})$	$q+(-2.00000 + 3.46410i) q^{5} +(-3.00000 + 1.73205i) q^{7} +(-10.5000 + 6.06218i) q^{11} +(-11.0000 + 19.0526i) q^{13} +11.0000 q^{17} +15.5885i q^{19} +(-21.0000 - 12.1244i) q^{23} +(4.50000 + 7.79423i) q^{25} +(-17.0000 - 29.4449i) q^{29} +(6.00000 + 3.46410i) q^{31} -13.8564i q^{35} +16.0000 q^{37} +(6.50000 - 11.2583i) q^{41} +(43.5000 - 25.1147i) q^{43} +(-3.00000 + 1.73205i) q^{47} +(-18.5000 + 32.0429i) q^{49} +52.0000 q^{53} -48.4974i q^{55} +(-46.5000 - 26.8468i) q^{59} +(-8.00000 - 13.8564i) q^{61} +(-44.0000 - 76.2102i) q^{65} +(-100.500 - 58.0237i) q^{67} -25.0000 q^{73} +(21.0000 - 36.3731i) q^{77} +(24.0000 - 13.8564i) q^{79} +(30.0000 - 17.3205i) q^{83} +(-22.0000 + 38.1051i) q^{85} +2.00000 q^{89} -76.2102i q^{91} +(-54.0000 - 31.1769i) q^{95} +(21.5000 + 37.2391i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{5} - 6 q^{7}+O(q^{10}) $ 2 * q - 4 * q^5 - 6 * q^7	$ 2 q - 4 q^{5} - 6 q^{7} - 21 q^{11} - 22 q^{13} + 22 q^{17} - 42 q^{23} + 9 q^{25} - 34 q^{29} + 12 q^{31} + 32 q^{37} + 13 q^{41} + 87 q^{43} - 6 q^{47} - 37 q^{49} + 104 q^{53} - 93 q^{59} - 16 q^{61} - 88 q^{65} - 201 q^{67} - 50 q^{73} + 42 q^{77} + 48 q^{79} + 60 q^{83} - 44 q^{85} + 4 q^{89} - 108 q^{95} + 43 q^{97}+O(q^{100}) $ 2 * q - 4 * q^5 - 6 * q^7 - 21 * q^11 - 22 * q^13 + 22 * q^17 - 42 * q^23 + 9 * q^25 - 34 * q^29 + 12 * q^31 + 32 * q^37 + 13 * q^41 + 87 * q^43 - 6 * q^47 - 37 * q^49 + 104 * q^53 - 93 * q^59 - 16 * q^61 - 88 * q^65 - 201 * q^67 - 50 * q^73 + 42 * q^77 + 48 * q^79 + 60 * q^83 - 44 * q^85 + 4 * q^89 - 108 * q^95 + 43 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−2.00000	+	3.46410i	−0.400000	+	0.692820i	−0.993725	−	0.111847i	$-0.964323\pi$
$5$	−2.00000	+	3.46410i	−0.400000	+	0.692820i	0.593725	+	0.804668i	$0.297657\pi$
$6$		0			0
$7$	−3.00000	+	1.73205i	−0.428571	+	0.247436i	−0.698738	−	0.715378i	$-0.746255\pi$
$7$	−3.00000	+	1.73205i	−0.428571	+	0.247436i	0.270166	+	0.962814i	$0.412921\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−10.5000	+	6.06218i	−0.954545	+	0.551107i	−0.894490	−	0.447088i	$-0.852461\pi$
$11$	−10.5000	+	6.06218i	−0.954545	+	0.551107i	−0.0600555	+	0.998195i	$0.519128\pi$
$12$		0			0
$13$	−11.0000	+	19.0526i	−0.846154	+	1.46558i	0.0384615	+	0.999260i	$0.487754\pi$
$13$	−11.0000	+	19.0526i	−0.846154	+	1.46558i	−0.884615	+	0.466321i	$0.845579\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	11.0000			0.647059			0.323529	−	0.946218i	$-0.395131\pi$
$17$	11.0000			0.647059			0.323529	+	0.946218i	$0.395131\pi$
$18$		0			0
$19$			15.5885i			0.820445i	0.911985	+	0.410223i	$0.134549\pi$
$19$			15.5885i			0.820445i	−0.911985	+	0.410223i	$0.865451\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−21.0000	−	12.1244i	−0.913043	−	0.527146i	−0.0316343	−	0.999500i	$-0.510071\pi$
$23$	−21.0000	−	12.1244i	−0.913043	−	0.527146i	−0.881409	+	0.472354i	$0.843405\pi$
$24$		0			0
$25$	4.50000	+	7.79423i	0.180000	+	0.311769i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−17.0000	−	29.4449i	−0.586207	−	1.01534i	−0.994724	−	0.102589i	$-0.967287\pi$
$29$	−17.0000	−	29.4449i	−0.586207	−	1.01534i	0.408517	−	0.912751i	$-0.366046\pi$
$30$		0			0
$31$	6.00000	+	3.46410i	0.193548	+	0.111745i	0.593643	−	0.804729i	$-0.297689\pi$
$31$	6.00000	+	3.46410i	0.193548	+	0.111745i	−0.400094	+	0.916474i	$0.631023\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		−	13.8564i		−	0.395897i
$36$		0			0
$37$	16.0000			0.432432			0.216216	−	0.976346i	$-0.430628\pi$
$37$	16.0000			0.432432			0.216216	+	0.976346i	$0.430628\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.50000	−	11.2583i	0.158537	−	0.274593i	−0.775805	−	0.630973i	$-0.782656\pi$
$41$	6.50000	−	11.2583i	0.158537	−	0.274593i	0.934341	+	0.356380i	$0.115989\pi$
$42$		0			0
$43$	43.5000	−	25.1147i	1.01163	−	0.584064i	0.0999600	−	0.994991i	$-0.468129\pi$
$43$	43.5000	−	25.1147i	1.01163	−	0.584064i	0.911668	+	0.410928i	$0.134795\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00000	+	1.73205i	−0.0638298	+	0.0368521i	−0.531575	−	0.847011i	$-0.678400\pi$
$47$	−3.00000	+	1.73205i	−0.0638298	+	0.0368521i	0.467745	+	0.883863i	$0.345066\pi$
$48$		0			0
$49$	−18.5000	+	32.0429i	−0.377551	+	0.653938i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	52.0000			0.981132			0.490566	−	0.871404i	$-0.336790\pi$
$53$	52.0000			0.981132			0.490566	+	0.871404i	$0.336790\pi$
$54$		0			0
$55$		−	48.4974i		−	0.881771i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−46.5000	−	26.8468i	−0.788136	−	0.455030i	0.0511702	−	0.998690i	$-0.483705\pi$
$59$	−46.5000	−	26.8468i	−0.788136	−	0.455030i	−0.839306	+	0.543660i	$0.817038\pi$
$60$		0			0
$61$	−8.00000	−	13.8564i	−0.131148	−	0.227154i	0.792972	−	0.609259i	$-0.208533\pi$
$61$	−8.00000	−	13.8564i	−0.131148	−	0.227154i	−0.924119	+	0.382104i	$0.875199\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−44.0000	−	76.2102i	−0.676923	−	1.17247i
$66$		0			0
$67$	−100.500	−	58.0237i	−1.50000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$67$	−100.500	−	58.0237i	−1.50000	−	0.866025i	−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−25.0000			−0.342466			−0.171233	−	0.985231i	$-0.554775\pi$
$73$	−25.0000			−0.342466			−0.171233	+	0.985231i	$0.554775\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	21.0000	−	36.3731i	0.272727	−	0.472377i
$78$		0			0
$79$	24.0000	−	13.8564i	0.303797	−	0.175398i	−0.340350	−	0.940299i	$-0.610546\pi$
$79$	24.0000	−	13.8564i	0.303797	−	0.175398i	0.644148	+	0.764901i	$0.277212\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	30.0000	−	17.3205i	0.361446	−	0.208681i	−0.308269	−	0.951299i	$-0.599750\pi$
$83$	30.0000	−	17.3205i	0.361446	−	0.208681i	0.669715	+	0.742618i	$0.266416\pi$
$84$		0			0
$85$	−22.0000	+	38.1051i	−0.258824	+	0.448296i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.00000			0.0224719			0.0112360	−	0.999937i	$-0.496423\pi$
