LMFDB - Embedded newform 1728.3.o.e.127.4

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

Embedding invariants

Embedding label			127.4
Root			$2.06288i$ of defining polynomial
Character	$\chi$	$=$	1728.127
Dual form			1728.3.o.e.1279.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.61660 + 7.99619i) q^{5} +(5.33093 + 3.07781i) q^{7} +O(q^{10})$	$q+(4.61660 + 7.99619i) q^{5} +(5.33093 + 3.07781i) q^{7} +(3.70016 + 2.13629i) q^{11} +(-0.869235 - 1.50556i) q^{13} -12.3476 q^{17} +33.9338i q^{19} +(-3.35035 + 1.93433i) q^{23} +(-30.1260 + 52.1798i) q^{25} +(17.8409 - 30.9014i) q^{29} +(-38.8262 + 22.4163i) q^{31} +56.8361i q^{35} +32.7130 q^{37} +(-21.8565 - 37.8565i) q^{41} +(33.9339 + 19.5918i) q^{43} +(39.8784 + 23.0238i) q^{47} +(-5.55415 - 9.62007i) q^{49} +46.3143 q^{53} +39.4496i q^{55} +(-23.2710 + 13.4355i) q^{59} +(-23.4545 + 40.6243i) q^{61} +(8.02582 - 13.9011i) q^{65} +(-56.9984 + 32.9080i) q^{67} -96.7955i q^{71} -14.0622 q^{73} +(13.1502 + 22.7768i) q^{77} +(-34.3954 - 19.8582i) q^{79} +(-81.7202 - 47.1812i) q^{83} +(-57.0039 - 98.7336i) q^{85} +81.8478 q^{89} -10.7014i q^{91} +(-271.341 + 156.659i) q^{95} +(-7.99028 + 13.8396i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{5} - 3 q^{7}+O(q^{10}) $ 8 * q + 3 * q^5 - 3 * q^7	$ 8 q + 3 q^{5} - 3 q^{7} - 18 q^{11} - 5 q^{13} - 6 q^{17} - 81 q^{23} - 23 q^{25} + 69 q^{29} - 45 q^{31} + 20 q^{37} - 54 q^{41} + 207 q^{47} + 41 q^{49} - 252 q^{53} + 306 q^{59} - 7 q^{61} - 93 q^{65} + 12 q^{67} + 74 q^{73} + 207 q^{77} - 33 q^{79} - 549 q^{83} + 30 q^{85} + 168 q^{89} - 684 q^{95} - 10 q^{97}+O(q^{100}) $ 8 * q + 3 * q^5 - 3 * q^7 - 18 * q^11 - 5 * q^13 - 6 * q^17 - 81 * q^23 - 23 * q^25 + 69 * q^29 - 45 * q^31 + 20 * q^37 - 54 * q^41 + 207 * q^47 + 41 * q^49 - 252 * q^53 + 306 * q^59 - 7 * q^61 - 93 * q^65 + 12 * q^67 + 74 * q^73 + 207 * q^77 - 33 * q^79 - 549 * q^83 + 30 * q^85 + 168 * q^89 - 684 * q^95 - 10 * q^97

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
$5$	4.61660	+	7.99619i	0.923321	+	1.59924i	0.794240	+	0.607604i	$0.207869\pi$
$5$	4.61660	+	7.99619i	0.923321	+	1.59924i	0.129080	+	0.991634i	$0.458797\pi$
$6$		0			0
$7$	5.33093	+	3.07781i	0.761561	+	0.439687i	0.829856	−	0.557978i	$-0.188423\pi$
$7$	5.33093	+	3.07781i	0.761561	+	0.439687i	−0.0682950	+	0.997665i	$0.521756\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.70016	+	2.13629i	0.336378	+	0.194208i	0.658669	−	0.752433i	$-0.271120\pi$
$11$	3.70016	+	2.13629i	0.336378	+	0.194208i	−0.322291	+	0.946641i	$0.604453\pi$
$12$		0			0
$13$	−0.869235	−	1.50556i	−0.0668642	−	0.115812i	0.830655	−	0.556787i	$-0.187966\pi$
$13$	−0.869235	−	1.50556i	−0.0668642	−	0.115812i	−0.897519	+	0.440975i	$0.854633\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−12.3476			−0.726329			−0.363164	−	0.931725i	$-0.618304\pi$
$17$	−12.3476			−0.726329			−0.363164	+	0.931725i	$0.618304\pi$
$18$		0			0
$19$			33.9338i			1.78599i	0.450065	+	0.892996i	$0.351401\pi$
$19$			33.9338i			1.78599i	−0.450065	+	0.892996i	$0.648599\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.35035	+	1.93433i	−0.145668	+	0.0841012i	−0.571062	−	0.820907i	$-0.693469\pi$
$23$	−3.35035	+	1.93433i	−0.145668	+	0.0841012i	0.425395	+	0.905008i	$0.360135\pi$
$24$		0			0
$25$	−30.1260	+	52.1798i	−1.20504	+	2.08719i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	17.8409	−	30.9014i	0.615204	−	1.06556i	−0.375145	−	0.926966i	$-0.622407\pi$
$29$	17.8409	−	30.9014i	0.615204	−	1.06556i	0.990349	−	0.138598i	$-0.0442596\pi$
$30$		0			0
$31$	−38.8262	+	22.4163i	−1.25246	+	0.723107i	−0.971597	−	0.236641i	$-0.923953\pi$
$31$	−38.8262	+	22.4163i	−1.25246	+	0.723107i	−0.280861	+	0.959748i	$0.590620\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			56.8361i			1.62389i
$36$		0			0
$37$	32.7130			0.884134			0.442067	−	0.896982i	$-0.354245\pi$
$37$	32.7130			0.884134			0.442067	+	0.896982i	$0.354245\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−21.8565	−	37.8565i	−0.533085	−	0.923330i	−0.999253	−	0.0386343i	$-0.987699\pi$
$41$	−21.8565	−	37.8565i	−0.533085	−	0.923330i	0.466168	−	0.884696i	$-0.345634\pi$
$42$		0			0
$43$	33.9339	+	19.5918i	0.789161	+	0.455622i	0.839667	−	0.543102i	$-0.182750\pi$
$43$	33.9339	+	19.5918i	0.789161	+	0.455622i	−0.0505063	+	0.998724i	$0.516084\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	39.8784	+	23.0238i	0.848477	+	0.489868i	0.860137	−	0.510064i	$-0.170378\pi$
$47$	39.8784	+	23.0238i	0.848477	+	0.489868i	−0.0116600	+	0.999932i	$0.503712\pi$
$48$		0			0
$49$	−5.55415	−	9.62007i	−0.113350	−	0.196328i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	46.3143			0.873854			0.436927	−	0.899497i	$-0.356067\pi$
$53$	46.3143			0.873854			0.436927	+	0.899497i	$0.356067\pi$
$54$		0			0
$55$			39.4496i			0.717265i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−23.2710	+	13.4355i	−0.394423	+	0.227720i	−0.684075	−	0.729412i	$-0.739794\pi$
$59$	−23.2710	+	13.4355i	−0.394423	+	0.227720i	0.289652	+	0.957132i	$0.406461\pi$
$60$		0			0
$61$	−23.4545	+	40.6243i	−0.384500	+	0.665973i	−0.991700	−	0.128576i	$-0.958959\pi$
$61$	−23.4545	+	40.6243i	−0.384500	+	0.665973i	0.607200	+	0.794549i	$0.292293\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.02582	−	13.9011i	0.123474	−	0.213864i
$66$		0			0
$67$	−56.9984	+	32.9080i	−0.850722	+	0.491164i	−0.860894	−	0.508784i	$-0.830095\pi$
$67$	−56.9984	+	32.9080i	−0.850722	+	0.491164i	0.0101725	+	0.999948i	$0.496762\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	96.7955i		−	1.36332i	−0.731671	−	0.681658i	$-0.761259\pi$
$71$		−	96.7955i		−	1.36332i	0.731671	−	0.681658i	$-0.238741\pi$
$72$		0			0
$73$	−14.0622			−0.192633			−0.0963163	−	0.995351i	$-0.530706\pi$
$73$	−14.0622			−0.192633			−0.0963163	+	0.995351i	$0.530706\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	13.1502	+	22.7768i	0.170782	+	0.295803i
$78$		0			0
$79$	−34.3954	−	19.8582i	−0.435385	−	0.251369i	0.266253	−	0.963903i	$-0.414214\pi$
