LMFDB - Embedded newform 432.4.i.c.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,4,Mod(145,432)]

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([0, 0, 2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, 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:	$25.4888251225$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			145.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	432.145
Dual form			432.4.i.c.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.31386 - 4.00772i) q^{5} +(6.05842 + 10.4935i) q^{7} +O(q^{10})$	$q+(2.31386 - 4.00772i) q^{5} +(6.05842 + 10.4935i) q^{7} +(-5.01087 - 8.67909i) q^{11} +(24.2921 - 42.0752i) q^{13} -75.3505 q^{17} +116.052 q^{19} +(19.0367 - 32.9725i) q^{23} +(51.7921 + 89.7066i) q^{25} +(-11.3139 - 19.5962i) q^{29} +(15.0584 - 26.0820i) q^{31} +56.0733 q^{35} +130.103 q^{37} +(173.742 - 300.930i) q^{41} +(13.3832 + 23.1803i) q^{43} +(-230.439 - 399.132i) q^{47} +(98.0910 - 169.899i) q^{49} +438.310 q^{53} -46.3778 q^{55} +(-4.18487 + 7.24841i) q^{59} +(41.0448 + 71.0916i) q^{61} +(-112.417 - 194.712i) q^{65} +(341.785 - 591.989i) q^{67} +1097.61 q^{71} +470.464 q^{73} +(60.7160 - 105.163i) q^{77} +(243.017 + 420.919i) q^{79} +(-49.5829 - 85.8802i) q^{83} +(-174.351 + 301.984i) q^{85} -8.80426 q^{89} +588.687 q^{91} +(268.527 - 465.103i) q^{95} +(-330.486 - 572.419i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 15 q^{5} + 7 q^{7}+O(q^{10}) $ 4 * q + 15 * q^5 + 7 * q^7	$ 4 q + 15 q^{5} + 7 q^{7} - 66 q^{11} + 11 q^{13} - 198 q^{17} + 154 q^{19} - 33 q^{23} + 121 q^{25} - 51 q^{29} + 43 q^{31} + 6 q^{35} - 100 q^{37} + 132 q^{41} + 88 q^{43} - 399 q^{47} + 513 q^{49} - 108 q^{53} - 1254 q^{55} - 798 q^{59} - 439 q^{61} + 165 q^{65} + 988 q^{67} + 2736 q^{71} - 910 q^{73} - 165 q^{77} - 803 q^{79} - 813 q^{83} - 594 q^{85} + 792 q^{89} + 1562 q^{91} + 132 q^{95} - 736 q^{97}+O(q^{100}) $ 4 * q + 15 * q^5 + 7 * q^7 - 66 * q^11 + 11 * q^13 - 198 * q^17 + 154 * q^19 - 33 * q^23 + 121 * q^25 - 51 * q^29 + 43 * q^31 + 6 * q^35 - 100 * q^37 + 132 * q^41 + 88 * q^43 - 399 * q^47 + 513 * q^49 - 108 * q^53 - 1254 * q^55 - 798 * q^59 - 439 * q^61 + 165 * q^65 + 988 * q^67 + 2736 * q^71 - 910 * q^73 - 165 * q^77 - 803 * q^79 - 813 * q^83 - 594 * q^85 + 792 * q^89 + 1562 * q^91 + 132 * q^95 - 736 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.31386	−	4.00772i	0.206958	−	0.358462i	−0.743797	−	0.668406i	$-0.766977\pi$
$5$	2.31386	−	4.00772i	0.206958	−	0.358462i	0.950755	+	0.309944i	$0.100310\pi$
$6$		0			0
$7$	6.05842	+	10.4935i	0.327124	+	0.566595i	0.981940	−	0.189193i	$-0.0605872\pi$
$7$	6.05842	+	10.4935i	0.327124	+	0.566595i	−0.654816	+	0.755788i	$0.727254\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.01087	−	8.67909i	−0.137349	−	0.237895i	0.789144	−	0.614209i	$-0.210525\pi$
$11$	−5.01087	−	8.67909i	−0.137349	−	0.237895i	−0.926492	+	0.376314i	$0.877191\pi$
$12$		0			0
$13$	24.2921	−	42.0752i	0.518263	−	0.897658i	−0.481512	−	0.876440i	$-0.659912\pi$
$13$	24.2921	−	42.0752i	0.518263	−	0.897658i	0.999775	−	0.0212183i	$-0.00675450\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−75.3505			−1.07501			−0.537506	−	0.843260i	$-0.680633\pi$
$17$	−75.3505			−1.07501			−0.537506	+	0.843260i	$0.680633\pi$
$18$		0			0
$19$	116.052			1.40127			0.700633	−	0.713522i	$-0.252901\pi$
$19$	116.052			1.40127			0.700633	+	0.713522i	$0.252901\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	19.0367	−	32.9725i	0.172584	−	0.298923i	−0.766739	−	0.641959i	$-0.778122\pi$
$23$	19.0367	−	32.9725i	0.172584	−	0.298923i	0.939322	+	0.343036i	$0.111455\pi$
$24$		0			0
$25$	51.7921	+	89.7066i	0.414337	+	0.717653i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−11.3139	−	19.5962i	−0.0724459	−	0.125480i	0.827527	−	0.561426i	$-0.189747\pi$
$29$	−11.3139	−	19.5962i	−0.0724459	−	0.125480i	−0.899973	+	0.435946i	$0.856414\pi$
$30$		0			0
$31$	15.0584	−	26.0820i	0.0872443	−	0.151112i	−0.819101	−	0.573649i	$-0.805527\pi$
$31$	15.0584	−	26.0820i	0.0872443	−	0.151112i	0.906345	+	0.422538i	$0.138861\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	56.0733			0.270804
$36$		0			0
$37$	130.103			0.578077			0.289038	−	0.957318i	$-0.406665\pi$
$37$	130.103			0.578077			0.289038	+	0.957318i	$0.406665\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	173.742	−	300.930i	0.661803	−	1.14628i	−0.318339	−	0.947977i	$-0.603125\pi$
$41$	173.742	−	300.930i	0.661803	−	1.14628i	0.980142	−	0.198299i	$-0.0635417\pi$
$42$		0			0
$43$	13.3832	+	23.1803i	0.0474631	+	0.0822085i	0.888781	−	0.458332i	$-0.151553\pi$
$43$	13.3832	+	23.1803i	0.0474631	+	0.0822085i	−0.841318	+	0.540541i	$0.818220\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−230.439	−	399.132i	−0.715169	−	1.23871i	−0.962894	−	0.269879i	$-0.913016\pi$
$47$	−230.439	−	399.132i	−0.715169	−	1.23871i	0.247725	−	0.968830i	$-0.420317\pi$
$48$		0			0
$49$	98.0910	−	169.899i	0.285980	−	0.495331i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	438.310			1.13597			0.567985	−	0.823039i	$-0.307723\pi$
$53$	438.310			1.13597			0.567985	+	0.823039i	$0.307723\pi$
$54$		0			0
$55$	−46.3778			−0.113702
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.18487	+	7.24841i	−0.00923430	+	0.0159943i	−0.870606	−	0.491982i	$-0.836273\pi$
$59$	−4.18487	+	7.24841i	−0.00923430	+	0.0159943i	0.861371	+	0.507976i	$0.169606\pi$
$60$		0			0
$61$	41.0448	+	71.0916i	0.0861515	+	0.149219i	0.905881	−	0.423532i	$-0.139210\pi$
$61$	41.0448	+	71.0916i	0.0861515	+	0.149219i	−0.819730	+	0.572750i	$0.805876\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−112.417	−	194.712i	−0.214517	−	0.371555i
$66$		0			0
$67$	341.785	−	591.989i	0.623220	−	1.07945i	−0.365663	−	0.930747i	$-0.619158\pi$