$89$	2.00000			0.0224719			0.0112360	+	0.999937i	$0.496423\pi$
$90$		0			0
$91$		−	76.2102i		−	0.837475i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−54.0000	−	31.1769i	−0.568421	−	0.328178i
$96$		0			0
$97$	21.5000	+	37.2391i	0.221649	+	0.383908i	0.955309	−	0.295609i	$-0.0955226\pi$
$97$	21.5000	+	37.2391i	0.221649	+	0.383908i	−0.733659	+	0.679517i	$0.762189\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10.0000	+	17.3205i	0.0990099	+	0.171490i	0.911275	−	0.411798i	$-0.135099\pi$
$101$	10.0000	+	17.3205i	0.0990099	+	0.171490i	−0.812265	+	0.583288i	$0.801766\pi$
$102$		0			0
$103$	−21.0000	−	12.1244i	−0.203883	−	0.117712i	0.394582	−	0.918861i	$-0.370889\pi$
$103$	−21.0000	−	12.1244i	−0.203883	−	0.117712i	−0.598466	+	0.801148i	$0.704223\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	15.5885i		−	0.145687i	−0.997343	−	0.0728433i	$-0.976793\pi$
$107$		−	15.5885i		−	0.145687i	0.997343	−	0.0728433i	$-0.0232073\pi$
$108$		0			0
$109$	88.0000			0.807339			0.403670	−	0.914905i	$-0.367734\pi$
$109$	88.0000			0.807339			0.403670	+	0.914905i	$0.367734\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−25.0000	+	43.3013i	−0.221239	+	0.383197i	−0.955184	−	0.296011i	$-0.904343\pi$
$113$	−25.0000	+	43.3013i	−0.221239	+	0.383197i	0.733946	+	0.679208i	$0.237677\pi$
$114$		0			0
$115$	84.0000	−	48.4974i	0.730435	−	0.421717i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−33.0000	+	19.0526i	−0.277311	+	0.160106i
$120$		0			0
$121$	13.0000	−	22.5167i	0.107438	−	0.186088i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−136.000			−1.08800
$126$		0			0
$127$		−	218.238i		−	1.71841i	−0.511629	−	0.859206i	$-0.670958\pi$
$127$		−	218.238i		−	1.71841i	0.511629	−	0.859206i	$-0.329042\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−168.000	−	96.9948i	−1.28244	−	0.740419i	−0.305148	−	0.952305i	$-0.598706\pi$
$131$	−168.000	−	96.9948i	−1.28244	−	0.740419i	−0.977294	+	0.211886i	$0.932039\pi$
$132$		0			0
$133$	−27.0000	−	46.7654i	−0.203008	−	0.351619i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	84.5000	+	146.358i	0.616788	+	1.06831i	0.990068	+	0.140590i	$0.0448999\pi$
$137$	84.5000	+	146.358i	0.616788	+	1.06831i	−0.373280	+	0.927719i	$0.621767\pi$
$138$		0			0
$139$	169.500	+	97.8609i	1.21942	+	0.704035i	0.964795	−	0.263004i	$-0.0847131\pi$
$139$	169.500	+	97.8609i	1.21942	+	0.704035i	0.254630	+	0.967039i	$0.418046\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	266.736i		−	1.86529i
$144$		0			0
$145$	136.000			0.937931
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−65.0000	+	112.583i	−0.436242	+	0.755593i	−0.997396	−	0.0721185i	$-0.977024\pi$
$149$	−65.0000	+	112.583i	−0.436242	+	0.755593i	0.561154	+	0.827711i	$0.310357\pi$
$150$		0			0
$151$	105.000	−	60.6218i	0.695364	−	0.401469i	−0.110254	−	0.993903i	$-0.535167\pi$
$151$	105.000	−	60.6218i	0.695364	−	0.401469i	0.805618	+	0.592435i	$0.201833\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−24.0000	+	13.8564i	−0.154839	+	0.0893962i
$156$		0			0
$157$	−2.00000	+	3.46410i	−0.0127389	+	0.0220643i	−0.872325	−	0.488927i	$-0.837388\pi$
$157$	−2.00000	+	3.46410i	−0.0127389	+	0.0220643i	0.859586	+	0.510992i	$0.170722\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	84.0000			0.521739
$162$		0			0
$163$		−	311.769i		−	1.91269i	−0.292233	−	0.956347i	$-0.594398\pi$
$163$		−	311.769i		−	1.91269i	0.292233	−	0.956347i	$-0.405602\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−156.000	−	90.0666i	−0.934132	−	0.539321i	−0.0460158	−	0.998941i	$-0.514652\pi$
$167$	−156.000	−	90.0666i	−0.934132	−	0.539321i	−0.888116	+	0.459620i	$0.847986\pi$
$168$		0			0
$169$	−157.500	−	272.798i	−0.931953	−	1.61419i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.00000	+	1.73205i	0.00578035	+	0.0100119i	0.868901	−	0.494986i	$-0.164827\pi$
$173$	1.00000	+	1.73205i	0.00578035	+	0.0100119i	−0.863121	+	0.504998i	$0.831493\pi$
$174$		0			0
$175$	−27.0000	−	15.5885i	−0.154286	−	0.0890769i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	187.061i		−	1.04504i	−0.852628	−	0.522518i	$-0.824993\pi$
$179$		−	187.061i		−	1.04504i	0.852628	−	0.522518i	$-0.175007\pi$
$180$		0			0
$181$	−254.000			−1.40331			−0.701657	−	0.712514i	$-0.747556\pi$
$181$	−254.000			−1.40331			−0.701657	+	0.712514i	$0.747556\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−32.0000	+	55.4256i	−0.172973	+	0.299598i
$186$		0			0
$187$	−115.500	+	66.6840i	−0.617647	+	0.356599i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.00000	+	1.73205i	−0.0157068	+	0.00906833i	−0.507833	−	0.861456i	$-0.669553\pi$
$191$	−3.00000	+	1.73205i	−0.0157068	+	0.00906833i	0.492126	+	0.870524i	$0.336220\pi$
$192$		0			0
$193$	33.5000	−	58.0237i	0.173575	−	0.300641i	−0.766092	−	0.642731i	$-0.777801\pi$
$193$	33.5000	−	58.0237i	0.173575	−	0.300641i	0.939667	+	0.342090i	$0.111135\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	268.000			1.36041			0.680203	−	0.733024i	$-0.261892\pi$
$197$	268.000			1.36041			0.680203	+	0.733024i	$0.261892\pi$
$198$		0			0
$199$			31.1769i			0.156668i	0.996927	+	0.0783340i	$0.0249600\pi$
$199$			31.1769i			0.156668i	−0.996927	+	0.0783340i	$0.975040\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	102.000	+	58.8897i	0.502463	+	0.290097i
$204$		0			0
$205$	26.0000	+	45.0333i	0.126829	+	0.219675i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−94.5000	−	163.679i	−0.452153	−	0.783152i
$210$		0			0
$211$	−114.000	−	65.8179i	−0.540284	−	0.311933i	0.204910	−	0.978781i	$-0.434310\pi$
$211$	−114.000	−	65.8179i	−0.540284	−	0.311933i	−0.745194	+	0.666848i	$0.767643\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			200.918i			0.934502i
$216$		0			0
$217$	−24.0000			−0.110599
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−121.000	+	209.578i	−0.547511	+	0.948317i
