LMFDB - Embedded newform 432.3.o.a.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(127,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, 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("432.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.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:	$11.7711474204$
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			127.1
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	432.127
Dual form			432.3.o.a.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.61660 - 7.99619i) q^{5} +(5.33093 + 3.07781i) q^{7} +O(q^{10})$	$q+(-4.61660 - 7.99619i) q^{5} +(5.33093 + 3.07781i) q^{7} +(-3.70016 - 2.13629i) q^{11} +(0.869235 + 1.50556i) q^{13} -12.3476 q^{17} -33.9338i q^{19} +(-3.35035 + 1.93433i) q^{23} +(-30.1260 + 52.1798i) q^{25} +(-17.8409 + 30.9014i) q^{29} +(-38.8262 + 22.4163i) q^{31} -56.8361i q^{35} -32.7130 q^{37} +(-21.8565 - 37.8565i) q^{41} +(-33.9339 - 19.5918i) q^{43} +(39.8784 + 23.0238i) q^{47} +(-5.55415 - 9.62007i) q^{49} -46.3143 q^{53} +39.4496i q^{55} +(23.2710 - 13.4355i) q^{59} +(23.4545 - 40.6243i) q^{61} +(8.02582 - 13.9011i) q^{65} +(56.9984 - 32.9080i) q^{67} -96.7955i q^{71} -14.0622 q^{73} +(-13.1502 - 22.7768i) q^{77} +(-34.3954 - 19.8582i) q^{79} +(81.7202 + 47.1812i) q^{83} +(57.0039 + 98.7336i) q^{85} +81.8478 q^{89} +10.7014i q^{91} +(-271.341 + 156.659i) q^{95} +(-7.99028 + 13.8396i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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	$-0.792131\pi$
$5$	−4.61660	−	7.99619i	−0.923321	−	1.59924i	−0.129080	−	0.991634i	$-0.541203\pi$
$6$		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	0.322291	−	0.946641i	$-0.395547\pi$
$11$	−3.70016	−	2.13629i	−0.336378	−	0.194208i	−0.658669	+	0.752433i	$0.728880\pi$
$12$		0			0
$13$	0.869235	+	1.50556i	0.0668642	+	0.115812i	0.897519	−	0.440975i	$-0.145367\pi$
$13$	0.869235	+	1.50556i	0.0668642	+	0.115812i	−0.830655	+	0.556787i	$0.812034\pi$
$14$		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	$-0.648599\pi$
$19$		−	33.9338i		−	1.78599i	0.450065	−	0.892996i	$-0.351401\pi$
$20$		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	$0.377593\pi$
$29$	−17.8409	+	30.9014i	−0.615204	+	1.06556i	−0.990349	+	0.138598i	$0.955740\pi$
$30$		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	$-0.645755\pi$
$37$	−32.7130			−0.884134			−0.442067	+	0.896982i	$0.645755\pi$
$38$		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	0.0505063	−	0.998724i	$-0.483916\pi$
$43$	−33.9339	−	19.5918i	−0.789161	−	0.455622i	−0.839667	+	0.543102i	$0.817250\pi$
$44$		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	$-0.643933\pi$
$53$	−46.3143			−0.873854			−0.436927	+	0.899497i	$0.643933\pi$
$54$		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	−0.289652	−	0.957132i	$-0.593539\pi$
$59$	23.2710	−	13.4355i	0.394423	−	0.227720i	0.684075	+	0.729412i	$0.260206\pi$
$60$		0			0
$61$	23.4545	−	40.6243i	0.384500	−	0.665973i	−0.607200	−	0.794549i	$-0.707707\pi$
$61$	23.4545	−	40.6243i	0.384500	−	0.665973i	0.991700	+	0.128576i	$0.0410407\pi$
$62$		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	−0.0101725	−	0.999948i	$-0.503238\pi$
$67$	56.9984	−	32.9080i	0.850722	−	0.491164i	0.860894	+	0.508784i	$0.169905\pi$