$67$	341.785	−	591.989i	0.623220	−	1.07945i	0.988882	−	0.148701i	$-0.0475091\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1097.61			1.83468			0.917339	−	0.398107i	$-0.130333\pi$
$71$	1097.61			1.83468			0.917339	+	0.398107i	$0.130333\pi$
$72$		0			0
$73$	470.464			0.754297			0.377149	−	0.926153i	$-0.376905\pi$
$73$	470.464			0.754297			0.377149	+	0.926153i	$0.376905\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	60.7160	−	105.163i	0.0898601	−	0.155642i
$78$		0			0
$79$	243.017	+	420.919i	0.346096	+	0.599456i	0.985552	−	0.169371i	$-0.0541737\pi$
$79$	243.017	+	420.919i	0.346096	+	0.599456i	−0.639456	+	0.768828i	$0.720840\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−49.5829	−	85.8802i	−0.0655715	−	0.113573i	0.831376	−	0.555711i	$-0.187554\pi$
$83$	−49.5829	−	85.8802i	−0.0655715	−	0.113573i	−0.896947	+	0.442137i	$0.854220\pi$
$84$		0			0
$85$	−174.351	+	301.984i	−0.222482	+	0.385350i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.80426			−0.0104859			−0.00524297	−	0.999986i	$-0.501669\pi$
$89$	−8.80426			−0.0104859			−0.00524297	+	0.999986i	$0.501669\pi$
$90$		0			0
$91$	588.687			0.678145
$92$		0			0
$93$		0			0
$94$		0			0
$95$	268.527	−	465.103i	0.290003	−	0.502300i
$96$		0			0
$97$	−330.486	−	572.419i	−0.345936	−	0.599179i	0.639587	−	0.768719i	$-0.279105\pi$
$97$	−330.486	−	572.419i	−0.345936	−	0.599179i	−0.985523	+	0.169540i	$0.945772\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−282.561	−	489.410i	−0.278375	−	0.482160i	0.692606	−	0.721316i	$-0.256463\pi$
$101$	−282.561	−	489.410i	−0.278375	−	0.482160i	−0.970981	+	0.239156i	$0.923129\pi$
$102$		0			0
$103$	−485.591	+	841.068i	−0.464531	+	0.804592i	−0.999180	−	0.0404826i	$-0.987110\pi$
$103$	−485.591	+	841.068i	−0.464531	+	0.804592i	0.534649	+	0.845074i	$0.320444\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−563.845			−0.509430			−0.254715	−	0.967016i	$-0.581982\pi$
$107$	−563.845			−0.509430			−0.254715	+	0.967016i	$0.581982\pi$
$108$		0			0
$109$	225.484			0.198142			0.0990709	−	0.995080i	$-0.468413\pi$
$109$	225.484			0.198142			0.0990709	+	0.995080i	$0.468413\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−345.531	+	598.478i	−0.287654	+	0.498231i	−0.973249	−	0.229752i	$-0.926209\pi$
$113$	−345.531	+	598.478i	−0.287654	+	0.498231i	0.685596	+	0.727983i	$0.259542\pi$
$114$		0			0
$115$	−88.0964	−	152.587i	−0.0714350	−	0.123729i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−456.505	−	790.690i	−0.351662	−	0.609096i
$120$		0			0
$121$	615.282	−	1065.70i	0.462271	−	0.800676i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1057.82			0.756917
$126$		0			0
$127$	895.897			0.625968			0.312984	−	0.949758i	$-0.398671\pi$
$127$	895.897			0.625968			0.312984	+	0.949758i	$0.398671\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−827.428	+	1433.15i	−0.551853	+	0.955837i	0.446288	+	0.894889i	$0.352746\pi$
$131$	−827.428	+	1433.15i	−0.551853	+	0.955837i	−0.998141	+	0.0609476i	$0.980588\pi$
$132$		0			0
$133$	703.090	+	1217.79i	0.458388	+	0.793951i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1325.55	−	2295.91i	−0.826635	−	1.43177i	−0.900663	−	0.434518i	$-0.856919\pi$
$137$	−1325.55	−	2295.91i	−0.826635	−	1.43177i	0.0740277	−	0.997256i	$-0.476415\pi$
$138$		0			0
$139$	317.084	−	549.206i	0.193487	−	0.335130i	−0.752916	−	0.658116i	$-0.771354\pi$
$139$	317.084	−	549.206i	0.193487	−	0.335130i	0.946404	+	0.322986i	$0.104687\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−486.899			−0.284731
$144$		0			0
$145$	−104.715			−0.0599730
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1703.16	+	2949.96i	−0.936432	+	1.62195i	−0.164372	+	0.986398i	$0.552560\pi$
$149$	−1703.16	+	2949.96i	−0.936432	+	1.62195i	−0.772060	+	0.635550i	$0.780773\pi$
$150$		0			0
$151$	−875.159	−	1515.82i	−0.471652	−	0.816925i	0.527822	−	0.849355i	$-0.323009\pi$
$151$	−875.159	−	1515.82i	−0.471652	−	0.816925i	−0.999474	+	0.0324302i	$0.989675\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−69.6861	−	120.700i	−0.0361118	−	0.0625474i
$156$		0			0
$157$	−1089.29	+	1886.70i	−0.553723	+	0.959076i	0.444279	+	0.895889i	$0.353460\pi$
$157$	−1089.29	+	1886.70i	−0.553723	+	0.959076i	−0.998002	+	0.0631876i	$0.979873\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	461.329			0.225825
$162$		0			0
$163$	−2188.41			−1.05159			−0.525797	−	0.850610i	$-0.676233\pi$
$163$	−2188.41			−1.05159			−0.525797	+	0.850610i	$0.676233\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−960.520	+	1663.67i	−0.445074	+	0.770890i	−0.998057	−	0.0623020i	$-0.980156\pi$
$167$	−960.520	+	1663.67i	−0.445074	+	0.770890i	0.552984	+	0.833192i	$0.313489\pi$
$168$		0			0
$169$	−81.7132	−	141.531i	−0.0371931	−	0.0644203i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1584.91	+	2745.15i	0.696525	+	1.20642i	0.969664	+	0.244442i	$0.0786047\pi$
$173$	1584.91	+	2745.15i	0.696525	+	1.20642i	−0.273139	+	0.961974i	$0.588062\pi$
$174$		0			0
$175$	−627.557	+	1086.96i	−0.271079	+	0.469523i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1368.78			0.571551			0.285776	−	0.958297i	$-0.407749\pi$
$179$	1368.78			0.571551			0.285776	+	0.958297i	$0.407749\pi$
$180$		0			0
$181$	−3951.44			−1.62270			−0.811350	−	0.584561i	$-0.801267\pi$
$181$	−3951.44			−1.62270			−0.811350	+	0.584561i	$0.801267\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	301.040	−	521.417i	0.119637	−	0.207218i
$186$		0			0
$187$	377.572	+	653.974i	0.147651	+	0.255740i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1201.29	+	2080.70i	0.455092	+	0.788243i	0.998693	−	0.0511008i	$-0.0162730\pi$
$191$	1201.29	+	2080.70i	0.455092	+	0.788243i	−0.543601	+	0.839344i	$0.682940\pi$
$192$		0			0