$79$	−34.3954	−	19.8582i	−0.435385	−	0.251369i	−0.701638	+	0.712534i	$0.747548\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−81.7202	−	47.1812i	−0.984581	−	0.568448i	−0.0809306	−	0.996720i	$-0.525789\pi$
$83$	−81.7202	−	47.1812i	−0.984581	−	0.568448i	−0.903650	+	0.428272i	$0.859123\pi$
$84$		0			0
$85$	−57.0039	−	98.7336i	−0.670634	−	1.16157i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	81.8478			0.919639			0.459819	−	0.888012i	$-0.347914\pi$
$89$	81.8478			0.919639			0.459819	+	0.888012i	$0.347914\pi$
$90$		0			0
$91$		−	10.7014i		−	0.117597i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−271.341	+	156.659i	−2.85623	+	1.64904i
$96$		0			0
$97$	−7.99028	+	13.8396i	−0.0823741	+	0.142676i	−0.904269	−	0.426963i	$-0.859584\pi$
$97$	−7.99028	+	13.8396i	−0.0823741	+	0.142676i	0.821895	+	0.569639i	$0.192917\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	50.6344	−	87.7014i	0.501331	−	0.868330i	−0.498668	−	0.866793i	$-0.666177\pi$
$101$	50.6344	−	87.7014i	0.501331	−	0.868330i	0.999999	−	0.00153723i	$-0.000489314\pi$
$102$		0			0
$103$	88.4092	−	51.0431i	0.858341	−	0.495564i	−0.00511517	−	0.999987i	$-0.501628\pi$
$103$	88.4092	−	51.0431i	0.858341	−	0.495564i	0.863456	+	0.504423i	$0.168295\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	73.1463i		−	0.683610i	−0.939771	−	0.341805i	$-0.888962\pi$
$107$		−	73.1463i		−	0.683610i	0.939771	−	0.341805i	$-0.111038\pi$
$108$		0			0
$109$	33.9344			0.311325			0.155663	−	0.987810i	$-0.450249\pi$
$109$	33.9344			0.311325			0.155663	+	0.987810i	$0.450249\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	13.9292	+	24.1262i	0.123268	+	0.213506i	0.921054	−	0.389434i	$-0.127329\pi$
$113$	13.9292	+	24.1262i	0.123268	+	0.213506i	−0.797787	+	0.602940i	$0.793996\pi$
$114$		0			0
$115$	−30.9345	−	17.8600i	−0.268996	−	0.155305i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−65.8241	−	38.0035i	−0.553143	−	0.319358i
$120$		0			0
$121$	−51.3725	−	88.9798i	−0.424566	−	0.735371i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−325.490			−2.60392
$126$		0			0
$127$			117.905i			0.928387i	0.885734	+	0.464193i	$0.153656\pi$
$127$			117.905i			0.928387i	−0.885734	+	0.464193i	$0.846344\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−73.5214	+	42.4476i	−0.561232	+	0.324027i	−0.753640	−	0.657288i	$-0.771704\pi$
$131$	−73.5214	+	42.4476i	−0.561232	+	0.324027i	0.192408	+	0.981315i	$0.438370\pi$
$132$		0			0
$133$	−104.442	+	180.899i	−0.785278	+	1.36014i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.97975	+	6.89314i	−0.0290493	+	0.0503149i	−0.880185	−	0.474632i	$-0.842581\pi$
$137$	−3.97975	+	6.89314i	−0.0290493	+	0.0503149i	0.851135	+	0.524946i	$0.175915\pi$
$138$		0			0
$139$	17.9239	−	10.3484i	0.128949	−	0.0744488i	−0.434138	−	0.900846i	$-0.642947\pi$
$139$	17.9239	−	10.3484i	0.128949	−	0.0744488i	0.563087	+	0.826398i	$0.309614\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	7.42775i		−	0.0519423i
$144$		0			0
$145$	329.458			2.27212
$146$		0			0
$147$		0			0
$148$		0			0
$149$	65.6122	+	113.644i	0.440350	+	0.762709i	0.997715	−	0.0675588i	$-0.0215210\pi$
$149$	65.6122	+	113.644i	0.440350	+	0.762709i	−0.557365	+	0.830267i	$0.688188\pi$
$150$		0			0
$151$	204.949	+	118.328i	1.35728	+	0.783627i	0.989257	−	0.146189i	$-0.0467009\pi$
$151$	204.949	+	118.328i	1.35728	+	0.783627i	0.368025	+	0.929816i	$0.380034\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−358.490	−	206.974i	−2.31284	−	1.33532i
$156$		0			0
$157$	74.8892	+	129.712i	0.477001	+	0.826190i	0.999653	−	0.0263562i	$-0.00839041\pi$
$157$	74.8892	+	129.712i	0.477001	+	0.826190i	−0.522651	+	0.852546i	$0.675057\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−23.8140			−0.147913
$162$		0			0
$163$			152.365i			0.934756i	0.884057	+	0.467378i	$0.154801\pi$
$163$			152.365i			0.934756i	−0.884057	+	0.467378i	$0.845199\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−21.5631	+	12.4494i	−0.129120	+	0.0745476i	−0.563169	−	0.826342i	$-0.690418\pi$
$167$	−21.5631	+	12.4494i	−0.129120	+	0.0745476i	0.434049	+	0.900889i	$0.357085\pi$
$168$		0			0
$169$	82.9889	−	143.741i	0.491058	−	0.850538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−54.0452	+	93.6091i	−0.312400	+	0.541093i	−0.978881	−	0.204429i	$-0.934466\pi$
$173$	−54.0452	+	93.6091i	−0.312400	+	0.541093i	0.666481	+	0.745522i	$0.267800\pi$
$174$		0			0
$175$	−321.199	+	185.445i	−1.83543	+	1.05968i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			313.318i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$179$			313.318i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$180$		0			0
$181$	−20.5886			−0.113749			−0.0568746	−	0.998381i	$-0.518114\pi$
$181$	−20.5886			−0.113749			−0.0568746	+	0.998381i	$0.518114\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	151.023	+	261.579i	0.816339	+	1.41394i
$186$		0			0
$187$	−45.6881	−	26.3780i	−0.244321	−	0.141059i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−23.6619	−	13.6612i	−0.123884	−	0.0715247i	0.436777	−	0.899570i	$-0.356120\pi$
$191$	−23.6619	−	13.6612i	−0.123884	−	0.0715247i	−0.560662	+	0.828045i	$0.689453\pi$
$192$		0			0
$193$	−65.7227	−	113.835i	−0.340532	−	0.589819i	0.644000	−	0.765026i	$-0.277274\pi$
$193$	−65.7227	−	113.835i	−0.340532	−	0.589819i	−0.984532	+	0.175207i	$0.943941\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−126.466			−0.641961			−0.320981	−	0.947086i	$-0.604012\pi$
$197$	−126.466			−0.641961			−0.320981	+	0.947086i	$0.604012\pi$
$198$		0			0
$199$			76.0070i			0.381945i	0.981595	+	0.190972i	$0.0611641\pi$
$199$			76.0070i			0.381945i	−0.981595	+	0.190972i	$0.938836\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	190.217	−	109.822i	0.937030	−	0.540995i
$204$		0			0
$205$	201.805	−	349.537i	0.984417	−	1.70506i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−72.4925	+	125.561i	−0.346854	+	0.600769i
$210$		0			0