$222$		0			0
$223$	51.0000	−	29.4449i	0.228700	−	0.132040i	−0.381272	−	0.924463i	$-0.624514\pi$
$223$	51.0000	−	29.4449i	0.228700	−	0.132040i	0.609972	+	0.792423i	$0.291181\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−388.500	+	224.301i	−1.71145	+	0.988108i	−0.778847	+	0.627214i	$0.784195\pi$
$227$	−388.500	+	224.301i	−1.71145	+	0.988108i	−0.932607	+	0.360894i	$0.882471\pi$
$228$		0			0
$229$	205.000	−	355.070i	0.895197	−	1.55053i	0.0616353	−	0.998099i	$-0.480368\pi$
$229$	205.000	−	355.070i	0.895197	−	1.55053i	0.833561	−	0.552427i	$-0.186298\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	65.0000			0.278970			0.139485	−	0.990224i	$-0.455455\pi$
$233$	65.0000			0.278970			0.139485	+	0.990224i	$0.455455\pi$
$234$		0			0
$235$		−	13.8564i		−	0.0589634i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	33.0000	+	19.0526i	0.138075	+	0.0797178i	0.567446	−	0.823410i	$-0.307931\pi$
$239$	33.0000	+	19.0526i	0.138075	+	0.0797178i	−0.429371	+	0.903128i	$0.641265\pi$
$240$		0			0
$241$	111.500	+	193.124i	0.462656	+	0.801343i	0.999092	−	0.0425975i	$-0.0135633\pi$
$241$	111.500	+	193.124i	0.462656	+	0.801343i	−0.536437	+	0.843941i	$0.680230\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−74.0000	−	128.172i	−0.302041	−	0.523150i
$246$		0			0
$247$	−297.000	−	171.473i	−1.20243	−	0.694223i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	109.119i		−	0.434738i	−0.976090	−	0.217369i	$-0.930253\pi$
$251$		−	109.119i		−	0.434738i	0.976090	−	0.217369i	$-0.0697475\pi$
$252$		0			0
$253$	294.000			1.16206
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−218.500	+	378.453i	−0.850195	+	1.47258i	0.0308379	+	0.999524i	$0.490182\pi$
$257$	−218.500	+	378.453i	−0.850195	+	1.47258i	−0.881032	+	0.473056i	$0.843151\pi$
$258$		0			0
$259$	−48.0000	+	27.7128i	−0.185328	+	0.106999i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−273.000	+	157.617i	−1.03802	+	0.599303i	−0.919273	−	0.393621i	$-0.871222\pi$
$263$	−273.000	+	157.617i	−1.03802	+	0.599303i	−0.118750	+	0.992924i	$0.537889\pi$
$264$		0			0
$265$	−104.000	+	180.133i	−0.392453	+	0.679748i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	304.000			1.13011			0.565056	−	0.825053i	$-0.308855\pi$
$269$	304.000			1.13011			0.565056	+	0.825053i	$0.308855\pi$
$270$		0			0
$271$			311.769i			1.15044i	0.817999	+	0.575220i	$0.195083\pi$
$271$			311.769i			1.15044i	−0.817999	+	0.575220i	$0.804917\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−94.5000	−	54.5596i	−0.343636	−	0.198399i
$276$		0			0
$277$	−17.0000	−	29.4449i	−0.0613718	−	0.106299i	0.833707	−	0.552207i	$-0.186214\pi$
$277$	−17.0000	−	29.4449i	−0.0613718	−	0.106299i	−0.895079	+	0.445908i	$0.852881\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−109.000	−	188.794i	−0.387900	−	0.671863i	0.604267	−	0.796782i	$-0.293466\pi$
$281$	−109.000	−	188.794i	−0.387900	−	0.671863i	−0.992167	+	0.124919i	$0.960133\pi$
$282$		0			0
$283$	−6.00000	−	3.46410i	−0.0212014	−	0.0122406i	0.489362	−	0.872081i	$-0.337230\pi$
$283$	−6.00000	−	3.46410i	−0.0212014	−	0.0122406i	−0.510563	+	0.859840i	$0.670563\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			45.0333i			0.156911i
$288$		0			0
$289$	−168.000			−0.581315
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−101.000	+	174.937i	−0.344710	+	0.597055i	−0.985301	−	0.170827i	$-0.945356\pi$
$293$	−101.000	+	174.937i	−0.344710	+	0.597055i	0.640591	+	0.767882i	$0.278689\pi$
$294$		0			0
$295$	186.000	−	107.387i	0.630508	−	0.364024i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	462.000	−	266.736i	1.54515	−	0.892093i
$300$		0			0
$301$	−87.0000	+	150.688i	−0.289037	+	0.500626i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	64.0000			0.209836
$306$		0			0
$307$			109.119i			0.355437i	0.984081	+	0.177719i	$0.0568717\pi$
$307$			109.119i			0.355437i	−0.984081	+	0.177719i	$0.943128\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−237.000	−	136.832i	−0.762058	−	0.439974i	0.0679762	−	0.997687i	$-0.478346\pi$
$311$	−237.000	−	136.832i	−0.762058	−	0.439974i	−0.830034	+	0.557713i	$0.811679\pi$
$312$		0			0
$313$	39.5000	+	68.4160i	0.126198	+	0.218581i	0.922201	−	0.386712i	$-0.126389\pi$
$313$	39.5000	+	68.4160i	0.126198	+	0.218581i	−0.796003	+	0.605293i	$0.793056\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−251.000	−	434.745i	−0.791798	−	1.37143i	−0.924853	−	0.380326i	$-0.875812\pi$
$317$	−251.000	−	434.745i	−0.791798	−	1.37143i	0.133054	−	0.991109i	$-0.457521\pi$
$318$		0			0
$319$	357.000	+	206.114i	1.11912	+	0.646126i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			171.473i			0.530876i
$324$		0			0
$325$	−198.000			−0.609231
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.00000	−	10.3923i	0.0182371	−	0.0315876i
$330$		0			0
$331$	354.000	−	204.382i	1.06949	−	0.617468i	0.141445	−	0.989946i	$-0.454825\pi$
$331$	354.000	−	204.382i	1.06949	−	0.617468i	0.928041	+	0.372478i	$0.121492\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	402.000	−	232.095i	1.20000	−	0.692820i
$336$		0			0
$337$	168.500	−	291.851i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$337$	168.500	−	291.851i	0.500000	−	0.866025i	1.00000			$0$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−84.0000			−0.246334
$342$		0			0
$343$		−	297.913i		−	0.868550i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−235.500	−	135.966i	−0.678674	−	0.391833i	0.120681	−	0.992691i	$-0.461492\pi$
$347$	−235.500	−	135.966i	−0.678674	−	0.391833i	−0.799355	+	0.600859i	$0.794826\pi$
$348$		0			0
$349$	136.000	+	235.559i	0.389685	+	0.674954i	0.992407	−	0.122997i	$-0.0392506\pi$
$349$	136.000	+	235.559i	0.389685	+	0.674954i	−0.602722	+	0.797951i	$0.705917\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−230.500	−	399.238i	−0.652975	−	1.13099i	−0.982397	−	0.186803i	$-0.940188\pi$