$193$	667.535	−	1156.20i	0.248965	−	0.431220i	−0.714274	−	0.699866i	$-0.753243\pi$
$193$	667.535	−	1156.20i	0.248965	−	0.431220i	0.963239	+	0.268646i	$0.0865763\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2630.89			0.951487			0.475743	−	0.879584i	$-0.342179\pi$
$197$	2630.89			0.951487			0.475743	+	0.879584i	$0.342179\pi$
$198$		0			0
$199$	−2477.34			−0.882483			−0.441241	−	0.897388i	$-0.645462\pi$
$199$	−2477.34			−0.882483			−0.441241	+	0.897388i	$0.645462\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	137.088	−	237.444i	0.0473976	−	0.0820950i
$204$		0			0
$205$	−804.028	−	1392.62i	−0.273931	−	0.474462i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−581.520	−	1007.22i	−0.192462	−	0.333354i
$210$		0			0
$211$	−1392.36	+	2411.65i	−0.454286	+	0.786847i	−0.998647	−	0.0520047i	$-0.983439\pi$
$211$	−1392.36	+	2411.65i	−0.454286	+	0.786847i	0.544361	+	0.838851i	$0.316772\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	123.867			0.0392914
$216$		0			0
$217$	364.921			0.114159
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1830.42	+	3170.39i	−0.557138	+	0.964992i
$222$		0			0
$223$	−21.5288	−	37.2890i	−0.00646491	−	0.0111976i	0.862775	−	0.505588i	$-0.168725\pi$
$223$	−21.5288	−	37.2890i	−0.00646491	−	0.0111976i	−0.869240	+	0.494391i	$0.835391\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−341.630	−	591.721i	−0.0998889	−	0.173013i	0.811750	−	0.584006i	$-0.198515\pi$
$227$	−341.630	−	591.721i	−0.0998889	−	0.173013i	−0.911639	+	0.410993i	$0.865182\pi$
$228$		0			0
$229$	−2147.15	+	3718.98i	−0.619598	+	1.07317i	0.369962	+	0.929047i	$0.379371\pi$
$229$	−2147.15	+	3718.98i	−0.619598	+	1.07317i	−0.989559	+	0.144127i	$0.953962\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3466.34			−0.974625			−0.487313	−	0.873228i	$-0.662023\pi$
$233$	−3466.34			−0.974625			−0.487313	+	0.873228i	$0.662023\pi$
$234$		0			0
$235$	−2132.81			−0.592040
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2821.69	+	4887.30i	−0.763681	+	1.32273i	0.177261	+	0.984164i	$0.443276\pi$
$239$	−2821.69	+	4887.30i	−0.763681	+	1.32273i	−0.940941	+	0.338570i	$0.890057\pi$
$240$		0			0
$241$	−3294.71	−	5706.61i	−0.880627	−	1.52529i	−0.850645	−	0.525741i	$-0.823788\pi$
$241$	−3294.71	−	5706.61i	−0.880627	−	1.52529i	−0.0299825	−	0.999550i	$-0.509545\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−453.938	−	786.243i	−0.118372	−	0.205025i
$246$		0			0
$247$	2819.14	−	4882.89i	0.726225	−	1.25786i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4135.47			1.03996			0.519978	−	0.854180i	$-0.325940\pi$
$251$	4135.47			1.03996			0.519978	+	0.854180i	$0.325940\pi$
$252$		0			0
$253$	−381.562			−0.0948165
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1672.31	+	2896.53i	−0.405898	+	0.703036i	−0.994426	−	0.105441i	$-0.966375\pi$
$257$	−1672.31	+	2896.53i	−0.405898	+	0.703036i	0.588527	+	0.808477i	$0.299708\pi$
$258$		0			0
$259$	788.220	+	1365.24i	0.189103	+	0.327536i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3260.75	−	5647.78i	−0.764511	−	1.32417i	−0.940505	−	0.339780i	$-0.889647\pi$
$263$	−3260.75	−	5647.78i	−0.764511	−	1.32417i	0.175994	−	0.984391i	$-0.443686\pi$
$264$		0			0
$265$	1014.19	−	1756.62i	0.235098	−	0.407202i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2904.99			0.658441			0.329220	−	0.944253i	$-0.393214\pi$
$269$	2904.99			0.658441			0.329220	+	0.944253i	$0.393214\pi$
$270$		0			0
$271$	1335.38			0.299331			0.149665	−	0.988737i	$-0.452180\pi$
$271$	1335.38			0.299331			0.149665	+	0.988737i	$0.452180\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	519.048	−	899.017i	0.113817	−	0.197137i
$276$		0			0
$277$	4187.82	+	7253.51i	0.908381	+	1.57336i	0.816313	+	0.577610i	$0.196015\pi$
$277$	4187.82	+	7253.51i	0.908381	+	1.57336i	0.0920685	+	0.995753i	$0.470652\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2589.67	−	4485.43i	−0.549774	−	0.952237i	−0.998290	−	0.0584616i	$-0.981380\pi$
$281$	−2589.67	−	4485.43i	−0.549774	−	0.952237i	0.448516	−	0.893775i	$-0.351953\pi$
$282$		0			0
$283$	−1540.03	+	2667.42i	−0.323482	+	0.560288i	−0.981204	−	0.192973i	$-0.938187\pi$
$283$	−1540.03	+	2667.42i	−0.323482	+	0.560288i	0.657722	+	0.753261i	$0.271520\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4210.40			0.865966
$288$		0			0
$289$	764.703			0.155649
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1824.45	−	3160.04i	0.363773	−	0.630073i	−0.624806	−	0.780780i	$-0.714822\pi$
$293$	1824.45	−	3160.04i	0.363773	−	0.630073i	0.988578	+	0.150708i	$0.0481552\pi$
$294$		0			0
$295$	19.3664	+	33.5436i	0.00382222	+	0.00662028i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−924.882	−	1601.94i	−0.178887	−	0.309842i
$300$		0			0
$301$	−162.162	+	280.872i	−0.0310526	+	0.0537847i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	379.887			0.0713190
$306$		0			0
$307$	3439.25			0.639376			0.319688	−	0.947523i	$-0.396422\pi$
$307$	3439.25			0.639376			0.319688	+	0.947523i	$0.396422\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3587.66	+	6214.02i	−0.654141	+	1.13301i	0.327968	+	0.944689i	$0.393636\pi$
$311$	−3587.66	+	6214.02i	−0.654141	+	1.13301i	−0.982108	+	0.188316i	$0.939697\pi$
$312$		0			0
$313$	2428.65	+	4206.54i	0.438579	+	0.759642i	0.997580	−	0.0695253i	$-0.0221485\pi$
$313$	2428.65	+	4206.54i	0.438579	+	0.759642i	−0.559001	+	0.829167i	$0.688815\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3773.97	+	6536.70i	0.668666	+	1.15816i	0.978277	+	0.207300i	$0.0664677\pi$
$317$	3773.97	+	6536.70i	0.668666	+	1.15816i	−0.309611	+	0.950863i	$0.600199\pi$
$318$		0			0
$319$	−113.385	+	196.388i	−0.0199007	+	0.0344690i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8744.55			−1.50638
$324$		0			0
$325$	5032.56			0.858942