$68$		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	0.903650	−	0.428272i	$-0.140877\pi$
$83$	81.7202	+	47.1812i	0.984581	+	0.568448i	0.0809306	+	0.996720i	$0.474211\pi$
$84$		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	$0.333823\pi$
$101$	−50.6344	+	87.7014i	−0.501331	+	0.868330i	−0.999999	+	0.00153723i	$0.999511\pi$
$102$		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	$0.111038\pi$
$107$			73.1463i			0.683610i	−0.939771	+	0.341805i	$0.888962\pi$
$108$		0			0
$109$	−33.9344			−0.311325			−0.155663	−	0.987810i	$-0.549751\pi$
$109$	−33.9344			−0.311325			−0.155663	+	0.987810i	$0.549751\pi$
$110$		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	−0.192408	−	0.981315i	$-0.561630\pi$
$131$	73.5214	−	42.4476i	0.561232	−	0.324027i	0.753640	+	0.657288i	$0.228296\pi$
$132$		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	−0.563087	−	0.826398i	$-0.690386\pi$
$139$	−17.9239	+	10.3484i	−0.128949	+	0.0744488i	0.434138	+	0.900846i	$0.357053\pi$
$140$		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	0.557365	−	0.830267i	$-0.311812\pi$
$149$	−65.6122	−	113.644i	−0.440350	−	0.762709i	−0.997715	+	0.0675588i	$0.978479\pi$
$150$		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	0.522651	−	0.852546i	$-0.324943\pi$
$157$	−74.8892	−	129.712i	−0.477001	−	0.826190i	−0.999653	+	0.0263562i	$0.991610\pi$
$158$		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	$-0.845199\pi$
$163$		−	152.365i		−	0.934756i	0.884057	−	0.467378i	$-0.154801\pi$
$164$		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	−0.666481	−	0.745522i	$-0.732200\pi$
$173$	54.0452	−	93.6091i	0.312400	−	0.541093i	0.978881	+	0.204429i	$0.0655337\pi$
$174$		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	$-0.660736\pi$
$179$		−	313.318i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$180$		0			0
$181$	20.5886			0.113749			0.0568746	−	0.998381i	$-0.481886\pi$
$181$	20.5886			0.113749			0.0568746	+	0.998381i	$0.481886\pi$
$182$		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	$-0.395988\pi$
$197$	126.466			0.641961			0.320981	+	0.947086i	$0.395988\pi$
$198$		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	−0.266280	−	0.963896i	$-0.585795\pi$
$211$	91.8563	−	53.0332i	0.435338	−	0.251342i	0.701618	+	0.712553i	$0.252461\pi$
$212$		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	−0.354933	−	0.934892i	$-0.615496\pi$
$227$	−304.643	−	175.886i	−1.34204	−	0.774827i	−0.987106	+	0.160065i	$0.948830\pi$
$228$		0			0
$229$	102.232	+	177.072i	0.446429	+	0.773238i	0.998151	−	0.0607903i	$-0.0193621\pi$
$229$	102.232	+	177.072i	0.446429	+	0.773238i	−0.551721	+	0.834029i	$0.686029\pi$
$230$		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	$-0.864960\pi$
$251$		−	206.637i		−	0.823257i	0.911352	−	0.411628i	$-0.135040\pi$
$252$		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	$-0.741815\pi$
$269$	−370.517			−1.37738			−0.688692	+	0.725054i	$0.741815\pi$
$270$		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	−0.892359	−	0.451327i	$-0.850951\pi$
$277$	−15.3234	+	26.5409i	−0.0553191	+	0.0958154i	0.837040	+	0.547142i	$0.184284\pi$
$278$		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	0.493642	−	0.869665i	$-0.335665\pi$
$283$	422.693	−	244.042i	1.49361	−	0.862339i	0.999973	+	0.00732653i	$0.00233213\pi$