$353$	−230.500	−	399.238i	−0.652975	−	1.13099i	0.329423	−	0.944182i	$-0.393146\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	530.008i		−	1.47634i	−0.674612	−	0.738172i	$-0.735689\pi$
$359$		−	530.008i		−	1.47634i	0.674612	−	0.738172i	$-0.264311\pi$
$360$		0			0
$361$	118.000			0.326870
$362$		0			0
$363$		0			0
$364$		0			0
$365$	50.0000	−	86.6025i	0.136986	−	0.237267i
$366$		0			0
$367$	−84.0000	+	48.4974i	−0.228883	+	0.132146i	−0.610057	−	0.792358i	$-0.708853\pi$
$367$	−84.0000	+	48.4974i	−0.228883	+	0.132146i	0.381174	+	0.924503i	$0.375520\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−156.000	+	90.0666i	−0.420485	+	0.242767i
$372$		0			0
$373$	−173.000	+	299.645i	−0.463807	+	0.803337i	−0.999147	−	0.0412995i	$-0.986850\pi$
$373$	−173.000	+	299.645i	−0.463807	+	0.803337i	0.535340	+	0.844637i	$0.320184\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	748.000			1.98408
$378$		0			0
$379$			327.358i			0.863740i	0.901936	+	0.431870i	$0.142146\pi$
$379$			327.358i			0.863740i	−0.901936	+	0.431870i	$0.857854\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	546.000	+	315.233i	1.42559	+	0.823063i	0.996769	−	0.0803272i	$-0.0255965\pi$
$383$	546.000	+	315.233i	1.42559	+	0.823063i	0.428819	+	0.903390i	$0.358930\pi$
$384$		0			0
$385$	84.0000	+	145.492i	0.218182	+	0.377902i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	73.0000	+	126.440i	0.187661	+	0.325038i	0.944470	−	0.328598i	$-0.106576\pi$
$389$	73.0000	+	126.440i	0.187661	+	0.325038i	−0.756809	+	0.653636i	$0.773243\pi$
$390$		0			0
$391$	−231.000	−	133.368i	−0.590793	−	0.341094i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			110.851i			0.280636i
$396$		0			0
$397$	−488.000			−1.22922			−0.614610	−	0.788831i	$-0.710686\pi$
$397$	−488.000			−1.22922			−0.614610	+	0.788831i	$0.710686\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	222.500	−	385.381i	0.554863	−	0.961051i	−0.443051	−	0.896496i	$-0.646104\pi$
$401$	222.500	−	385.381i	0.554863	−	0.961051i	0.997914	−	0.0645544i	$-0.0205626\pi$
$402$		0			0
$403$	−132.000	+	76.2102i	−0.327543	+	0.189107i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−168.000	+	96.9948i	−0.412776	+	0.238317i
$408$		0			0
$409$	33.5000	−	58.0237i	0.0819071	−	0.141867i	−0.822162	−	0.569254i	$-0.807232\pi$
$409$	33.5000	−	58.0237i	0.0819071	−	0.141867i	0.904069	+	0.427386i	$0.140566\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	186.000			0.450363
$414$		0			0
$415$			138.564i			0.333889i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	534.000	+	308.305i	1.27446	+	0.735812i	0.975825	−	0.218555i	$-0.0701342\pi$
$419$	534.000	+	308.305i	1.27446	+	0.735812i	0.298638	+	0.954366i	$0.403468\pi$
$420$		0			0
$421$	136.000	+	235.559i	0.323040	+	0.559522i	0.981114	−	0.193431i	$-0.0619617\pi$
$421$	136.000	+	235.559i	0.323040	+	0.559522i	−0.658073	+	0.752954i	$0.728628\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	49.5000	+	85.7365i	0.116471	+	0.201733i
$426$		0			0
$427$	48.0000	+	27.7128i	0.112412	+	0.0649012i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			405.300i			0.940371i	0.882568	+	0.470185i	$0.155813\pi$
$431$			405.300i			0.940371i	−0.882568	+	0.470185i	$0.844187\pi$
$432$		0			0
$433$	−439.000			−1.01386			−0.506928	−	0.861988i	$-0.669219\pi$
$433$	−439.000			−1.01386			−0.506928	+	0.861988i	$0.669219\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	189.000	−	327.358i	0.432494	−	0.749102i
$438$		0			0
$439$	−732.000	+	422.620i	−1.66743	+	0.962689i	−0.698408	+	0.715700i	$0.746108\pi$
$439$	−732.000	+	422.620i	−1.66743	+	0.962689i	−0.969018	+	0.246989i	$0.920559\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	286.500	−	165.411i	0.646727	−	0.373388i	−0.140474	−	0.990084i	$-0.544863\pi$
$443$	286.500	−	165.411i	0.646727	−	0.373388i	0.787201	+	0.616696i	$0.211529\pi$
$444$		0			0
$445$	−4.00000	+	6.92820i	−0.00898876	+	0.0155690i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	47.0000			0.104677			0.0523385	−	0.998629i	$-0.483333\pi$
$449$	47.0000			0.104677			0.0523385	+	0.998629i	$0.483333\pi$
$450$		0			0
$451$			157.617i			0.349483i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	264.000	+	152.420i	0.580220	+	0.334990i
$456$		0			0
$457$	165.500	+	286.654i	0.362144	+	0.627253i	0.988314	−	0.152435i	$-0.0487114\pi$
$457$	165.500	+	286.654i	0.362144	+	0.627253i	−0.626169	+	0.779687i	$0.715378\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−269.000	−	465.922i	−0.583514	−	1.01068i	−0.995059	−	0.0992865i	$-0.968344\pi$
$461$	−269.000	−	465.922i	−0.583514	−	1.01068i	0.411545	−	0.911390i	$-0.364989\pi$
$462$		0			0
$463$	492.000	+	284.056i	1.06263	+	0.613513i	0.926160	−	0.377131i	$-0.123089\pi$
$463$	492.000	+	284.056i	1.06263	+	0.613513i	0.136475	+	0.990644i	$0.456423\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			639.127i			1.36858i	0.729210	+	0.684290i	$0.239888\pi$
$467$			639.127i			1.36858i	−0.729210	+	0.684290i	$0.760112\pi$
$468$		0			0
$469$	402.000			0.857143
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−304.500	+	527.409i	−0.643763	+	1.11503i
$474$		0			0
$475$	−121.500	+	70.1481i	−0.255789	+	0.147680i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	105.000	−	60.6218i	0.219207	−	0.126559i	−0.386376	−	0.922341i	$-0.626273\pi$
$479$	105.000	−	60.6218i	0.219207	−	0.126559i	0.605583	+	0.795782i	$0.292940\pi$
$480$		0			0
$481$	−176.000	+	304.841i	−0.365904	+	0.633765i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−172.000			−0.354639
$486$		0			0
$487$		−	405.300i		−	0.832238i	−0.909310	−	0.416119i	$-0.863390\pi$
$487$		−	405.300i		−	0.832238i	0.909310	−	0.416119i	$-0.136610\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	628.500	+	362.865i	1.28004	+	0.739032i	0.976856	−	0.213900i	$-0.0686166\pi$
$491$	628.500	+	362.865i	1.28004	+	0.739032i	0.303185	+	0.952932i	$0.401950\pi$