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2792.19	−	4836.22i	0.467898	−	0.810423i
$330$		0			0
$331$	−1564.86	−	2710.41i	−0.259856	−	0.450084i	0.706347	−	0.707866i	$-0.250342\pi$
$331$	−1564.86	−	2710.41i	−0.259856	−	0.450084i	−0.966203	+	0.257782i	$0.917008\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1581.69	−	2739.56i	−0.257960	−	0.446801i
$336$		0			0
$337$	4614.99	−	7993.39i	0.745978	−	1.29207i	−0.203759	−	0.979021i	$-0.565316\pi$
$337$	4614.99	−	7993.39i	0.745978	−	1.29207i	0.949737	−	0.313050i	$-0.101351\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−301.823			−0.0479315
$342$		0			0
$343$	6533.19			1.02845
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4052.20	−	7018.61i	0.626897	−	1.08582i	−0.361273	−	0.932460i	$-0.617658\pi$
$347$	4052.20	−	7018.61i	0.626897	−	1.08582i	0.988171	−	0.153358i	$-0.0490088\pi$
$348$		0			0
$349$	−1538.21	−	2664.26i	−0.235927	−	0.408638i	0.723615	−	0.690204i	$-0.242479\pi$
$349$	−1538.21	−	2664.26i	−0.235927	−	0.408638i	−0.959542	+	0.281566i	$0.909146\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3075.04	−	5326.13i	−0.463649	−	0.803063i	0.535491	−	0.844541i	$-0.320127\pi$
$353$	−3075.04	−	5326.13i	−0.463649	−	0.803063i	−0.999139	+	0.0414780i	$0.986793\pi$
$354$		0			0
$355$	2539.71	−	4398.91i	0.379701	−	0.657662i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3307.94			0.486313			0.243156	−	0.969987i	$-0.421817\pi$
$359$	3307.94			0.486313			0.243156	+	0.969987i	$0.421817\pi$
$360$		0			0
$361$	6608.97			0.963548
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1088.59	−	1885.49i	0.156108	−	0.270387i
$366$		0			0
$367$	1474.65	+	2554.16i	0.209744	+	0.363287i	0.951634	−	0.307235i	$-0.0994037\pi$
$367$	1474.65	+	2554.16i	0.209744	+	0.363287i	−0.741890	+	0.670522i	$0.766070\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2655.46	+	4599.40i	0.371603	+	0.643636i
$372$		0			0
$373$	−581.790	+	1007.69i	−0.0807612	+	0.139883i	−0.903577	−	0.428425i	$-0.859068\pi$
$373$	−581.790	+	1007.69i	−0.0807612	+	0.139883i	0.822816	+	0.568308i	$0.192402\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1099.35			−0.150184
$378$		0			0
$379$	4016.67			0.544387			0.272193	−	0.962243i	$-0.412251\pi$
$379$	4016.67			0.544387			0.272193	+	0.962243i	$0.412251\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5401.65	−	9355.93i	0.720656	−	1.24821i	−0.240081	−	0.970753i	$-0.577174\pi$
$383$	5401.65	−	9355.93i	0.720656	−	1.24821i	0.960737	−	0.277460i	$-0.0894926\pi$
$384$		0			0
$385$	−280.977	−	486.666i	−0.0371945	−	0.0644228i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1032.29	+	1787.99i	0.134549	+	0.233045i	0.925425	−	0.378931i	$-0.123708\pi$
$389$	1032.29	+	1787.99i	0.134549	+	0.233045i	−0.790876	+	0.611976i	$0.790375\pi$
$390$		0			0
$391$	−1434.42	+	2484.49i	−0.185529	+	0.321346i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2249.23			0.286509
$396$		0			0
$397$	−7937.61			−1.00347			−0.501735	−	0.865022i	$-0.667305\pi$
$397$	−7937.61			−1.00347			−0.501735	+	0.865022i	$0.667305\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1289.10	−	2232.79i	0.160536	−	0.278056i	−0.774525	−	0.632543i	$-0.782011\pi$
$401$	1289.10	−	2232.79i	0.160536	−	0.278056i	0.935061	+	0.354487i	$0.115344\pi$
$402$		0			0
$403$	−731.602	−	1267.17i	−0.0904310	−	0.156631i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−651.931	−	1129.18i	−0.0793981	−	0.137521i
$408$		0			0
$409$	−2922.88	+	5062.57i	−0.353367	+	0.612049i	−0.986837	−	0.161718i	$-0.948297\pi$
$409$	−2922.88	+	5062.57i	−0.353367	+	0.612049i	0.633470	+	0.773767i	$0.281630\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−101.415			−0.0120830
$414$		0			0
$415$	−458.912			−0.0542822
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4370.66	−	7570.20i	0.509596	−	0.882646i	−0.490343	−	0.871530i	$-0.663128\pi$
$419$	4370.66	−	7570.20i	0.509596	−	0.882646i	0.999938	−	0.0111158i	$-0.00353834\pi$
$420$		0			0
$421$	−528.254	−	914.963i	−0.0611533	−	0.105921i	0.833828	−	0.552024i	$-0.186145\pi$
$421$	−528.254	−	914.963i	−0.0611533	−	0.105921i	−0.894981	+	0.446104i	$0.852811\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3902.56	−	6759.44i	−0.445417	−	0.771484i
$426$		0			0
$427$	−497.333	+	861.406i	−0.0563645	+	0.0976261i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9868.64			1.10291			0.551457	−	0.834203i	$-0.314072\pi$
$431$	9868.64			1.10291			0.551457	+	0.834203i	$0.314072\pi$
$432$		0			0
$433$	477.948			0.0530456			0.0265228	−	0.999648i	$-0.491557\pi$
$433$	477.948			0.0530456			0.0265228	+	0.999648i	$0.491557\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2209.24	−	3826.51i	0.241835	−	0.418871i
$438$		0			0
$439$	−526.239	−	911.473i	−0.0572119	−	0.0990939i	0.836001	−	0.548728i	$-0.184888\pi$
$439$	−526.239	−	911.473i	−0.0572119	−	0.0990939i	−0.893213	+	0.449634i	$0.851554\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5249.35	+	9092.14i	0.562989	+	0.975126i	0.997234	+	0.0743307i	$0.0236820\pi$
$443$	5249.35	+	9092.14i	0.562989	+	0.975126i	−0.434245	+	0.900795i	$0.642985\pi$
$444$		0			0
$445$	−20.3718	+	35.2850i	−0.00217015	+	0.00375881i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7329.40			0.770369			0.385184	−	0.922840i	$-0.374138\pi$
$449$	7329.40			0.770369			0.385184	+	0.922840i	$0.374138\pi$
$450$		0			0
$451$	−3482.39			−0.363591
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1362.14	−	2359.30i	0.140347	−	0.243089i
$456$		0			0
$457$	−3572.20	−	6187.23i	−0.365646	−	0.633318i	0.623233	−	0.782036i	$-0.285819\pi$
$457$	−3572.20	−	6187.23i	−0.365646	−	0.633318i	−0.988880	+	0.148718i	$0.952485\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2859.34	+	4952.53i	0.288878	+	0.500352i	0.973542	−	0.228507i	$-0.0733843\pi$