$284$		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	$-0.904370\pi$
$293$	−215.030	−	372.442i	−0.733890	−	1.27113i	0.221319	−	0.975201i	$-0.428964\pi$
$294$		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	$0.148508\pi$
$307$			276.184i			0.899621i	−0.893124	+	0.449810i	$0.851492\pi$
$308$		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	$0.375359\pi$
$317$	−193.261	+	334.738i	−0.609657	+	1.05596i	−0.991297	+	0.131645i	$0.957974\pi$
$318$		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	0.00787942	−	0.999969i	$-0.497492\pi$
$331$	−282.733	−	163.236i	−0.854179	−	0.493161i	−0.862059	+	0.506808i	$0.830825\pi$
$332$		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	0.450963	−	0.892543i	$-0.351081\pi$
$347$	502.945	−	290.375i	1.44941	−	0.836817i	0.998446	+	0.0557260i	$0.0177473\pi$
$348$		0			0
$349$	−175.463	+	303.912i	−0.502761	+	0.870807i	0.497234	+	0.867616i	$0.334349\pi$
$349$	−175.463	+	303.912i	−0.502761	+	0.870807i	−0.999995	+	0.00319067i	$0.998984\pi$
$350$		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	0.840117	−	0.542405i	$-0.182486\pi$
$373$	−18.5300	−	32.0949i	−0.0496783	−	0.0860454i	−0.889795	+	0.456360i	$0.849153\pi$
$374$		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	$0.247166\pi$
$379$			531.193i			1.40156i	−0.713375	+	0.700782i	$0.752834\pi$
$380$		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	$0.412674\pi$
$389$	−271.593	+	470.412i	−0.698182	+	1.20929i	−0.969096	+	0.246683i	$0.920659\pi$
$390$		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	$-0.223555\pi$
$397$	606.097			1.52669			0.763346	+	0.645990i	$0.223555\pi$
$398$		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	−0.811509	−	0.584340i	$-0.801353\pi$
$419$	−297.997	+	172.049i	−0.711210	+	0.410617i	0.100299	+	0.994957i	$0.468020\pi$
$420$		0			0
$421$	153.263	−	265.460i	0.364046	−	0.630546i	−0.624576	−	0.780964i	$-0.714728\pi$
$421$	153.263	−	265.460i	0.364046	−	0.630546i	0.988623	+	0.150417i	$0.0480617\pi$
$422$		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	0.728652	−	0.684884i	$-0.240147\pi$
$443$	221.434	+	127.845i	0.499851	+	0.288589i	−0.228801	+	0.973473i	$0.573480\pi$
$444$		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	$-0.538220\pi$
$461$	368.753	−	638.699i	0.799898	−	1.38546i	0.919682	−	0.392664i	$-0.128447\pi$
$462$		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	$0.219844\pi$
$467$			595.000i			1.27409i	−0.770827	+	0.637045i	$0.780156\pi$
$468$		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	−0.828668	−	0.559741i	$-0.810901\pi$
$491$	−372.302	+	214.949i	−0.758252	+	0.437777i	0.0704158	+	0.997518i	$0.477567\pi$
$492$		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	−0.976994	−	0.213268i	$-0.931589\pi$
$499$	−639.117	+	368.994i	−1.28080	+	0.739467i	−0.303802	+	0.952735i	$0.598256\pi$
$500$		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	0.826403	−	0.563079i	$-0.190384\pi$
$509$	−37.8898	−	65.6271i	−0.0744398	−	0.128933i	−0.900843	+	0.434146i	$0.857050\pi$
$510$		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	$-0.949332\pi$
$523$		−	165.798i		−	0.317013i	0.987358	−	0.158506i	$-0.0506678\pi$
$524$		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	$-0.554491\pi$
$541$	−184.323			−0.340708			−0.170354	+	0.985383i	$0.554491\pi$