$492$		0			0
$493$	−187.000	−	323.894i	−0.379310	−	0.656985i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−451.500	−	260.674i	−0.904810	−	0.522392i	−0.0260521	−	0.999661i	$-0.508294\pi$
$499$	−451.500	−	260.674i	−0.904810	−	0.522392i	−0.878758	+	0.477269i	$0.841627\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			872.954i			1.73549i	0.497006	+	0.867747i	$0.334433\pi$
$503$			872.954i			1.73549i	−0.497006	+	0.867747i	$0.665567\pi$
$504$		0			0
$505$	−80.0000			−0.158416
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−380.000	+	658.179i	−0.746562	+	1.29308i	0.202900	+	0.979200i	$0.434963\pi$
$509$	−380.000	+	658.179i	−0.746562	+	1.29308i	−0.949461	+	0.313884i	$0.898370\pi$
$510$		0			0
$511$	75.0000	−	43.3013i	0.146771	−	0.0847383i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	84.0000	−	48.4974i	0.163107	−	0.0941698i
$516$		0			0
$517$	21.0000	−	36.3731i	0.0406190	−	0.0703541i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−745.000			−1.42994			−0.714971	−	0.699154i	$-0.753560\pi$
$521$	−745.000			−1.42994			−0.714971	+	0.699154i	$0.753560\pi$
$522$		0			0
$523$			561.184i			1.07301i	0.843897	+	0.536505i	$0.180256\pi$
$523$			561.184i			1.07301i	−0.843897	+	0.536505i	$0.819744\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	66.0000	+	38.1051i	0.125237	+	0.0723057i
$528$		0			0
$529$	29.5000	+	51.0955i	0.0557656	+	0.0965888i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	143.000	+	247.683i	0.268293	+	0.464697i
$534$		0			0
$535$	54.0000	+	31.1769i	0.100935	+	0.0582746i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	448.601i		−	0.832284i
$540$		0			0
$541$	520.000			0.961183			0.480591	−	0.876945i	$-0.340422\pi$
$541$	520.000			0.961183			0.480591	+	0.876945i	$0.340422\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−176.000	+	304.841i	−0.322936	+	0.559341i
$546$		0			0
$547$	−334.500	+	193.124i	−0.611517	+	0.353060i	−0.773559	−	0.633724i	$-0.781525\pi$
$547$	−334.500	+	193.124i	−0.611517	+	0.353060i	0.162042	+	0.986784i	$0.448192\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	459.000	−	265.004i	0.833031	−	0.480951i
$552$		0			0
$553$	−48.0000	+	83.1384i	−0.0867993	+	0.150341i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	934.000			1.67684			0.838420	−	0.545025i	$-0.183480\pi$
$557$	934.000			1.67684			0.838420	+	0.545025i	$0.183480\pi$
$558$		0			0
$559$			1105.05i			1.97683i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−613.500	−	354.204i	−1.08970	−	0.629137i	−0.156202	−	0.987725i	$-0.549925\pi$
$563$	−613.500	−	354.204i	−1.08970	−	0.629137i	−0.933496	+	0.358588i	$0.883258\pi$
$564$		0			0
$565$	−100.000	−	173.205i	−0.176991	−	0.306558i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−347.500	−	601.888i	−0.610721	−	1.05780i	−0.991119	−	0.132976i	$-0.957547\pi$
$569$	−347.500	−	601.888i	−0.610721	−	1.05780i	0.380399	−	0.924823i	$-0.375787\pi$
$570$		0			0
$571$	466.500	+	269.334i	0.816988	+	0.471688i	0.849377	−	0.527787i	$-0.176978\pi$
$571$	466.500	+	269.334i	0.816988	+	0.471688i	−0.0323889	+	0.999475i	$0.510311\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	218.238i		−	0.379545i
$576$		0			0
$577$	227.000			0.393414			0.196707	−	0.980462i	$-0.436975\pi$
$577$	227.000			0.393414			0.196707	+	0.980462i	$0.436975\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−60.0000	+	103.923i	−0.103270	+	0.178869i
$582$		0			0
$583$	−546.000	+	315.233i	−0.936535	+	0.540709i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	124.500	−	71.8801i	0.212095	−	0.122453i	−0.390189	−	0.920735i	$-0.627590\pi$
$587$	124.500	−	71.8801i	0.212095	−	0.122453i	0.602285	+	0.798281i	$0.294257\pi$
$588$		0			0
$589$	−54.0000	+	93.5307i	−0.0916808	+	0.158796i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	506.000			0.853288			0.426644	−	0.904420i	$-0.359696\pi$
$593$	506.000			0.853288			0.426644	+	0.904420i	$0.359696\pi$
$594$		0			0
$595$		−	152.420i		−	0.256169i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−48.0000	−	27.7128i	−0.0801336	−	0.0462651i	0.459398	−	0.888231i	$-0.348065\pi$
$599$	−48.0000	−	27.7128i	−0.0801336	−	0.0462651i	−0.539531	+	0.841965i	$0.681399\pi$
$600$		0			0
$601$	−167.500	−	290.119i	−0.278702	−	0.482726i	0.692360	−	0.721552i	$-0.256571\pi$
$601$	−167.500	−	290.119i	−0.278702	−	0.482726i	−0.971062	+	0.238826i	$0.923238\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	52.0000	+	90.0666i	0.0859504	+	0.148870i
$606$		0			0
$607$	546.000	+	315.233i	0.899506	+	0.519330i	0.877040	−	0.480418i	$-0.159515\pi$
$607$	546.000	+	315.233i	0.899506	+	0.519330i	0.0224660	+	0.999748i	$0.492848\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	76.2102i		−	0.124730i
$612$		0			0
$613$	340.000			0.554649			0.277325	−	0.960776i	$-0.410552\pi$
$613$	340.000			0.554649			0.277325	+	0.960776i	$0.410552\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	195.500	−	338.616i	0.316856	−	0.548810i	−0.662974	−	0.748642i	$-0.730706\pi$
$617$	195.500	−	338.616i	0.316856	−	0.548810i	0.979830	+	0.199832i	$0.0640396\pi$
$618$		0			0
$619$	−10.5000	+	6.06218i	−0.0169628	+	0.00979350i	−0.508457	−	0.861087i	$-0.669784\pi$
$619$	−10.5000	+	6.06218i	−0.0169628	+	0.00979350i	0.491495	+	0.870881i	$0.336451\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.00000	+	3.46410i	−0.00963082	+	0.00556036i
$624$		0			0
$625$	159.500	−	276.262i	0.255200	−	0.442019i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	176.000			0.279809
$630$		0			0
$631$			436.477i			0.691722i	0.938286	+	0.345861i	$0.112413\pi$
$631$			436.477i			0.691722i	−0.938286	+	0.345861i	$0.887587\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	756.000	+	436.477i	1.19055	+	0.687365i
$636$		0			0