$461$	2859.34	+	4952.53i	0.288878	+	0.500352i	−0.684664	+	0.728859i	$0.740051\pi$
$462$		0			0
$463$	394.233	−	682.831i	0.0395714	−	0.0685397i	−0.845561	−	0.533878i	$-0.820734\pi$
$463$	394.233	−	682.831i	0.0395714	−	0.0685397i	0.885133	+	0.465339i	$0.154067\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17068.0			−1.69125			−0.845626	−	0.533776i	$-0.820772\pi$
$467$	−17068.0			−1.69125			−0.845626	+	0.533776i	$0.820772\pi$
$468$		0			0
$469$	8282.72			0.815481
$470$		0			0
$471$		0			0
$472$		0			0
$473$	134.123	−	232.307i	0.0130380	−	0.0225824i
$474$		0			0
$475$	6010.56	+	10410.6i	0.580596	+	1.00562i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−758.994	−	1314.62i	−0.0723994	−	0.125399i	0.827553	−	0.561388i	$-0.189732\pi$
$479$	−758.994	−	1314.62i	−0.0723994	−	0.125399i	−0.899952	+	0.435988i	$0.856399\pi$
$480$		0			0
$481$	3160.48	−	5474.11i	0.299596	−	0.518915i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3058.80			−0.286377
$486$		0			0
$487$	−12737.3			−1.18518			−0.592591	−	0.805503i	$-0.701895\pi$
$487$	−12737.3			−1.18518			−0.592591	+	0.805503i	$0.701895\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2823.85	+	4891.05i	−0.259549	+	0.449552i	−0.966121	−	0.258089i	$-0.916907\pi$
$491$	−2823.85	+	4891.05i	−0.259549	+	0.449552i	0.706572	+	0.707641i	$0.250241\pi$
$492$		0			0
$493$	852.505	+	1476.58i	0.0778801	+	0.134892i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6649.78	+	11517.7i	0.600167	+	1.03952i
$498$		0			0
$499$	5423.14	−	9393.15i	0.486519	−	0.842676i	−0.513361	−	0.858173i	$-0.671600\pi$
$499$	5423.14	−	9393.15i	0.486519	−	0.842676i	0.999880	+	0.0154970i	$0.00493306\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12345.7			−1.09437			−0.547186	−	0.837011i	$-0.684301\pi$
$503$	−12345.7			−1.09437			−0.547186	+	0.837011i	$0.684301\pi$
$504$		0			0
$505$	−2615.23			−0.230448
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2947.87	+	5105.87i	−0.256704	+	0.444624i	−0.965357	−	0.260933i	$-0.915970\pi$
$509$	−2947.87	+	5105.87i	−0.256704	+	0.444624i	0.708653	+	0.705557i	$0.249303\pi$
$510$		0			0
$511$	2850.27	+	4936.82i	0.246749	+	0.427381i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2247.18	+	3892.23i	0.192277	+	0.333033i
$516$		0			0
$517$	−2309.40	+	4000.00i	−0.196455	+	0.340270i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5211.51			−0.438235			−0.219118	−	0.975698i	$-0.570318\pi$
$521$	−5211.51			−0.438235			−0.219118	+	0.975698i	$0.570318\pi$
$522$		0			0
$523$	9809.86			0.820182			0.410091	−	0.912045i	$-0.365497\pi$
$523$	9809.86			0.820182			0.410091	+	0.912045i	$0.365497\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1134.66	+	1965.29i	−0.0937886	+	0.162447i
$528$		0			0
$529$	5358.71	+	9281.56i	0.440430	+	0.762847i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8441.11	−	14620.4i	−0.685976	−	1.18814i
$534$		0			0
$535$	−1304.66	+	2259.73i	−0.105430	+	0.182611i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1966.09			−0.157116
$540$		0			0
$541$	8084.25			0.642456			0.321228	−	0.947002i	$-0.395904\pi$
$541$	8084.25			0.642456			0.321228	+	0.947002i	$0.395904\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	521.738	−	903.677i	0.0410070	−	0.0710262i
$546$		0			0
$547$	−12033.6	−	20842.7i	−0.940617	−	1.62920i	−0.764298	−	0.644863i	$-0.776914\pi$
$547$	−12033.6	−	20842.7i	−0.940617	−	1.62920i	−0.176319	−	0.984333i	$-0.556419\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1312.99	−	2274.17i	−0.101516	−	0.175831i
$552$		0			0
$553$	−2944.60	+	5100.20i	−0.226433	+	0.392193i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4582.37			−0.348584			−0.174292	−	0.984694i	$-0.555764\pi$
$557$	−4582.37			−0.348584			−0.174292	+	0.984694i	$0.555764\pi$
$558$		0			0
$559$	1300.42			0.0983934
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1547.66	−	2680.62i	0.115854	−	0.200666i	−0.802267	−	0.596966i	$-0.796373\pi$
$563$	1547.66	−	2680.62i	0.115854	−	0.200666i	0.918121	+	0.396300i	$0.129706\pi$
$564$		0			0
$565$	1599.02	+	2769.59i	0.119064	+	0.206226i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10282.5	+	17809.9i	0.757586	+	1.31218i	0.944078	+	0.329721i	$0.106955\pi$
$569$	10282.5	+	17809.9i	0.757586	+	1.31218i	−0.186492	+	0.982456i	$0.559712\pi$
$570$		0			0
$571$	−584.992	+	1013.24i	−0.0428742	+	0.0742602i	−0.886666	−	0.462410i	$-0.846985\pi$
$571$	−584.992	+	1013.24i	−0.0428742	+	0.0742602i	0.843792	+	0.536670i	$0.180318\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3943.80			0.286031
$576$		0			0
$577$	−13073.0			−0.943214			−0.471607	−	0.881809i	$-0.656326\pi$
$577$	−13073.0			−0.943214			−0.471607	+	0.881809i	$0.656326\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	600.789	−	1040.60i	0.0429000	−	0.0743050i
$582$		0			0
$583$	−2196.31	−	3804.13i	−0.156024	−	0.270242i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7273.91	+	12598.8i	0.511459	+	0.885873i	0.999912	+	0.0132825i	$0.00422807\pi$
$587$	7273.91	+	12598.8i	0.511459	+	0.885873i	−0.488453	+	0.872590i	$0.662439\pi$
$588$		0			0
$589$	1747.55	−	3026.85i	0.122252	−	0.211747i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19018.0			−1.31699			−0.658494	−	0.752586i	$-0.728806\pi$
$593$	−19018.0			−1.31699			−0.658494	+	0.752586i	$0.728806\pi$
$594$		0			0
$595$	−4225.16			−0.291117
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5587.20	+	9677.32i	−0.381113	+	0.660108i	−0.991222	−	0.132210i	$-0.957793\pi$
$599$	−5587.20	+	9677.32i	−0.381113	+	0.660108i	0.610108	+	0.792318i	$0.291126\pi$
$600$		0			0
$601$	−2294.27	−	3973.79i	−0.155716	−	0.269708i	0.777604	−	0.628755i	$-0.216435\pi$