$211$	−91.8563	+	53.0332i	−0.435338	+	0.251342i	−0.701618	−	0.712553i	$-0.747539\pi$
$211$	−91.8563	+	53.0332i	−0.435338	+	0.251342i	0.266280	+	0.963896i	$0.414205\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			361.789i			1.68274i
$216$		0			0
$217$	−275.973			−1.27176
$218$		0			0
$219$		0			0
$220$		0			0
$221$	10.7330	+	18.5900i	0.0485654	+	0.0841177i
$222$		0			0
$223$	−55.1700	−	31.8524i	−0.247399	−	0.142836i	0.371174	−	0.928563i	$-0.378955\pi$
$223$	−55.1700	−	31.8524i	−0.247399	−	0.142836i	−0.618573	+	0.785728i	$0.712289\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	304.643	+	175.886i	1.34204	+	0.774827i	0.987106	−	0.160065i	$-0.0511704\pi$
$227$	304.643	+	175.886i	1.34204	+	0.774827i	0.354933	+	0.934892i	$0.384504\pi$
$228$		0			0
$229$	−102.232	−	177.072i	−0.446429	−	0.773238i	0.551721	−	0.834029i	$-0.313971\pi$
$229$	−102.232	−	177.072i	−0.446429	−	0.773238i	−0.998151	+	0.0607903i	$0.980638\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−236.626			−1.01556			−0.507782	−	0.861486i	$-0.669534\pi$
$233$	−236.626			−1.01556			−0.507782	+	0.861486i	$0.669534\pi$
$234$		0			0
$235$			425.167i			1.80922i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.1578	−	9.32873i	0.0676060	−	0.0390324i	−0.465816	−	0.884882i	$-0.654239\pi$
$239$	16.1578	−	9.32873i	0.0676060	−	0.0390324i	0.533422	+	0.845849i	$0.320906\pi$
$240$		0			0
$241$	−37.2290	+	64.4826i	−0.154477	+	0.267562i	−0.932869	−	0.360217i	$-0.882703\pi$
$241$	−37.2290	+	64.4826i	−0.154477	+	0.267562i	0.778391	+	0.627779i	$0.216036\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	51.2826	−	88.8241i	0.209317	−	0.362547i
$246$		0			0
$247$	51.0894	−	29.4965i	0.206840	−	0.119419i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			206.637i			0.823257i	0.911352	+	0.411628i	$0.135040\pi$
$251$			206.637i			0.823257i	−0.911352	+	0.411628i	$0.864960\pi$
$252$		0			0
$253$	−16.5291			−0.0653325
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−148.678	−	257.517i	−0.578513	−	1.00201i	−0.995650	−	0.0931698i	$-0.970300\pi$
$257$	−148.678	−	257.517i	−0.578513	−	1.00201i	0.417138	−	0.908843i	$-0.363033\pi$
$258$		0			0
$259$	174.390	+	100.684i	0.673322	+	0.388743i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	123.730	+	71.4357i	0.470457	+	0.271619i	0.716431	−	0.697658i	$-0.245774\pi$
$263$	123.730	+	71.4357i	0.470457	+	0.271619i	−0.245974	+	0.969276i	$0.579108\pi$
$264$		0			0
$265$	213.815	+	370.338i	0.806847	+	1.39750i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	370.517			1.37738			0.688692	−	0.725054i	$-0.258185\pi$
$269$	370.517			1.37738			0.688692	+	0.725054i	$0.258185\pi$
$270$		0			0
$271$			368.022i			1.35801i	0.734132	+	0.679007i	$0.237589\pi$
$271$			368.022i			1.35801i	−0.734132	+	0.679007i	$0.762411\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−222.942	+	128.716i	−0.810700	+	0.468058i
$276$		0			0
$277$	15.3234	−	26.5409i	0.0553191	−	0.0958154i	−0.837040	−	0.547142i	$-0.815716\pi$
$277$	15.3234	−	26.5409i	0.0553191	−	0.0958154i	0.892359	+	0.451327i	$0.149049\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	231.041	−	400.176i	0.822212	−	1.42411i	−0.0818203	−	0.996647i	$-0.526073\pi$
$281$	231.041	−	400.176i	0.822212	−	1.42411i	0.904032	−	0.427465i	$-0.140593\pi$
$282$		0			0
$283$	−422.693	+	244.042i	−1.49361	+	0.862339i	−0.999973	−	0.00732653i	$-0.997668\pi$
$283$	−422.693	+	244.042i	−1.49361	+	0.862339i	−0.493642	+	0.869665i	$0.664335\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	269.081i		−	0.937563i
$288$		0			0
$289$	−136.537			−0.472447
$290$		0			0
$291$		0			0
$292$		0			0
$293$	215.030	+	372.442i	0.733890	+	1.27113i	0.955209	+	0.295933i	$0.0956305\pi$
$293$	215.030	+	372.442i	0.733890	+	1.27113i	−0.221319	+	0.975201i	$0.571036\pi$
$294$		0			0
$295$	−214.866	−	124.053i	−0.728358	−	0.420518i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.82449	+	3.36277i	0.0194799	+	0.0112467i
$300$		0			0
$301$	120.599	+	208.884i	0.400663	+	0.693968i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−433.120			−1.42007
$306$		0			0
$307$		−	276.184i		−	0.899621i	−0.893124	−	0.449810i	$-0.851492\pi$
$307$		−	276.184i		−	0.899621i	0.893124	−	0.449810i	$-0.148508\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	172.998	−	99.8806i	0.556264	−	0.321159i	−0.195380	−	0.980728i	$-0.562594\pi$
$311$	172.998	−	99.8806i	0.556264	−	0.321159i	0.751645	+	0.659568i	$0.229261\pi$
$312$		0			0
$313$	59.3385	−	102.777i	0.189580	−	0.328362i	−0.755530	−	0.655114i	$-0.772621\pi$
$313$	59.3385	−	102.777i	0.189580	−	0.328362i	0.945110	+	0.326752i	$0.105954\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	193.261	−	334.738i	0.609657	−	1.05596i	−0.381640	−	0.924311i	$-0.624641\pi$
$317$	193.261	−	334.738i	0.609657	−	1.05596i	0.991297	−	0.131645i	$-0.0420260\pi$
$318$		0			0
$319$	132.028	−	76.2267i	0.413882	−	0.238955i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	419.001i		−	1.29722i
$324$		0			0
$325$	104.746			0.322297
$326$		0			0
$327$		0			0
$328$		0			0
$329$	141.726	+	245.476i	0.430778	+	0.746129i
$330$		0			0
$331$	282.733	+	163.236i	0.854179	+	0.493161i	0.862059	−	0.506808i	$-0.169175\pi$
$331$	282.733	+	163.236i	0.854179	+	0.493161i	−0.00787942	+	0.999969i	$0.502508\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−526.278	−	303.847i	−1.57098	−	0.907005i
$336$		0			0
$337$	57.4906	+	99.5766i	0.170595	+	0.295479i	0.938628	−	0.344931i	$-0.112098\pi$
$337$	57.4906	+	99.5766i	0.170595	+	0.295479i	−0.768033	+	0.640410i	$0.778764\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−191.551			−0.561733
$342$		0			0
$343$		−	370.004i		−	1.07873i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−502.945	+	290.375i	−1.44941	+	0.836817i	−0.998446	−	0.0557260i	$-0.982253\pi$
$347$	−502.945	+	290.375i	−1.44941	+	0.836817i	−0.450963	+	0.892543i	$0.648919\pi$
$348$		0			0
$349$	175.463	−	303.912i	0.502761	−	0.870807i	−0.497234	−	0.867616i	$-0.665651\pi$