$637$	−407.000	−	704.945i	−0.638932	−	1.10666i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	210.500	+	364.597i	0.328393	+	0.568794i	0.982193	−	0.187874i	$-0.0601596\pi$
$641$	210.500	+	364.597i	0.328393	+	0.568794i	−0.653800	+	0.756667i	$0.726826\pi$
$642$		0			0
$643$	358.500	+	206.980i	0.557543	+	0.321897i	0.752159	−	0.658982i	$-0.229013\pi$
$643$	358.500	+	206.980i	0.557543	+	0.321897i	−0.194616	+	0.980880i	$0.562346\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			405.300i			0.626430i	0.949682	+	0.313215i	$0.101406\pi$
$647$			405.300i			0.626430i	−0.949682	+	0.313215i	$0.898594\pi$
$648$		0			0
$649$	651.000			1.00308
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−443.000	+	767.299i	−0.678407	+	1.17504i	0.297053	+	0.954861i	$0.403996\pi$
$653$	−443.000	+	767.299i	−0.678407	+	1.17504i	−0.975460	+	0.220175i	$0.929337\pi$
$654$		0			0
$655$	672.000	−	387.979i	1.02595	−	0.592335i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−726.000	+	419.156i	−1.10167	+	0.636049i	−0.936659	−	0.350243i	$-0.886099\pi$
$659$	−726.000	+	419.156i	−1.10167	+	0.636049i	−0.165010	+	0.986292i	$0.552766\pi$
$660$		0			0
$661$	124.000	−	214.774i	0.187595	−	0.324923i	−0.756853	−	0.653585i	$-0.773264\pi$
$661$	124.000	−	214.774i	0.187595	−	0.324923i	0.944448	+	0.328662i	$0.106598\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	216.000			0.324812
$666$		0			0
$667$			824.456i			1.23607i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	168.000	+	96.9948i	0.250373	+	0.144553i
$672$		0			0
$673$	−577.000	−	999.393i	−0.857355	−	1.48498i	−0.874443	−	0.485129i	$-0.838773\pi$
$673$	−577.000	−	999.393i	−0.857355	−	1.48498i	0.0170877	−	0.999854i	$-0.494561\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−566.000	−	980.341i	−0.836041	−	1.44807i	−0.893180	−	0.449700i	$-0.851531\pi$
$677$	−566.000	−	980.341i	−0.836041	−	1.44807i	0.0571384	−	0.998366i	$-0.481802\pi$
$678$		0			0
$679$	−129.000	−	74.4782i	−0.189985	−	0.109688i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			795.011i			1.16400i	0.813189	+	0.582000i	$0.197729\pi$
$683$			795.011i			1.16400i	−0.813189	+	0.582000i	$0.802271\pi$
$684$		0			0
$685$	−676.000			−0.986861
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−572.000	+	990.733i	−0.830189	+	1.43793i
$690$		0			0
$691$	−780.000	+	450.333i	−1.12880	+	0.651712i	−0.943633	−	0.330995i	$-0.892616\pi$
$691$	−780.000	+	450.333i	−1.12880	+	0.651712i	−0.185166	+	0.982707i	$0.559282\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−678.000	+	391.443i	−0.975540	+	0.563228i
$696$		0			0
$697$	71.5000	−	123.842i	0.102582	−	0.177678i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	142.000			0.202568			0.101284	−	0.994858i	$-0.467705\pi$
$701$	142.000			0.202568			0.101284	+	0.994858i	$0.467705\pi$
$702$		0			0
$703$			249.415i			0.354787i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−60.0000	−	34.6410i	−0.0848656	−	0.0489972i
$708$		0			0
$709$	370.000	+	640.859i	0.521862	+	0.903891i	0.999677	+	0.0254305i	$0.00809566\pi$
$709$	370.000	+	640.859i	0.521862	+	0.903891i	−0.477815	+	0.878461i	$0.658571\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−84.0000	−	145.492i	−0.117812	−	0.204056i
$714$		0			0
$715$	924.000	+	533.472i	1.29231	+	0.746114i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			124.708i			0.173446i	0.996232	+	0.0867230i	$0.0276395\pi$
$719$			124.708i			0.173446i	−0.996232	+	0.0867230i	$0.972360\pi$
$720$		0			0
$721$	84.0000			0.116505
$722$		0			0
$723$		0			0
$724$		0			0
$725$	153.000	−	265.004i	0.211034	−	0.365522i
$726$		0			0
$727$	−705.000	+	407.032i	−0.969739	+	0.559879i	−0.899157	−	0.437627i	$-0.855819\pi$
$727$	−705.000	+	407.032i	−0.969739	+	0.559879i	−0.0705821	+	0.997506i	$0.522486\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	478.500	−	276.262i	0.654583	−	0.377924i
$732$		0			0
$733$	457.000	−	791.547i	0.623465	−	1.07987i	−0.365370	−	0.930862i	$-0.619058\pi$
$733$	457.000	−	791.547i	0.623465	−	1.07987i	0.988836	−	0.149011i	$-0.0476090\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1407.00			1.90909
$738$		0			0
$739$		−	358.535i		−	0.485162i	−0.970131	−	0.242581i	$-0.922006\pi$
$739$		−	358.535i		−	0.485162i	0.970131	−	0.242581i	$-0.0779940\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−345.000	−	199.186i	−0.464334	−	0.268083i	0.249531	−	0.968367i	$-0.419724\pi$
$743$	−345.000	−	199.186i	−0.464334	−	0.268083i	−0.713865	+	0.700284i	$0.753057\pi$
$744$		0			0
$745$	−260.000	−	450.333i	−0.348993	−	0.604474i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	27.0000	+	46.7654i	0.0360481	+	0.0624371i
$750$		0			0
$751$	−966.000	−	557.720i	−1.28628	−	0.742637i	−0.308295	−	0.951291i	$-0.599759\pi$
$751$	−966.000	−	557.720i	−1.28628	−	0.742637i	−0.977990	+	0.208654i	$0.933092\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			484.974i			0.642350i
$756$		0			0
$757$	−758.000			−1.00132			−0.500661	−	0.865644i	$-0.666909\pi$
$757$	−758.000			−1.00132			−0.500661	+	0.865644i	$0.666909\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−187.000	+	323.894i	−0.245729	+	0.425616i	−0.962336	−	0.271861i	$-0.912361\pi$
$761$	−187.000	+	323.894i	−0.245729	+	0.425616i	0.716607	+	0.697477i	$0.245694\pi$
$762$		0			0
$763$	−264.000	+	152.420i	−0.346003	+	0.199765i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1023.00	−	590.629i	1.33377	−	0.770051i
$768$		0			0
$769$	11.0000	−	19.0526i	0.0143043	−	0.0247758i	−0.858785	−	0.512337i	$-0.828780\pi$
$769$	11.0000	−	19.0526i	0.0143043	−	0.0247758i	0.873089	+	0.487561i	$0.162113\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1334.00			−1.72574			−0.862872	−	0.505423i	$-0.831337\pi$
$773$	−1334.00			−1.72574			−0.862872	+	0.505423i	$0.831337\pi$
$774$		0			0
$775$			62.3538i			0.0804566i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	175.500	+	101.325i	0.225289	+	0.130071i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.00000	−	13.8564i	−0.0101911	−	0.0176515i