$601$	−2294.27	−	3973.79i	−0.155716	−	0.269708i	−0.933319	+	0.359047i	$0.883102\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2847.35	−	4931.76i	−0.191341	−	0.331413i
$606$		0			0
$607$	−5744.99	+	9950.61i	−0.384155	+	0.665375i	−0.991652	−	0.128947i	$-0.958840\pi$
$607$	−5744.99	+	9950.61i	−0.384155	+	0.665375i	0.607497	+	0.794322i	$0.292174\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−22391.4			−1.48258
$612$		0			0
$613$	−22966.9			−1.51326			−0.756628	−	0.653846i	$-0.773154\pi$
$613$	−22966.9			−1.51326			−0.756628	+	0.653846i	$0.773154\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4248.31	+	7358.29i	−0.277197	+	0.480120i	−0.970687	−	0.240347i	$-0.922739\pi$
$617$	−4248.31	+	7358.29i	−0.277197	+	0.480120i	0.693490	+	0.720466i	$0.256072\pi$
$618$		0			0
$619$	7169.94	+	12418.7i	0.465564	+	0.806381i	0.999227	−	0.0393163i	$-0.0125180\pi$
$619$	7169.94	+	12418.7i	0.465564	+	0.806381i	−0.533662	+	0.845698i	$0.679185\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−53.3399	−	92.3874i	−0.00343021	−	0.00594129i
$624$		0			0
$625$	−4026.36	+	6973.86i	−0.257687	+	0.446327i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9803.34			−0.621439
$630$		0			0
$631$	−17834.3			−1.12516			−0.562578	−	0.826744i	$-0.690190\pi$
$631$	−17834.3			−1.12516			−0.562578	+	0.826744i	$0.690190\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2072.98	−	3590.51i	0.129549	−	0.224386i
$636$		0			0
$637$	−4765.68	−	8254.39i	−0.296425	−	0.513424i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13173.0	+	22816.3i	0.811705	+	1.40591i	0.911670	+	0.410923i	$0.134793\pi$
$641$	13173.0	+	22816.3i	0.811705	+	1.40591i	−0.0999654	+	0.994991i	$0.531873\pi$
$642$		0			0
$643$	−10782.5	+	18675.9i	−0.661309	+	1.14542i	0.318963	+	0.947767i	$0.396665\pi$
$643$	−10782.5	+	18675.9i	−0.661309	+	1.14542i	−0.980272	+	0.197653i	$0.936668\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4186.32			0.254376			0.127188	−	0.991879i	$-0.459405\pi$
$647$	4186.32			0.254376			0.127188	+	0.991879i	$0.459405\pi$
$648$		0			0
$649$	83.8794			0.00507328
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1402.57	−	2429.33i	0.0840534	−	0.145585i	−0.820934	−	0.571023i	$-0.806547\pi$
$653$	1402.57	−	2429.33i	0.0840534	−	0.145585i	0.904987	+	0.425438i	$0.139880\pi$
$654$		0			0
$655$	3829.10	+	6632.20i	0.228420	+	0.395636i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9536.15	+	16517.1i	0.563696	+	0.976350i	0.997170	+	0.0751839i	$0.0239544\pi$
$659$	9536.15	+	16517.1i	0.563696	+	0.976350i	−0.433474	+	0.901166i	$0.642712\pi$
$660$		0			0
$661$	12256.5	−	21228.9i	0.721216	−	1.24918i	−0.239296	−	0.970947i	$-0.576917\pi$
$661$	12256.5	−	21228.9i	0.721216	−	1.24918i	0.960513	−	0.278237i	$-0.0897500\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6507.40			0.379468
$666$		0			0
$667$	−861.513			−0.0500119
$668$		0			0
$669$		0			0
$670$		0			0
$671$	411.340	−	712.462i	0.0236656	−	0.0409900i
$672$		0			0
$673$	1773.32	+	3071.49i	0.101570	+	0.175924i	0.912332	−	0.409452i	$-0.134280\pi$
$673$	1773.32	+	3071.49i	0.101570	+	0.175924i	−0.810762	+	0.585376i	$0.800947\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8937.50	+	15480.2i	0.507380	+	0.878807i	0.999964	+	0.00854232i	$0.00271914\pi$
$677$	8937.50	+	15480.2i	0.507380	+	0.878807i	−0.492584	+	0.870265i	$0.663948\pi$
$678$		0			0
$679$	4004.45	−	6935.91i	0.226328	−	0.392012i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2857.23			0.160072			0.0800358	−	0.996792i	$-0.474497\pi$
$683$	2857.23			0.160072			0.0800358	+	0.996792i	$0.474497\pi$
$684$		0			0
$685$	−12268.5			−0.684315
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10647.5	−	18441.9i	0.588732	−	1.01971i
$690$		0			0
$691$	−7813.79	−	13533.9i	−0.430175	−	0.745084i	0.566714	−	0.823915i	$-0.308215\pi$
$691$	−7813.79	−	13533.9i	−0.430175	−	0.745084i	−0.996888	+	0.0788308i	$0.974881\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1467.38	−	2541.57i	−0.0800874	−	0.138716i
$696$		0			0
$697$	−13091.5	+	22675.2i	−0.711445	+	1.23226i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−17562.6			−0.946264			−0.473132	−	0.880992i	$-0.656877\pi$
$701$	−17562.6			−0.946264			−0.473132	+	0.880992i	$0.656877\pi$
$702$		0			0
$703$	15098.7			0.810039
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3423.75	−	5930.11i	0.182126	−	0.315452i
$708$		0			0
$709$	−10001.8	−	17323.6i	−0.529795	−	0.917632i	−0.999396	−	0.0347532i	$-0.988935\pi$
$709$	−10001.8	−	17323.6i	−0.529795	−	0.917632i	0.469601	−	0.882879i	$-0.344398\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−573.324	−	993.027i	−0.0301138	−	0.0521587i
$714$		0			0
$715$	−1126.62	+	1951.36i	−0.0589273	+	0.102065i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	25504.1			1.32287			0.661435	−	0.750002i	$-0.269948\pi$
$719$	25504.1			1.32287			0.661435	+	0.750002i	$0.269948\pi$
$720$		0			0
$721$	−11767.7			−0.607837
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1171.94	−	2029.85i	0.0600340	−	0.103982i
$726$		0			0
$727$	−11954.9	−	20706.5i	−0.609879	−	1.05634i	−0.991260	−	0.131924i	$-0.957885\pi$
$727$	−11954.9	−	20706.5i	−0.609879	−	1.05634i	0.381380	−	0.924418i	$-0.375449\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1008.43	−	1746.65i	−0.0510233	−	0.0883750i
$732$		0			0
$733$	4252.77	−	7366.02i	0.214297	−	0.371173i	−0.738758	−	0.673971i	$-0.764587\pi$
$733$	4252.77	−	7366.02i	0.214297	−	0.371173i	0.953055	+	0.302798i	$0.0979206\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6850.57			−0.342394
$738$		0			0
$739$	−25802.5			−1.28438			−0.642192	−	0.766544i	$-0.721975\pi$
$739$	−25802.5			−1.28438			−0.642192	+	0.766544i	$0.721975\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13668.8	+	23675.0i	−0.674911	+	1.16898i	0.301584	+	0.953440i	$0.402485\pi$