$349$	175.463	−	303.912i	0.502761	−	0.870807i	0.999995	−	0.00319067i	$-0.00101562\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	67.7870	−	117.411i	0.192031	−	0.332608i	−0.753892	−	0.656998i	$-0.771826\pi$
$353$	67.7870	−	117.411i	0.192031	−	0.332608i	0.945923	+	0.324390i	$0.105159\pi$
$354$		0			0
$355$	773.995	−	446.866i	2.18027	−	1.25878i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			108.852i			0.303210i	0.988441	+	0.151605i	$0.0484441\pi$
$359$			108.852i			0.303210i	−0.988441	+	0.151605i	$0.951556\pi$
$360$		0			0
$361$	−790.506			−2.18977
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−64.9195	−	112.444i	−0.177862	−	0.308065i
$366$		0			0
$367$	−14.6619	−	8.46503i	−0.0399506	−	0.0230655i	0.479892	−	0.877328i	$-0.340676\pi$
$367$	−14.6619	−	8.46503i	−0.0399506	−	0.0230655i	−0.519842	+	0.854262i	$0.674009\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	246.898	+	142.547i	0.665493	+	0.384223i
$372$		0			0
$373$	18.5300	+	32.0949i	0.0496783	+	0.0860454i	0.889795	−	0.456360i	$-0.150847\pi$
$373$	18.5300	+	32.0949i	0.0496783	+	0.0860454i	−0.840117	+	0.542405i	$0.817514\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−62.0318			−0.164540
$378$		0			0
$379$		−	531.193i		−	1.40156i	−0.713375	−	0.700782i	$-0.752834\pi$
$379$		−	531.193i		−	1.40156i	0.713375	−	0.700782i	$-0.247166\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	324.004	−	187.064i	0.845963	−	0.488417i	−0.0133235	−	0.999911i	$-0.504241\pi$
$383$	324.004	−	187.064i	0.845963	−	0.488417i	0.859287	+	0.511494i	$0.170908\pi$
$384$		0			0
$385$	−121.418	+	210.303i	−0.315373	+	0.546241i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	271.593	−	470.412i	0.698182	−	1.20929i	−0.270915	−	0.962603i	$-0.587326\pi$
$389$	271.593	−	470.412i	0.698182	−	1.20929i	0.969096	−	0.246683i	$-0.0793406\pi$
$390$		0			0
$391$	41.3688	−	23.8843i	0.105802	−	0.0610851i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	366.709i		−	0.928378i
$396$		0			0
$397$	−606.097			−1.52669			−0.763346	−	0.645990i	$-0.776445\pi$
$397$	−606.097			−1.52669			−0.763346	+	0.645990i	$0.776445\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	293.529	+	508.408i	0.731994	+	1.26785i	0.956030	+	0.293269i	$0.0947433\pi$
$401$	293.529	+	508.408i	0.731994	+	1.26785i	−0.224036	+	0.974581i	$0.571923\pi$
$402$		0			0
$403$	67.4982	+	38.9701i	0.167489	+	0.0967000i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	121.043	+	69.8844i	0.297404	+	0.171706i
$408$		0			0
$409$	129.882	+	224.961i	0.317559	+	0.550028i	0.979978	−	0.199105i	$-0.0638036\pi$
$409$	129.882	+	224.961i	0.317559	+	0.550028i	−0.662419	+	0.749133i	$0.730470\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−165.408			−0.400503
$414$		0			0
$415$		−	871.267i		−	2.09944i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	297.997	−	172.049i	0.711210	−	0.410617i	−0.100299	−	0.994957i	$-0.531980\pi$
$419$	297.997	−	172.049i	0.711210	−	0.410617i	0.811509	+	0.584340i	$0.198647\pi$
$420$		0			0
$421$	−153.263	+	265.460i	−0.364046	+	0.630546i	−0.988623	−	0.150417i	$-0.951938\pi$
$421$	−153.263	+	265.460i	−0.364046	+	0.630546i	0.624576	+	0.780964i	$0.285272\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	371.984	−	644.295i	0.875256	−	1.51599i
$426$		0			0
$427$	−250.068	+	144.377i	−0.585640	+	0.338119i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	208.029i		−	0.482667i	−0.970442	−	0.241333i	$-0.922415\pi$
$431$		−	208.029i		−	0.482667i	0.970442	−	0.241333i	$-0.0775847\pi$
$432$		0			0
$433$	353.874			0.817260			0.408630	−	0.912700i	$-0.366007\pi$
$433$	353.874			0.817260			0.408630	+	0.912700i	$0.366007\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−65.6392	−	113.690i	−0.150204	−	0.260161i
$438$		0			0
$439$	200.356	+	115.675i	0.456391	+	0.263497i	0.710525	−	0.703672i	$-0.248457\pi$
$439$	200.356	+	115.675i	0.456391	+	0.263497i	−0.254135	+	0.967169i	$0.581791\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−221.434	−	127.845i	−0.499851	−	0.288589i	0.228801	−	0.973473i	$-0.426520\pi$
$443$	−221.434	−	127.845i	−0.499851	−	0.288589i	−0.728652	+	0.684884i	$0.759853\pi$
$444$		0			0
$445$	377.859	+	654.471i	0.849121	+	1.47072i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−323.060			−0.719509			−0.359755	−	0.933047i	$-0.617140\pi$
$449$	−323.060			−0.719509			−0.359755	+	0.933047i	$0.617140\pi$
$450$		0			0
$451$		−	186.767i		−	0.414118i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	85.5702	−	49.4039i	0.188066	−	0.108580i
$456$		0			0
$457$	277.264	−	480.235i	0.606704	−	1.05084i	−0.385076	−	0.922885i	$-0.625825\pi$
$457$	277.264	−	480.235i	0.606704	−	1.05084i	0.991780	−	0.127957i	$-0.0408418\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−368.753	+	638.699i	−0.799898	+	1.38546i	0.119784	+	0.992800i	$0.461780\pi$
$461$	−368.753	+	638.699i	−0.799898	+	1.38546i	−0.919682	+	0.392664i	$0.871553\pi$
$462$		0			0
$463$	116.461	−	67.2386i	0.251535	−	0.145224i	−0.368932	−	0.929456i	$-0.620276\pi$
$463$	116.461	−	67.2386i	0.251535	−	0.145224i	0.620467	+	0.784233i	$0.286943\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	595.000i		−	1.27409i	−0.770827	−	0.637045i	$-0.780156\pi$
$467$		−	595.000i		−	1.27409i	0.770827	−	0.637045i	$-0.219844\pi$
$468$		0			0
$469$	−405.139			−0.863835
$470$		0			0
$471$		0			0
$472$		0			0
$473$	83.7073	+	144.985i	0.176971	+	0.306523i
$474$		0			0
$475$	−1770.66	−	1022.29i	−3.72771	−	2.15219i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−388.924	−	224.545i	−0.811950	−	0.468779i	0.0356829	−	0.999363i	$-0.488639\pi$
$479$	−388.924	−	224.545i	−0.811950	−	0.468779i	−0.847632	+	0.530584i	$0.821973\pi$
$480$		0			0
$481$	−28.4352	−	49.2513i	−0.0591169	−	0.102394i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−147.552			−0.304231
$486$		0			0
$487$			120.044i			0.246497i	0.992376	+	0.123249i	$0.0393312\pi$