$786$		0			0
$787$	−762.000	−	439.941i	−0.968234	−	0.559010i	−0.0695365	−	0.997579i	$-0.522152\pi$
$787$	−762.000	−	439.941i	−0.968234	−	0.559010i	−0.898697	+	0.438569i	$0.855485\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	173.205i		−	0.218970i
$792$		0			0
$793$	352.000			0.443884
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−416.000	+	720.533i	−0.521957	+	0.904057i	0.477716	+	0.878514i	$0.341465\pi$
$797$	−416.000	+	720.533i	−0.521957	+	0.904057i	−0.999674	+	0.0255425i	$0.991869\pi$
$798$		0			0
$799$	−33.0000	+	19.0526i	−0.0413016	+	0.0238455i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	262.500	−	151.554i	0.326899	−	0.188735i
$804$		0			0
$805$	−168.000	+	290.985i	−0.208696	+	0.361471i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−493.000			−0.609394			−0.304697	−	0.952449i	$-0.598555\pi$
$809$	−493.000			−0.609394			−0.304697	+	0.952449i	$0.598555\pi$
$810$		0			0
$811$		−	327.358i		−	0.403647i	−0.979422	−	0.201823i	$-0.935313\pi$
$811$		−	327.358i		−	0.403647i	0.979422	−	0.201823i	$-0.0646867\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1080.00	+	623.538i	1.32515	+	0.765078i
$816$		0			0
$817$	391.500	+	678.098i	0.479192	+	0.829985i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	379.000	+	656.447i	0.461632	+	0.799570i	0.999042	−	0.0437505i	$-0.0139307\pi$
$821$	379.000	+	656.447i	0.461632	+	0.799570i	−0.537410	+	0.843321i	$0.680597\pi$
$822$		0			0
$823$	−750.000	−	433.013i	−0.911300	−	0.526139i	−0.0304509	−	0.999536i	$-0.509694\pi$
$823$	−750.000	−	433.013i	−0.911300	−	0.526139i	−0.880849	+	0.473397i	$0.843028\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	436.477i		−	0.527783i	−0.964552	−	0.263892i	$-0.914994\pi$
$827$		−	436.477i		−	0.527783i	0.964552	−	0.263892i	$-0.0850061\pi$
$828$		0			0
$829$	718.000			0.866104			0.433052	−	0.901369i	$-0.357437\pi$
$829$	718.000			0.866104			0.433052	+	0.901369i	$0.357437\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−203.500	+	352.472i	−0.244298	+	0.423136i
$834$		0			0
$835$	624.000	−	360.267i	0.747305	−	0.431457i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−786.000	+	453.797i	−0.936830	+	0.540879i	−0.888965	−	0.457975i	$-0.848575\pi$
$839$	−786.000	+	453.797i	−0.936830	+	0.540879i	−0.0478645	+	0.998854i	$0.515242\pi$
$840$		0			0
$841$	−157.500	+	272.798i	−0.187277	+	0.324373i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1260.00			1.49112
$846$		0			0
$847$			90.0666i			0.106336i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−336.000	−	193.990i	−0.394830	−	0.227955i
$852$		0			0
$853$	73.0000	+	126.440i	0.0855803	+	0.148229i	0.905638	−	0.424051i	$-0.139392\pi$
$853$	73.0000	+	126.440i	0.0855803	+	0.148229i	−0.820058	+	0.572280i	$0.806059\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−73.0000	−	126.440i	−0.0851809	−	0.147538i	0.820287	−	0.571952i	$-0.193813\pi$
$857$	−73.0000	−	126.440i	−0.0851809	−	0.147538i	−0.905468	+	0.424414i	$0.860480\pi$
$858$		0			0
$859$	−73.5000	−	42.4352i	−0.0855646	−	0.0494008i	0.456607	−	0.889668i	$-0.349064\pi$
$859$	−73.5000	−	42.4352i	−0.0855646	−	0.0494008i	−0.542172	+	0.840268i	$0.682398\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1184.72i		−	1.37280i	−0.727226	−	0.686398i	$-0.759191\pi$
$863$		−	1184.72i		−	1.37280i	0.727226	−	0.686398i	$-0.240809\pi$
$864$		0			0
$865$	−8.00000			−0.00924855
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−168.000	+	290.985i	−0.193326	+	0.334850i
$870$		0			0
$871$	2211.00	−	1276.52i	2.53846	−	1.46558i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	408.000	−	235.559i	0.466286	−	0.269210i
$876$		0			0
$877$	−740.000	+	1281.72i	−0.843786	+	1.46148i	0.0428860	+	0.999080i	$0.486345\pi$
$877$	−740.000	+	1281.72i	−0.843786	+	1.46148i	−0.886672	+	0.462400i	$0.846989\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−142.000			−0.161180			−0.0805902	−	0.996747i	$-0.525681\pi$
$881$	−142.000			−0.161180			−0.0805902	+	0.996747i	$0.525681\pi$
$882$		0			0
$883$		−	1200.31i		−	1.35936i	−0.733511	−	0.679678i	$-0.762120\pi$
$883$		−	1200.31i		−	1.35936i	0.733511	−	0.679678i	$-0.237880\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	546.000	+	315.233i	0.615558	+	0.355393i	0.775138	−	0.631792i	$-0.217681\pi$
$887$	546.000	+	315.233i	0.615558	+	0.355393i	−0.159580	+	0.987185i	$0.551014\pi$
$888$		0			0
$889$	378.000	+	654.715i	0.425197	+	0.736463i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−27.0000	−	46.7654i	−0.0302352	−	0.0523688i
$894$		0			0
$895$	648.000	+	374.123i	0.724022	+	0.418014i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	235.559i		−	0.262023i
$900$		0			0
$901$	572.000			0.634850
$902$		0			0
$903$		0			0
$904$		0			0
$905$	508.000	−	879.882i	0.561326	−	0.972245i
$906$		0			0
$907$	556.500	−	321.295i	0.613561	−	0.354240i	−0.160797	−	0.986988i	$-0.551406\pi$
$907$	556.500	−	321.295i	0.613561	−	0.354240i	0.774358	+	0.632748i	$0.218073\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	348.000	−	200.918i	0.381998	−	0.220547i	−0.296689	−	0.954974i	$-0.595883\pi$
$911$	348.000	−	200.918i	0.381998	−	0.220547i	0.678687	+	0.734428i	$0.262549\pi$
$912$		0			0
$913$	−210.000	+	363.731i	−0.230011	+	0.398391i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	672.000			0.732824
$918$		0			0
$919$		−	779.423i		−	0.848121i	−0.905634	−	0.424060i	$-0.860604\pi$
$919$		−	779.423i		−	0.848121i	0.905634	−	0.424060i	$-0.139396\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	72.0000	+	124.708i	0.0778378	+	0.134819i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−379.000	−	656.447i	−0.407966	−	0.706617i	0.586696	−	0.809807i	$-0.300428\pi$
$929$	−379.000	−	656.447i	−0.407966	−	0.706617i	−0.994662	+	0.103190i	$0.967095\pi$
$930$		0			0