$743$	−13668.8	+	23675.0i	−0.674911	+	1.16898i	−0.976495	+	0.215541i	$0.930849\pi$
$744$		0			0
$745$	7881.75	+	13651.6i	0.387604	+	0.671350i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3416.01	−	5916.71i	−0.166647	−	0.288641i
$750$		0			0
$751$	1668.32	−	2889.61i	0.0810623	−	0.140404i	−0.822644	−	0.568557i	$-0.807502\pi$
$751$	1668.32	−	2889.61i	0.0810623	−	0.140404i	0.903706	+	0.428153i	$0.140835\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8099.98			−0.390448
$756$		0			0
$757$	33149.5			1.59160			0.795798	−	0.605562i	$-0.207052\pi$
$757$	33149.5			1.59160			0.795798	+	0.605562i	$0.207052\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5498.42	+	9523.54i	−0.261915	+	0.453651i	−0.966751	−	0.255720i	$-0.917687\pi$
$761$	−5498.42	+	9523.54i	−0.261915	+	0.453651i	0.704836	+	0.709371i	$0.251021\pi$
$762$		0			0
$763$	1366.08	+	2366.12i	0.0648169	+	0.112266i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	203.319	+	352.158i	0.00957159	+	0.0165785i
$768$		0			0
$769$	−16642.5	+	28825.6i	−0.780420	+	1.35173i	0.151277	+	0.988491i	$0.451661\pi$
$769$	−16642.5	+	28825.6i	−0.780420	+	1.35173i	−0.931697	+	0.363236i	$0.881672\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7242.46			0.336990			0.168495	−	0.985703i	$-0.446109\pi$
$773$	7242.46			0.336990			0.168495	+	0.985703i	$0.446109\pi$
$774$		0			0
$775$	3119.63			0.144594
$776$		0			0
$777$		0			0
$778$		0			0
$779$	20163.0	−	34923.4i	0.927362	−	1.60624i
$780$		0			0
$781$	−5499.98	−	9526.24i	−0.251991	−	0.436461i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5040.91	+	8731.11i	0.229195	+	0.396977i
$786$		0			0
$787$	8707.15	−	15081.2i	0.394379	−	0.683084i	−0.598643	−	0.801016i	$-0.704293\pi$
$787$	8707.15	−	15081.2i	0.394379	−	0.683084i	0.993022	+	0.117932i	$0.0376264\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8373.50			−0.376394
$792$		0			0
$793$	3988.26			0.178597
$794$		0			0
$795$		0			0
$796$		0			0
$797$	14566.5	−	25229.9i	0.647391	−	1.12131i	−0.336353	−	0.941736i	$-0.609193\pi$
$797$	14566.5	−	25229.9i	0.647391	−	1.12131i	0.983744	−	0.179578i	$-0.0574732\pi$
$798$		0			0
$799$	17363.7	+	30074.8i	0.768815	+	1.33163i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2357.44	−	4083.20i	−0.103602	−	0.179443i
$804$		0			0
$805$	1067.45	−	1848.88i	0.0467362	−	0.0809495i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	36440.1			1.58364			0.791820	−	0.610754i	$-0.209134\pi$
$809$	36440.1			1.58364			0.791820	+	0.610754i	$0.209134\pi$
$810$		0			0
$811$	18922.0			0.819286			0.409643	−	0.912246i	$-0.365653\pi$
$811$	18922.0			0.819286			0.409643	+	0.912246i	$0.365653\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5063.68	+	8770.55i	−0.217636	+	0.376956i
$816$		0			0
$817$	1553.14	+	2690.11i	0.0665084	+	0.115196i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8955.36	−	15511.1i	−0.380687	−	0.659369i	0.610474	−	0.792037i	$-0.290979\pi$
$821$	−8955.36	−	15511.1i	−0.380687	−	0.659369i	−0.991161	+	0.132667i	$0.957646\pi$
$822$		0			0
$823$	8762.22	−	15176.6i	0.371120	−	0.642799i	−0.618618	−	0.785692i	$-0.712307\pi$
$823$	8762.22	−	15176.6i	0.371120	−	0.642799i	0.989738	+	0.142893i	$0.0456405\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−17643.9			−0.741885			−0.370943	−	0.928656i	$-0.620965\pi$
$827$	−17643.9			−0.741885			−0.370943	+	0.928656i	$0.620965\pi$
$828$		0			0
$829$	45178.6			1.89278			0.946391	−	0.323023i	$-0.104699\pi$
$829$	45178.6			1.89278			0.946391	+	0.323023i	$0.104699\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7391.21	+	12802.0i	−0.307431	+	0.532487i
$834$		0			0
$835$	4445.02	+	7699.00i	0.184223	+	0.319084i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13388.0	−	23188.7i	−0.550901	−	0.954188i	−0.998210	−	0.0598087i	$-0.980951\pi$
$839$	−13388.0	−	23188.7i	−0.550901	−	0.954188i	0.447309	−	0.894379i	$-0.352382\pi$
$840$		0			0
$841$	11938.5	−	20678.1i	0.489503	−	0.847844i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−756.291			−0.0307896
$846$		0			0
$847$	14910.6			0.604879
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2476.73	−	4289.83i	0.0997665	−	0.172801i
$852$		0			0
$853$	3955.88	+	6851.78i	0.158789	+	0.275030i	0.934432	−	0.356141i	$-0.115908\pi$
$853$	3955.88	+	6851.78i	0.158789	+	0.275030i	−0.775644	+	0.631171i	$0.782575\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	924.149	+	1600.67i	0.0368359	+	0.0638016i	0.883856	−	0.467760i	$-0.154939\pi$
$857$	924.149	+	1600.67i	0.0368359	+	0.0638016i	−0.847020	+	0.531561i	$0.821605\pi$
$858$		0			0
$859$	−9427.10	+	16328.2i	−0.374445	+	0.648558i	−0.990244	−	0.139345i	$-0.955500\pi$
$859$	−9427.10	+	16328.2i	−0.374445	+	0.648558i	0.615799	+	0.787904i	$0.288833\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2086.03			0.0822821			0.0411410	−	0.999153i	$-0.486901\pi$
$863$	2086.03			0.0822821			0.0411410	+	0.999153i	$0.486901\pi$
$864$		0			0
$865$	14669.1			0.576605
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2435.46	−	4218.34i	0.0950717	−	0.164669i
$870$		0			0
$871$	−16605.4	−	28761.3i	−0.645983	−	1.11888i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6408.74	+	11100.3i	0.247606	+	0.428866i
$876$		0			0
$877$	12388.6	−	21457.7i	0.477005	−	0.826197i	−0.522648	−	0.852549i	$-0.675056\pi$
$877$	12388.6	−	21457.7i	0.477005	−	0.826197i	0.999653	+	0.0263520i	$0.00838907\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3741.26			−0.143072			−0.0715359	−	0.997438i	$-0.522790\pi$
$881$	−3741.26			−0.143072			−0.0715359	+	0.997438i	$0.522790\pi$
$882$		0			0
$883$	−14131.6			−0.538580			−0.269290	−	0.963059i	$-0.586789\pi$