$487$			120.044i			0.246497i	−0.992376	+	0.123249i	$0.960669\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	372.302	−	214.949i	0.758252	−	0.437777i	−0.0704158	−	0.997518i	$-0.522433\pi$
$491$	372.302	−	214.949i	0.758252	−	0.437777i	0.828668	+	0.559741i	$0.189099\pi$
$492$		0			0
$493$	−220.292	+	381.557i	−0.446840	+	0.773950i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	297.918	−	516.010i	0.599433	−	1.03825i
$498$		0			0
$499$	639.117	−	368.994i	1.28080	−	0.739467i	0.303802	−	0.952735i	$-0.401744\pi$
$499$	639.117	−	368.994i	1.28080	−	0.739467i	0.976994	+	0.213268i	$0.0684107\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			951.782i			1.89221i	0.323859	+	0.946105i	$0.395020\pi$
$503$			951.782i			1.89221i	−0.323859	+	0.946105i	$0.604980\pi$
$504$		0			0
$505$	935.036			1.85156
$506$		0			0
$507$		0			0
$508$		0			0
$509$	37.8898	+	65.6271i	0.0744398	+	0.128933i	0.900843	−	0.434146i	$-0.142950\pi$
$509$	37.8898	+	65.6271i	0.0744398	+	0.128933i	−0.826403	+	0.563079i	$0.809616\pi$
$510$		0			0
$511$	−74.9644	−	43.2807i	−0.146701	−	0.0846981i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	816.300	+	471.291i	1.58505	+	0.915128i
$516$		0			0
$517$	98.3710	+	170.384i	0.190273	+	0.329562i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−24.6152			−0.0472461			−0.0236230	−	0.999721i	$-0.507520\pi$
$521$	−24.6152			−0.0472461			−0.0236230	+	0.999721i	$0.507520\pi$
$522$		0			0
$523$			165.798i			0.317013i	0.987358	+	0.158506i	$0.0506678\pi$
$523$			165.798i			0.317013i	−0.987358	+	0.158506i	$0.949332\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	479.410	−	276.787i	0.909696	−	0.525213i
$528$		0			0
$529$	−257.017	+	445.166i	−0.485854	+	0.841524i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−37.9968	+	65.8124i	−0.0712886	+	0.123476i
$534$		0			0
$535$	584.892	−	337.687i	1.09326	−	0.631191i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	47.4611i		−	0.0880539i
$540$		0			0
$541$	184.323			0.340708			0.170354	−	0.985383i	$-0.445509\pi$
$541$	184.323			0.340708			0.170354	+	0.985383i	$0.445509\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	156.662	+	271.346i	0.287453	+	0.497883i
$546$		0			0
$547$	803.354	+	463.817i	1.46865	+	0.847928i	0.999383	−	0.0351259i	$-0.0111832\pi$
$547$	803.354	+	463.817i	1.46865	+	0.847928i	0.469272	+	0.883054i	$0.344517\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1048.60	+	605.411i	1.90309	+	1.09875i
$552$		0			0
$553$	−122.240	−	211.725i	−0.221048	−	0.382866i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−492.087			−0.883459			−0.441730	−	0.897148i	$-0.645635\pi$
$557$	−492.087			−0.883459			−0.441730	+	0.897148i	$0.645635\pi$
$558$		0			0
$559$		−	68.1193i		−	0.121859i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	626.453	−	361.683i	1.11271	−	0.642421i	0.173177	−	0.984891i	$-0.444597\pi$
$563$	626.453	−	361.683i	1.11271	−	0.642421i	0.939529	+	0.342470i	$0.111264\pi$
$564$		0			0
$565$	−128.612	+	222.762i	−0.227631	+	0.394269i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−435.816	+	754.855i	−0.765933	+	1.32664i	0.173819	+	0.984778i	$0.444389\pi$
$569$	−435.816	+	754.855i	−0.765933	+	1.32664i	−0.939752	+	0.341857i	$0.888944\pi$
$570$		0			0
$571$	−210.649	+	121.618i	−0.368912	+	0.212991i	−0.672983	−	0.739658i	$-0.734987\pi$
$571$	−210.649	+	121.618i	−0.368912	+	0.212991i	0.304071	+	0.952649i	$0.401654\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	233.094i		−	0.405382i
$576$		0			0
$577$	−201.625			−0.349436			−0.174718	−	0.984619i	$-0.555901\pi$
$577$	−201.625			−0.349436			−0.174718	+	0.984619i	$0.555901\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−290.430	−	503.039i	−0.499879	−	0.865815i
$582$		0			0
$583$	171.370	+	98.9406i	0.293945	+	0.169710i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	688.983	+	397.784i	1.17374	+	0.677656i	0.954557	−	0.298029i	$-0.0963291\pi$
$587$	688.983	+	397.784i	1.17374	+	0.677656i	0.219178	+	0.975685i	$0.429662\pi$
$588$		0			0
$589$	−760.672	−	1317.52i	−1.29146	−	2.23688i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1078.05			1.81796			0.908980	−	0.416839i	$-0.136862\pi$
$593$	1078.05			1.81796			0.908980	+	0.416839i	$0.136862\pi$
$594$		0			0
$595$		−	701.789i		−	1.17948i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	209.699	−	121.070i	0.350082	−	0.202120i	−0.314639	−	0.949211i	$-0.601883\pi$
$599$	209.699	−	121.070i	0.350082	−	0.202120i	0.664722	+	0.747091i	$0.268550\pi$
$600$		0			0
$601$	135.406	−	234.529i	0.225300	−	0.390232i	−0.731109	−	0.682261i	$-0.760997\pi$
$601$	135.406	−	234.529i	0.225300	−	0.390232i	0.956410	+	0.292029i	$0.0943303\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	474.333	−	821.569i	0.784022	−	1.35797i
$606$		0			0
$607$	−335.657	+	193.792i	−0.552977	+	0.319261i	−0.750322	−	0.661073i	$-0.770101\pi$
$607$	−335.657	+	193.792i	−0.552977	+	0.319261i	0.197345	+	0.980334i	$0.436768\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	80.0524i		−	0.131019i
$612$		0			0
$613$	1120.09			1.82722			0.913610	−	0.406591i	$-0.133282\pi$
$613$	1120.09			1.82722			0.913610	+	0.406591i	$0.133282\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	266.289	+	461.226i	0.431587	+	0.747530i	0.997010	−	0.0772706i	$-0.0246205\pi$
$617$	266.289	+	461.226i	0.431587	+	0.747530i	−0.565423	+	0.824801i	$0.691287\pi$
$618$		0			0
$619$	761.814	+	439.833i	1.23072	+	0.710555i	0.967179	−	0.254095i	$-0.0817774\pi$
$619$	761.814	+	439.833i	1.23072	+	0.710555i	0.263537	+	0.964649i	$0.415111\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	436.325	+	251.912i	0.700361	+	0.404354i
$624$		0			0
$625$	−749.506	−	1298.18i	−1.19921	−	2.07709i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−403.926			−0.642172
$630$		0			0
$631$			310.499i			0.492075i	0.969260	+	0.246037i	$0.0791286\pi$
$631$			310.499i			0.492075i	−0.969260	+	0.246037i	$0.920871\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−942.792	+	544.321i	−1.48471	+	0.857199i