$931$	−499.500	−	288.386i	−0.536520	−	0.309760i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	533.472i		−	0.570558i
$936$		0			0
$937$	−754.000			−0.804696			−0.402348	−	0.915487i	$-0.631806\pi$
$937$	−754.000			−0.804696			−0.402348	+	0.915487i	$0.631806\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	898.000	−	1555.38i	0.954304	−	1.65290i	0.218351	−	0.975870i	$-0.429932\pi$
$941$	898.000	−	1555.38i	0.954304	−	1.65290i	0.735953	−	0.677033i	$-0.236734\pi$
$942$		0			0
$943$	−273.000	+	157.617i	−0.289502	+	0.167144i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−91.5000	+	52.8275i	−0.0966209	+	0.0557841i	−0.547532	−	0.836785i	$-0.684433\pi$
$947$	−91.5000	+	52.8275i	−0.0966209	+	0.0557841i	0.450911	+	0.892569i	$0.351099\pi$
$948$		0			0
$949$	275.000	−	476.314i	0.289779	−	0.501911i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1213.00			−1.27282			−0.636411	−	0.771350i	$-0.719582\pi$
$953$	−1213.00			−1.27282			−0.636411	+	0.771350i	$0.719582\pi$
$954$		0			0
$955$		−	13.8564i		−	0.0145093i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−507.000	−	292.717i	−0.528676	−	0.305231i
$960$		0			0
$961$	−456.500	−	790.681i	−0.475026	−	0.822769i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	134.000	+	232.095i	0.138860	+	0.240513i
$966$		0			0
$967$	303.000	+	174.937i	0.313340	+	0.180907i	0.648420	−	0.761283i	$-0.275430\pi$
$967$	303.000	+	174.937i	0.313340	+	0.180907i	−0.335080	+	0.942190i	$0.608763\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1434.14i		−	1.47697i	−0.674270	−	0.738485i	$-0.735542\pi$
$971$		−	1434.14i		−	1.47697i	0.674270	−	0.738485i	$-0.264458\pi$
$972$		0			0
$973$	−678.000			−0.696814
$974$		0			0
$975$		0			0
$976$		0			0
$977$	78.5000	−	135.966i	0.0803480	−	0.139167i	−0.823051	−	0.567967i	$-0.807730\pi$
$977$	78.5000	−	135.966i	0.0803480	−	0.139167i	0.903399	+	0.428800i	$0.141064\pi$
$978$		0			0
$979$	−21.0000	+	12.1244i	−0.0214505	+	0.0123844i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1218.00	+	703.213i	−1.23906	+	0.715374i	−0.968903	−	0.247441i	$-0.920410\pi$
$983$	−1218.00	+	703.213i	−1.23906	+	0.715374i	−0.270161	+	0.962815i	$0.587077\pi$
$984$		0			0
$985$	−536.000	+	928.379i	−0.544162	+	0.942517i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1218.00			−1.23155
$990$		0			0
$991$			249.415i			0.251680i	0.992051	+	0.125840i	$0.0401627\pi$
$991$			249.415i			0.251680i	−0.992051	+	0.125840i	$0.959837\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−108.000	−	62.3538i	−0.108543	−	0.0626672i
$996$		0			0
$997$	−206.000	−	356.802i	−0.206620	−	0.357876i	0.744028	−	0.668149i	$-0.232913\pi$
$997$	−206.000	−	356.802i	−0.206620	−	0.357876i	−0.950648	+	0.310273i	$0.899580\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.a.1279.1		2
3.2	odd	2		576.3.o.b.319.1		2
4.3	odd	2		1728.3.o.b.1279.1		2
8.3	odd	2		108.3.f.b.91.1		2
8.5	even	2		108.3.f.a.91.1		2
9.2	odd	6		576.3.o.a.511.1		2
9.7	even	3		1728.3.o.b.127.1		2
12.11	even	2		576.3.o.a.319.1		2
24.5	odd	2		36.3.f.b.31.1	yes	2
24.11	even	2		36.3.f.a.31.1	yes	2
36.7	odd	6	inner	1728.3.o.a.127.1		2
36.11	even	6		576.3.o.b.511.1		2
72.5	odd	6		324.3.d.b.163.2		2
72.11	even	6		36.3.f.b.7.1	yes	2
72.13	even	6		324.3.d.c.163.1		2
72.29	odd	6		36.3.f.a.7.1	✓	2
72.43	odd	6		108.3.f.a.19.1		2
72.59	even	6		324.3.d.b.163.1		2
72.61	even	6		108.3.f.b.19.1		2
72.67	odd	6		324.3.d.c.163.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.a.7.1	✓	2	72.29	odd	6
36.3.f.a.31.1	yes	2	24.11	even	2
36.3.f.b.7.1	yes	2	72.11	even	6
36.3.f.b.31.1	yes	2	24.5	odd	2
108.3.f.a.19.1		2	72.43	odd	6
108.3.f.a.91.1		2	8.5	even	2
108.3.f.b.19.1		2	72.61	even	6
108.3.f.b.91.1		2	8.3	odd	2
324.3.d.b.163.1		2	72.59	even	6
324.3.d.b.163.2		2	72.5	odd	6
324.3.d.c.163.1		2	72.13	even	6
324.3.d.c.163.2		2	72.67	odd	6
576.3.o.a.319.1		2	12.11	even	2
576.3.o.a.511.1		2	9.2	odd	6
576.3.o.b.319.1		2	3.2	odd	2
576.3.o.b.511.1		2	36.11	even	6
1728.3.o.a.127.1		2	36.7	odd	6	inner
1728.3.o.a.1279.1		2	1.1	even	1	trivial
1728.3.o.b.127.1		2	9.7	even	3
1728.3.o.b.1279.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{5} +(-3.00000 + 1.73205i) q^{7} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{5} +(-3.00000 + 1.73205i) q^{7} +(-10.5000 + 6.06218i) q^{11} +(-11.0000 + 19.0526i) q^{13} +11.0000 q^{17} +15.5885i q^{19} +(-21.0000 - 12.1244i) q^{23} +(4.50000 + 7.79423i) q^{25} +(-17.0000 - 29.4449i) q^{29} +(6.00000 + 3.46410i) q^{31} -13.8564i q^{35} +16.0000 q^{37} +(6.50000 - 11.2583i) q^{41} +(43.5000 - 25.1147i) q^{43} +(-3.00000 + 1.73205i) q^{47} +(-18.5000 + 32.0429i) q^{49} +52.0000 q^{53} -48.4974i q^{55} +(-46.5000 - 26.8468i) q^{59} +(-8.00000 - 13.8564i) q^{61} +(-44.0000 - 76.2102i) q^{65} +(-100.500 - 58.0237i) q^{67} -25.0000 q^{73} +(21.0000 - 36.3731i) q^{77} +(24.0000 - 13.8564i) q^{79} +(30.0000 - 17.3205i) q^{83} +(-22.0000 + 38.1051i) q^{85} +2.00000 q^{89} -76.2102i q^{91} +(-54.0000 - 31.1769i) q^{95} +(21.5000 + 37.2391i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{5} - 6 q^{7}+O(q^{10}) \) 2 * q - 4 * q^5 - 6 * q^7	\( 2 q - 4 q^{5} - 6 q^{7} - 21 q^{11} - 22 q^{13} + 22 q^{17} - 42 q^{23} + 9 q^{25} - 34 q^{29} + 12 q^{31} + 32 q^{37} + 13 q^{41} + 87 q^{43} - 6 q^{47} - 37 q^{49} + 104 q^{53} - 93 q^{59} - 16 q^{61} - 88 q^{65} - 201 q^{67} - 50 q^{73} + 42 q^{77} + 48 q^{79} + 60 q^{83} - 44 q^{85} + 4 q^{89} - 108 q^{95} + 43 q^{97}+O(q^{100}) \) 2 * q - 4 * q^5 - 6 * q^7 - 21 * q^11 - 22 * q^13 + 22 * q^17 - 42 * q^23 + 9 * q^25 - 34 * q^29 + 12 * q^31 + 32 * q^37 + 13 * q^41 + 87 * q^43 - 6 * q^47 - 37 * q^49 + 104 * q^53 - 93 * q^59 - 16 * q^61 - 88 * q^65 - 201 * q^67 - 50 * q^73 + 42 * q^77 + 48 * q^79 + 60 * q^83 - 44 * q^85 + 4 * q^89 - 108 * q^95 + 43 * q^97

Introduction

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