$542$		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	−0.469272	−	0.883054i	$-0.655483\pi$
$547$	−803.354	−	463.817i	−1.46865	−	0.847928i	−0.999383	+	0.0351259i	$0.988817\pi$
$548$		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	$-0.354365\pi$
$557$	492.087			0.883459			0.441730	+	0.897148i	$0.354365\pi$
$558$		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	−0.939529	−	0.342470i	$-0.888736\pi$
$563$	−626.453	+	361.683i	−1.11271	+	0.642421i	−0.173177	+	0.984891i	$0.555403\pi$
$564$		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	−0.304071	−	0.952649i	$-0.598346\pi$
$571$	210.649	−	121.618i	0.368912	−	0.212991i	0.672983	+	0.739658i	$0.265013\pi$
$572$		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	−0.219178	−	0.975685i	$-0.570338\pi$
$587$	−688.983	−	397.784i	−1.17374	−	0.677656i	−0.954557	+	0.298029i	$0.903671\pi$
$588$		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	$-0.866718\pi$
$613$	−1120.09			−1.82722			−0.913610	+	0.406591i	$0.866718\pi$
$614$		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	−0.263537	−	0.964649i	$-0.584889\pi$
$619$	−761.814	−	439.833i	−1.23072	−	0.710555i	−0.967179	+	0.254095i	$0.918223\pi$
$620$		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	−0.200611	−	0.979671i	$-0.564293\pi$
$643$	352.044	−	203.253i	0.547503	−	0.316101i	0.748114	+	0.663570i	$0.230959\pi$
$644$		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	$-0.878414\pi$
$653$	−513.767	−	889.870i	−0.786779	−	1.36274i	0.141151	−	0.989988i	$-0.454920\pi$
$654$		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	0.515532	−	0.856870i	$-0.327594\pi$
$659$	20.5780	+	11.8807i	0.0312261	+	0.0180284i	−0.484306	+	0.874899i	$0.660928\pi$
$660$		0			0
$661$	328.164	+	568.396i	0.496465	+	0.859903i	0.999992	−	0.00407665i	$-0.00129764\pi$
$661$	328.164	+	568.396i	0.496465	+	0.859903i	−0.503526	+	0.863980i	$0.667964\pi$
$662$		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	−0.680138	−	0.733084i	$-0.738080\pi$
$677$	199.580	−	345.683i	0.294801	−	0.510610i	0.974939	+	0.222474i	$0.0714133\pi$
$678$		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	$0.0476238\pi$
$683$			203.612i			0.298114i	−0.988829	+	0.149057i	$0.952376\pi$
$684$		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	0.673443	−	0.739239i	$-0.264815\pi$
$691$	255.646	+	147.597i	0.369965	+	0.213599i	−0.303478	+	0.952838i	$0.598148\pi$
$692$		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	$-0.564713\pi$
$701$	−283.069			−0.403808			−0.201904	+	0.979405i	$0.564713\pi$
$702$		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	−0.975065	−	0.221920i	$-0.928768\pi$
$709$	−209.399	+	362.690i	−0.295344	+	0.511551i	0.679721	+	0.733471i	$0.262101\pi$
$710$		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	0.685468	−	0.728103i	$-0.259598\pi$
$733$	−210.973	−	365.416i	−0.287822	−	0.498522i	−0.973289	+	0.229581i	$0.926264\pi$
$734$		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	$0.0324044\pi$
$739$			150.203i			0.203251i	−0.994823	+	0.101626i	$0.967596\pi$
$740$		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	$-0.910986\pi$
$757$	−1455.19			−1.92231			−0.961153	+	0.276015i	$0.910986\pi$
$758$		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	$-0.281052\pi$
$773$	981.517			1.26975			0.634875	+	0.772615i	$0.281052\pi$