$636$		0			0
$637$	−9.65572	+	16.7242i	−0.0151581	+	0.0262546i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	275.610	−	477.371i	0.429969	−	0.744728i	−0.566901	−	0.823786i	$-0.691858\pi$
$641$	275.610	−	477.371i	0.429969	−	0.744728i	0.996870	+	0.0790578i	$0.0251912\pi$
$642$		0			0
$643$	−352.044	+	203.253i	−0.547503	+	0.316101i	−0.748114	−	0.663570i	$-0.769041\pi$
$643$	−352.044	+	203.253i	−0.547503	+	0.316101i	0.200611	+	0.979671i	$0.435707\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	652.891i		−	1.00910i	−0.863381	−	0.504552i	$-0.831658\pi$
$647$		−	652.891i		−	1.00910i	0.863381	−	0.504552i	$-0.168342\pi$
$648$		0			0
$649$	−114.808			−0.176900
$650$		0			0
$651$		0			0
$652$		0			0
$653$	513.767	+	889.870i	0.786779	+	1.36274i	0.927930	+	0.372754i	$0.121586\pi$
$653$	513.767	+	889.870i	0.786779	+	1.36274i	−0.141151	+	0.989988i	$0.545080\pi$
$654$		0			0
$655$	−678.838	−	391.927i	−1.03639	−	0.598362i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−20.5780	−	11.8807i	−0.0312261	−	0.0180284i	0.484306	−	0.874899i	$-0.339072\pi$
$659$	−20.5780	−	11.8807i	−0.0312261	−	0.0180284i	−0.515532	+	0.856870i	$0.672406\pi$
$660$		0			0
$661$	−328.164	−	568.396i	−0.496465	−	0.859903i	0.503526	−	0.863980i	$-0.332036\pi$
$661$	−328.164	−	568.396i	−0.496465	−	0.859903i	−0.999992	+	0.00407665i	$0.998702\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1928.67			−2.90025
$666$		0			0
$667$			138.041i			0.206957i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−173.571	+	100.211i	−0.258675	+	0.149346i
$672$		0			0
$673$	405.169	−	701.773i	0.602034	−	1.04275i	−0.390479	−	0.920612i	$-0.627691\pi$
$673$	405.169	−	701.773i	0.602034	−	1.04275i	0.992513	−	0.122141i	$-0.0389760\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−199.580	+	345.683i	−0.294801	+	0.510610i	−0.974939	−	0.222474i	$-0.928587\pi$
$677$	−199.580	+	345.683i	−0.294801	+	0.510610i	0.680138	+	0.733084i	$0.261920\pi$
$678$		0			0
$679$	−85.1912	+	49.1852i	−0.125466	+	0.0724377i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	203.612i		−	0.298114i	−0.988829	−	0.149057i	$-0.952376\pi$
$683$		−	203.612i		−	0.298114i	0.988829	−	0.149057i	$-0.0476238\pi$
$684$		0			0
$685$	−73.4918			−0.107287
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−40.2580	−	69.7288i	−0.0584296	−	0.101203i
$690$		0			0
$691$	−255.646	−	147.597i	−0.369965	−	0.213599i	0.303478	−	0.952838i	$-0.401852\pi$
$691$	−255.646	−	147.597i	−0.369965	−	0.213599i	−0.673443	+	0.739239i	$0.735185\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	165.495	+	95.5487i	0.238123	+	0.137480i
$696$		0			0
$697$	269.875	+	467.437i	0.387195	+	0.670641i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	283.069			0.403808			0.201904	−	0.979405i	$-0.435287\pi$
$701$	283.069			0.403808			0.201904	+	0.979405i	$0.435287\pi$
$702$		0			0
$703$			1110.08i			1.57906i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	539.857	−	311.686i	0.763588	−	0.440858i
$708$		0			0
$709$	209.399	−	362.690i	0.295344	−	0.511551i	−0.679721	−	0.733471i	$-0.737899\pi$
$709$	209.399	−	362.690i	0.295344	−	0.511551i	0.975065	+	0.221920i	$0.0712324\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	86.7210	−	150.205i	0.121628	−	0.210666i
$714$		0			0
$715$	59.3937	−	34.2910i	0.0830681	−	0.0479594i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	454.879i		−	0.632655i	−0.948650	−	0.316328i	$-0.897550\pi$
$719$		−	454.879i		−	0.632655i	0.948650	−	0.316328i	$-0.102450\pi$
$720$		0			0
$721$	628.404			0.871572
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1074.95	+	1861.87i	1.48269	+	2.56810i
$726$		0			0
$727$	207.375	+	119.728i	0.285247	+	0.164688i	0.635797	−	0.771857i	$-0.280672\pi$
$727$	207.375	+	119.728i	0.285247	+	0.164688i	−0.350549	+	0.936544i	$0.614005\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−419.002	−	241.911i	−0.573190	−	0.330931i
$732$		0			0
$733$	210.973	+	365.416i	0.287822	+	0.498522i	0.973289	−	0.229581i	$-0.0737357\pi$
$733$	210.973	+	365.416i	0.287822	+	0.498522i	−0.685468	+	0.728103i	$0.740402\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−281.204			−0.381552
$738$		0			0
$739$		−	150.203i		−	0.203251i	−0.994823	−	0.101626i	$-0.967596\pi$
$739$		−	150.203i		−	0.203251i	0.994823	−	0.101626i	$-0.0324044\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	726.756	−	419.593i	0.978137	−	0.564728i	0.0764298	−	0.997075i	$-0.475648\pi$
$743$	726.756	−	419.593i	0.978137	−	0.564728i	0.901707	+	0.432347i	$0.142315\pi$
$744$		0			0
$745$	−605.810	+	1049.29i	−0.813168	+	1.40845i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	225.130	−	389.937i	0.300575	−	0.520611i
$750$		0			0
$751$	634.488	−	366.322i	0.844858	−	0.487779i	−0.0140549	−	0.999901i	$-0.504474\pi$
$751$	634.488	−	366.322i	0.844858	−	0.487779i	0.858912	+	0.512122i	$0.171141\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			2185.09i			2.89415i
$756$		0			0
$757$	1455.19			1.92231			0.961153	−	0.276015i	$-0.0890139\pi$
$757$	1455.19			1.92231			0.961153	+	0.276015i	$0.0890139\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−365.230	−	632.596i	−0.479934	−	0.831270i	0.519801	−	0.854287i	$-0.326006\pi$
$761$	−365.230	−	632.596i	−0.479934	−	0.831270i	−0.999735	+	0.0230176i	$0.992673\pi$
$762$		0			0
$763$	180.902	+	104.444i	0.237093	+	0.136886i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	40.4559	+	23.3572i	0.0527456	+	0.0304527i
$768$		0			0
$769$	430.746	+	746.074i	0.560138	+	0.970187i	0.997484	+	0.0708938i	$0.0225851\pi$
$769$	430.746	+	746.074i	0.560138	+	0.970187i	−0.437346	+	0.899293i	$0.644082\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−981.517			−1.26975			−0.634875	−	0.772615i	$-0.718948\pi$
$773$	−981.517			−1.26975			−0.634875	+	0.772615i	$0.718948\pi$
$774$		0			0
$775$		−	2701.26i		−	3.48550i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1284.62	−	741.675i	1.64906	−	0.952085i
$780$		0			0
$781$	206.783	−	358.159i	0.264767	−	0.458590i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−691.467	+	1197.66i	−0.880850	+	1.52568i
$786$		0			0
$787$	614.292	−	354.662i	0.780549	−	0.450650i	−0.0560758	−	0.998427i	$-0.517859\pi$
$787$	614.292	−	354.662i	0.780549	−	0.450650i	0.836625	+	0.547776i	$0.184526\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			171.486i			0.216797i
$792$		0			0
$793$	81.5498			0.102837
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−591.856	−	1025.12i	−0.742605	−	1.28623i	−0.951306	−	0.308249i	$-0.900257\pi$
$797$	−591.856	−	1025.12i	−0.742605	−	1.28623i	0.208701	−	0.977980i	$-0.433076\pi$
$798$		0			0
$799$	−492.402	−	284.288i	−0.616273	−	0.355805i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−52.0323	−	30.0409i	−0.0647974	−	0.0374108i
$804$		0			0
$805$	−109.940	−	190.421i	−0.136571	−	0.236548i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−522.491			−0.645847			−0.322924	−	0.946425i	$-0.604666\pi$
$809$	−522.491			−0.645847			−0.322924	+	0.946425i	$0.604666\pi$
$810$		0			0
$811$			115.368i			0.142254i	0.997467	+	0.0711271i	$0.0226596\pi$
$811$			115.368i			0.142254i	−0.997467	+	0.0711271i	$0.977340\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1218.34	+	703.410i	−1.49490	+	0.863080i
$816$		0			0
$817$	−664.823	+	1151.51i	−0.813737	+	1.40943i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	417.973	−	723.951i	0.509102	−	0.881791i	−0.490842	−	0.871249i	$-0.663311\pi$
$821$	417.973	−	723.951i	0.509102	−	0.881791i	0.999944	−	0.0105427i	$-0.00335589\pi$
$822$		0			0
$823$	629.895	−	363.670i	0.765364	−	0.441883i	−0.0658543	−	0.997829i	$-0.520977\pi$
$823$	629.895	−	363.670i	0.765364	−	0.441883i	0.831218	+	0.555946i	$0.187644\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1271.70i		−	1.53773i	−0.639413	−	0.768864i	$-0.720822\pi$
$827$		−	1271.70i		−	1.53773i	0.639413	−	0.768864i	$-0.279178\pi$
$828$		0			0
$829$	−577.896			−0.697100			−0.348550	−	0.937290i	$-0.613326\pi$
$829$	−577.896			−0.697100			−0.348550	+	0.937290i	$0.613326\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	68.5803	+	118.785i	0.0823293	+	0.142599i
$834$		0			0
$835$	−199.096	−	114.948i	−0.238439	−	0.137663i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−620.279	−	358.118i	−0.739308	−	0.426839i	0.0825099	−	0.996590i	$-0.473706\pi$
$839$	−620.279	−	358.118i	−0.739308	−	0.426839i	−0.821818	+	0.569751i	$0.807040\pi$
$840$		0			0
$841$	−216.096	−	374.289i	−0.256951	−	0.445053i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1532.51			1.81362
$846$		0			0
$847$		−	632.460i		−	0.746706i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−109.600	+	63.2776i	−0.128790	+	0.0743567i
$852$		0			0
$853$	522.638	−	905.235i	0.612705	−	1.06124i	−0.378077	−	0.925774i	$-0.623415\pi$
$853$	522.638	−	905.235i	0.612705	−	1.06124i	0.990782	−	0.135463i	$-0.0432521\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	411.368	−	712.510i	0.480009	−	0.831400i	−0.519728	−	0.854332i	$-0.673967\pi$
$857$	411.368	−	712.510i	0.480009	−	0.831400i	0.999737	+	0.0229317i	$0.00730001\pi$
$858$		0			0
$859$	53.7624	−	31.0397i	0.0625871	−	0.0361347i	−0.468380	−	0.883527i	$-0.655162\pi$
$859$	53.7624	−	31.0397i	0.0625871	−	0.0361347i	0.530967	+	0.847392i	$0.321829\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1250.20i		−	1.44867i	−0.689448	−	0.724335i	$-0.742147\pi$
$863$		−	1250.20i		−	1.44867i	0.689448	−	0.724335i	$-0.257853\pi$
$864$		0			0
$865$	−998.022			−1.15378
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−84.8456	−	146.957i	−0.0976360	−	0.169110i
$870$		0			0
$871$	99.0899	+	57.2096i	0.113766	+	0.0656827i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1735.16	−	1001.80i	−1.98304	−	1.14491i
$876$		0			0
$877$	105.302	+	182.388i	0.120071	+	0.207968i	0.919795	−	0.392398i	$-0.128355\pi$
$877$	105.302	+	182.388i	0.120071	+	0.207968i	−0.799725	+	0.600367i	$0.795021\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	366.361			0.415846			0.207923	−	0.978145i	$-0.433330\pi$
$881$	366.361			0.415846			0.207923	+	0.978145i	$0.433330\pi$
$882$		0			0
$883$			266.329i			0.301619i	0.988563	+	0.150809i	$0.0481879\pi$
$883$			266.329i			0.301619i	−0.988563	+	0.150809i	$0.951812\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−175.292	+	101.205i	−0.197623	+	0.114098i	−0.595546	−	0.803321i	$-0.703064\pi$
$887$	−175.292	+	101.205i	−0.197623	+	0.114098i	0.397923	+	0.917419i	$0.369731\pi$
$888$		0			0
$889$	−362.890	+	628.544i	−0.408200	+	0.707023i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−781.286	+	1353.23i	−0.874901	+	1.51537i
$894$		0			0
$895$	−2505.35	+	1446.47i	−2.79928	+	1.61616i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			1599.71i			1.77943i
$900$		0			0
$901$	−571.869			−0.634705
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−95.0495	−	164.630i	−0.105027	−	0.181912i
$906$		0			0
$907$	−1048.89	−	605.576i	−1.15644	−	0.667669i	−0.205989	−	0.978554i	$-0.566041\pi$
$907$	−1048.89	−	605.576i	−1.15644	−	0.667669i	−0.950448	+	0.310885i	$0.899375\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−640.792	−	369.962i	−0.703394	−	0.406105i	0.105216	−	0.994449i	$-0.466447\pi$
$911$	−640.792	−	369.962i	−0.703394	−	0.406105i	−0.808610	+	0.588344i	$0.799780\pi$
$912$		0			0
$913$	−201.585	−	349.156i	−0.220794	−	0.382427i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−522.583			−0.569883
$918$		0			0
$919$			1080.71i			1.17596i	0.808874	+	0.587982i	$0.200078\pi$
$919$			1080.71i			1.17596i	−0.808874	+	0.587982i	$0.799922\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−145.731	+	84.1380i	−0.157889	+	0.0911571i
$924$		0			0
$925$	−985.512	+	1706.96i	−1.06542	+	1.84536i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−594.530	+	1029.76i	−0.639968	+	1.10846i	0.345472	+	0.938429i	$0.387719\pi$