$774$		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	−0.836625	−	0.547776i	$-0.815474\pi$
$787$	−614.292	+	354.662i	−0.780549	+	0.450650i	0.0560758	+	0.998427i	$0.482141\pi$
$788$		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	$0.0997432\pi$
$797$	591.856	+	1025.12i	0.742605	+	1.28623i	−0.208701	+	0.977980i	$0.566924\pi$
$798$		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	$-0.977340\pi$
$811$		−	115.368i		−	0.142254i	0.997467	−	0.0711271i	$-0.0226596\pi$
$812$		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	$0.336689\pi$
$821$	−417.973	+	723.951i	−0.509102	+	0.881791i	−0.999944	+	0.0105427i	$0.996644\pi$
$822$		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	$0.279178\pi$
$827$			1271.70i			1.53773i	−0.639413	+	0.768864i	$0.720822\pi$
$828$		0			0
$829$	577.896			0.697100			0.348550	−	0.937290i	$-0.386674\pi$
$829$	577.896			0.697100			0.348550	+	0.937290i	$0.386674\pi$
$830$		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	$0.376585\pi$
$853$	−522.638	+	905.235i	−0.612705	+	1.06124i	−0.990782	+	0.135463i	$0.956748\pi$
$854$		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	−0.530967	−	0.847392i	$-0.678171\pi$
$859$	−53.7624	+	31.0397i	−0.0625871	+	0.0361347i	0.468380	+	0.883527i	$0.344838\pi$
$860$		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	0.799725	−	0.600367i	$-0.204979\pi$
$877$	−105.302	−	182.388i	−0.120071	−	0.207968i	−0.919795	+	0.392398i	$0.871645\pi$
$878$		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	$-0.951812\pi$
$883$		−	266.329i		−	0.301619i	0.988563	−	0.150809i	$-0.0481879\pi$
$884$		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	0.950448	−	0.310885i	$-0.100625\pi$
$907$	1048.89	+	605.576i	1.15644	+	0.667669i	0.205989	+	0.978554i	$0.433959\pi$
$908$		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	0.540086	−	0.841610i	$-0.318392\pi$
$941$	−431.742	−	747.800i	−0.458812	−	0.794686i	−0.998898	+	0.0469234i	$0.985058\pi$
$942$		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	0.922740	−	0.385423i	$-0.125945\pi$
$947$	994.656	+	574.265i	1.05032	+	0.606404i	0.127583	+	0.991828i	$0.459278\pi$
$948$		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	$0.0438666\pi$
$971$			266.782i			0.274750i	−0.990519	+	0.137375i	$0.956133\pi$
$972$		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	$-0.612572\pi$
$997$	637.348	−	1103.92i	0.639266	−	1.10724i	0.985594	−	0.169128i	$-0.0540950\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.3	✓	8	9.5	odd	6
144.3.o.a.79.3	yes	8	12.11	even	2
144.3.o.c.31.2	yes	8	36.23	even	6
144.3.o.c.79.2	yes	8	3.2	odd	2
432.3.o.a.127.1		8	1.1	even	1	trivial
432.3.o.a.415.1		8	36.31	odd	6	inner
432.3.o.b.127.1		8	4.3	odd	2
432.3.o.b.415.1		8	9.4	even	3
576.3.o.d.319.3		8	72.59	even	6
576.3.o.d.511.3		8	24.5	odd	2
576.3.o.f.319.2		8	72.5	odd	6
576.3.o.f.511.2		8	24.11	even	2
1296.3.g.j.1135.1		8	9.2	odd	6
1296.3.g.j.1135.2		8	36.11	even	6
1296.3.g.k.1135.7		8	9.7	even	3
1296.3.g.k.1135.8		8	36.7	odd	6
1728.3.o.e.127.4		8	8.5	even	2
1728.3.o.e.1279.4		8	72.67	odd	6
1728.3.o.f.127.4		8	8.3	odd	2
1728.3.o.f.1279.4		8	72.13	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.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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