$929$	−594.530	+	1029.76i	−0.639968	+	1.10846i	−0.985439	+	0.170027i	$0.945614\pi$
$930$		0			0
$931$	326.446	−	188.474i	0.350640	−	0.202442i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	487.107i		−	0.520970i
$936$		0			0
$937$	1165.30			1.24364			0.621822	−	0.783158i	$-0.286393\pi$
$937$	1165.30			1.24364			0.621822	+	0.783158i	$0.286393\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	431.742	+	747.800i	0.458812	+	0.794686i	0.998898	−	0.0469234i	$-0.0149417\pi$
$941$	431.742	+	747.800i	0.458812	+	0.794686i	−0.540086	+	0.841610i	$0.681608\pi$
$942$		0			0
$943$	146.454	+	84.5552i	0.155306	+	0.0896662i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−994.656	−	574.265i	−1.05032	−	0.606404i	−0.127583	−	0.991828i	$-0.540722\pi$
$947$	−994.656	−	574.265i	−1.05032	−	0.606404i	−0.922740	+	0.385423i	$0.874055\pi$
$948$		0			0
$949$	12.2233	+	21.1714i	0.0128802	+	0.0223092i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1447.80			1.51920			0.759600	−	0.650391i	$-0.225395\pi$
$953$	1447.80			1.51920			0.759600	+	0.650391i	$0.225395\pi$
$954$		0			0
$955$		−	252.274i		−	0.264161i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−42.4316	+	24.4979i	−0.0442456	+	0.0255452i
$960$		0			0
$961$	524.483	−	908.431i	0.545768	−	0.945297i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	606.831	−	1051.06i	0.628840	−	1.08918i
$966$		0			0
$967$	1318.80	−	761.408i	1.36380	−	0.787392i	0.373675	−	0.927560i	$-0.378097\pi$
$967$	1318.80	−	761.408i	1.36380	−	0.787392i	0.990128	+	0.140168i	$0.0447641\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	266.782i		−	0.274750i	−0.990519	−	0.137375i	$-0.956133\pi$
$971$		−	266.782i		−	0.274750i	0.990519	−	0.137375i	$-0.0438666\pi$
$972$		0			0
$973$	127.401			0.130937
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−874.915	−	1515.40i	−0.895512	−	1.55107i	−0.833170	−	0.553017i	$-0.813476\pi$
$977$	−874.915	−	1515.40i	−0.895512	−	1.55107i	−0.0623423	−	0.998055i	$-0.519857\pi$
$978$		0			0
$979$	302.850	+	174.851i	0.309347	+	0.178601i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1127.06	+	650.711i	1.14656	+	0.661964i	0.948046	−	0.318135i	$-0.103056\pi$
$983$	1127.06	+	650.711i	1.14656	+	0.661964i	0.198510	+	0.980099i	$0.436390\pi$
$984$		0			0
$985$	−583.845	−	1011.25i	−0.592736	−	1.02665i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−151.587			−0.153273
$990$		0			0
$991$		−	136.009i		−	0.137245i	−0.997643	−	0.0686223i	$-0.978140\pi$
$991$		−	136.009i		−	0.137245i	0.997643	−	0.0686223i	$-0.0218603\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−607.766	+	350.894i	−0.610820	+	0.352657i
$996$		0			0
$997$	−637.348	+	1103.92i	−0.639266	+	1.10724i	0.346328	+	0.938113i	$0.387428\pi$
$997$	−637.348	+	1103.92i	−0.639266	+	1.10724i	−0.985594	+	0.169128i	$0.945905\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.o.e.127.4		8
3.2	odd	2		576.3.o.d.511.3		8
4.3	odd	2		1728.3.o.f.127.4		8
8.3	odd	2		432.3.o.b.127.1		8
8.5	even	2		432.3.o.a.127.1		8
9.4	even	3		1728.3.o.f.1279.4		8
9.5	odd	6		576.3.o.f.319.2		8
12.11	even	2		576.3.o.f.511.2		8
24.5	odd	2		144.3.o.c.79.2	yes	8
24.11	even	2		144.3.o.a.79.3	yes	8
36.23	even	6		576.3.o.d.319.3		8
36.31	odd	6	inner	1728.3.o.e.1279.4		8
72.5	odd	6		144.3.o.a.31.3	✓	8
72.11	even	6		1296.3.g.j.1135.2		8
72.13	even	6		432.3.o.b.415.1		8
72.29	odd	6		1296.3.g.j.1135.1		8
72.43	odd	6		1296.3.g.k.1135.8		8
72.59	even	6		144.3.o.c.31.2	yes	8
72.61	even	6		1296.3.g.k.1135.7		8
72.67	odd	6		432.3.o.a.415.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.3	✓	8	72.5	odd	6
144.3.o.a.79.3	yes	8	24.11	even	2
144.3.o.c.31.2	yes	8	72.59	even	6
144.3.o.c.79.2	yes	8	24.5	odd	2
432.3.o.a.127.1		8	8.5	even	2
432.3.o.a.415.1		8	72.67	odd	6
432.3.o.b.127.1		8	8.3	odd	2
432.3.o.b.415.1		8	72.13	even	6
576.3.o.d.319.3		8	36.23	even	6
576.3.o.d.511.3		8	3.2	odd	2
576.3.o.f.319.2		8	9.5	odd	6
576.3.o.f.511.2		8	12.11	even	2
1296.3.g.j.1135.1		8	72.29	odd	6
1296.3.g.j.1135.2		8	72.11	even	6
1296.3.g.k.1135.7		8	72.61	even	6
1296.3.g.k.1135.8		8	72.43	odd	6
1728.3.o.e.127.4		8	1.1	even	1	trivial
1728.3.o.e.1279.4		8	36.31	odd	6	inner
1728.3.o.f.127.4		8	4.3	odd	2
1728.3.o.f.1279.4		8	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(4.61660 + 7.99619i) q^{5} +(5.33093 + 3.07781i) q^{7} +O(q^{10})\)	\(q+(4.61660 + 7.99619i) q^{5} +(5.33093 + 3.07781i) q^{7} +(3.70016 + 2.13629i) q^{11} +(-0.869235 - 1.50556i) q^{13} -12.3476 q^{17} +33.9338i q^{19} +(-3.35035 + 1.93433i) q^{23} +(-30.1260 + 52.1798i) q^{25} +(17.8409 - 30.9014i) q^{29} +(-38.8262 + 22.4163i) q^{31} +56.8361i q^{35} +32.7130 q^{37} +(-21.8565 - 37.8565i) q^{41} +(33.9339 + 19.5918i) q^{43} +(39.8784 + 23.0238i) q^{47} +(-5.55415 - 9.62007i) q^{49} +46.3143 q^{53} +39.4496i q^{55} +(-23.2710 + 13.4355i) q^{59} +(-23.4545 + 40.6243i) q^{61} +(8.02582 - 13.9011i) q^{65} +(-56.9984 + 32.9080i) q^{67} -96.7955i q^{71} -14.0622 q^{73} +(13.1502 + 22.7768i) q^{77} +(-34.3954 - 19.8582i) q^{79} +(-81.7202 - 47.1812i) q^{83} +(-57.0039 - 98.7336i) q^{85} +81.8478 q^{89} -10.7014i q^{91} +(-271.341 + 156.659i) q^{95} +(-7.99028 + 13.8396i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{5} - 3 q^{7}+O(q^{10}) \) 8 * q + 3 * q^5 - 3 * q^7	\( 8 q + 3 q^{5} - 3 q^{7} - 18 q^{11} - 5 q^{13} - 6 q^{17} - 81 q^{23} - 23 q^{25} + 69 q^{29} - 45 q^{31} + 20 q^{37} - 54 q^{41} + 207 q^{47} + 41 q^{49} - 252 q^{53} + 306 q^{59} - 7 q^{61} - 93 q^{65} + 12 q^{67} + 74 q^{73} + 207 q^{77} - 33 q^{79} - 549 q^{83} + 30 q^{85} + 168 q^{89} - 684 q^{95} - 10 q^{97}+O(q^{100}) \) 8 * q + 3 * q^5 - 3 * q^7 - 18 * q^11 - 5 * q^13 - 6 * q^17 - 81 * q^23 - 23 * q^25 + 69 * q^29 - 45 * q^31 + 20 * q^37 - 54 * q^41 + 207 * q^47 + 41 * q^49 - 252 * q^53 + 306 * q^59 - 7 * q^61 - 93 * q^65 + 12 * q^67 + 74 * q^73 + 207 * q^77 - 33 * q^79 - 549 * q^83 + 30 * q^85 + 168 * q^89 - 684 * q^95 - 10 * q^97

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