$883$	−14131.6			−0.538580			−0.269290	+	0.963059i	$0.586789\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13311.3	+	23055.8i	−0.503888	+	0.872759i	0.496102	+	0.868264i	$0.334764\pi$
$887$	−13311.3	+	23055.8i	−0.503888	+	0.872759i	−0.999990	+	0.00449496i	$0.998569\pi$
$888$		0			0
$889$	5427.72	+	9401.09i	0.204769	+	0.354671i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−26742.8	−	46319.9i	−1.00214	−	1.73576i
$894$		0			0
$895$	3167.17	−	5485.70i	0.118287	−	0.204879i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−681.475			−0.0252820
$900$		0			0
$901$	−33026.9			−1.22118
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9143.09	+	15836.3i	−0.335830	+	0.581675i
$906$		0			0
$907$	26309.7	+	45569.7i	0.963174	+	1.66827i	0.714443	+	0.699694i	$0.246680\pi$
$907$	26309.7	+	45569.7i	0.963174	+	1.66827i	0.248731	+	0.968572i	$0.419986\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5090.22	−	8816.52i	−0.185122	−	0.320641i	0.758495	−	0.651678i	$-0.225935\pi$
$911$	−5090.22	−	8816.52i	−0.185122	−	0.320641i	−0.943618	+	0.331037i	$0.892601\pi$
$912$		0			0
$913$	−496.908	+	860.670i	−0.0180123	+	0.0311983i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20051.6			−0.722097
$918$		0			0
$919$	45618.2			1.63744			0.818718	−	0.574195i	$-0.194685\pi$
$919$	45618.2			1.63744			0.818718	+	0.574195i	$0.194685\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	26663.2	−	46182.1i	0.950846	−	1.64691i
$924$		0			0
$925$	6738.32	+	11671.1i	0.239518	+	0.414858i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6600.20	−	11431.9i	−0.233095	−	0.403733i	0.725622	−	0.688093i	$-0.241552\pi$
$929$	−6600.20	−	11431.9i	−0.233095	−	0.403733i	−0.958717	+	0.284361i	$0.908219\pi$
$930$		0			0
$931$	11383.6	−	19717.0i	0.400734	−	0.694091i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3494.59			0.122230
$936$		0			0
$937$	−13468.1			−0.469565			−0.234783	−	0.972048i	$-0.575438\pi$
$937$	−13468.1			−0.469565			−0.234783	+	0.972048i	$0.575438\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6942.05	−	12024.0i	0.240493	−	0.416547i	−0.720362	−	0.693599i	$-0.756024\pi$
$941$	6942.05	−	12024.0i	0.240493	−	0.416547i	0.960855	+	0.277052i	$0.0893574\pi$
$942$		0			0
$943$	−6614.93	−	11457.4i	−0.228432	−	0.395657i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2638.32	−	4569.70i	−0.0905320	−	0.156806i	0.817203	−	0.576350i	$-0.195523\pi$
$947$	−2638.32	−	4569.70i	−0.0905320	−	0.156806i	−0.907735	+	0.419544i	$0.862190\pi$
$948$		0			0
$949$	11428.6	−	19794.9i	0.390924	−	0.677101i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	26131.4			0.888225			0.444112	−	0.895971i	$-0.353519\pi$
$953$	26131.4			0.888225			0.444112	+	0.895971i	$0.353519\pi$
$954$		0			0
$955$	11118.5			0.376740
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16061.4	−	27819.2i	0.540825	−	0.936736i
$960$		0			0
$961$	14442.0	+	25014.3i	0.484777	+	0.839658i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3089.16	−	5350.59i	−0.103050	−	0.178489i
$966$		0			0
$967$	−1998.77	+	3461.96i	−0.0664695	+	0.115128i	−0.897345	−	0.441330i	$-0.854507\pi$
$967$	−1998.77	+	3461.96i	−0.0664695	+	0.115128i	0.830875	+	0.556458i	$0.187840\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	41785.1			1.38100			0.690499	−	0.723334i	$-0.257391\pi$
$971$	41785.1			1.38100			0.690499	+	0.723334i	$0.257391\pi$
$972$		0			0
$973$	7684.12			0.253177
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6122.55	−	10604.6i	0.200489	−	0.347257i	−0.748197	−	0.663476i	$-0.769080\pi$
$977$	6122.55	−	10604.6i	0.200489	−	0.347257i	0.948686	+	0.316220i	$0.102414\pi$
$978$		0			0
$979$	44.1170	+	76.4129i	0.00144023	+	0.00249455i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21891.5	−	37917.3i	−0.710307	−	1.23029i	−0.964742	−	0.263198i	$-0.915223\pi$
$983$	−21891.5	−	37917.3i	−0.710307	−	1.23029i	0.254435	−	0.967090i	$-0.418111\pi$
$984$		0			0
$985$	6087.50	−	10543.9i	0.196918	−	0.341071i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1019.08			0.0327654
$990$		0			0
$991$	−5178.38			−0.165991			−0.0829953	−	0.996550i	$-0.526449\pi$
$991$	−5178.38			−0.165991			−0.0829953	+	0.996550i	$0.526449\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5732.22	+	9928.50i	−0.182637	+	0.316336i
$996$		0			0
$997$	−12860.5	−	22275.0i	−0.408520	−	0.707578i	0.586204	−	0.810164i	$-0.300622\pi$
$997$	−12860.5	−	22275.0i	−0.408520	−	0.707578i	−0.994724	+	0.102586i	$0.967288\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.4.i.c.145.1		4
3.2	odd	2		144.4.i.c.49.1		4
4.3	odd	2		27.4.c.a.10.2		4
9.2	odd	6		144.4.i.c.97.1		4
9.4	even	3		1296.4.a.i.1.2		2
9.5	odd	6		1296.4.a.u.1.1		2
9.7	even	3	inner	432.4.i.c.289.1		4
12.11	even	2		9.4.c.a.4.1	✓	4
36.7	odd	6		27.4.c.a.19.2		4
36.11	even	6		9.4.c.a.7.1	yes	4
36.23	even	6		81.4.a.d.1.2		2
36.31	odd	6		81.4.a.a.1.1		2
60.23	odd	4		225.4.k.b.49.1		8
60.47	odd	4		225.4.k.b.49.4		8
60.59	even	2		225.4.e.b.76.2		4
180.47	odd	12		225.4.k.b.124.1		8
180.59	even	6		2025.4.a.g.1.1		2
180.83	odd	12		225.4.k.b.124.4		8
180.119	even	6		225.4.e.b.151.2		4
180.139	odd	6		2025.4.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.1	✓	4	12.11	even	2
9.4.c.a.7.1	yes	4	36.11	even	6
27.4.c.a.10.2		4	4.3	odd	2
27.4.c.a.19.2		4	36.7	odd	6
81.4.a.a.1.1		2	36.31	odd	6
81.4.a.d.1.2		2	36.23	even	6
144.4.i.c.49.1		4	3.2	odd	2
144.4.i.c.97.1		4	9.2	odd	6
225.4.e.b.76.2		4	60.59	even	2
225.4.e.b.151.2		4	180.119	even	6
225.4.k.b.49.1		8	60.23	odd	4
225.4.k.b.49.4		8	60.47	odd	4
225.4.k.b.124.1		8	180.47	odd	12
225.4.k.b.124.4		8	180.83	odd	12
432.4.i.c.145.1		4	1.1	even	1	trivial
432.4.i.c.289.1		4	9.7	even	3	inner
1296.4.a.i.1.2		2	9.4	even	3
1296.4.a.u.1.1		2	9.5	odd	6
2025.4.a.g.1.1		2	180.59	even	6
2025.4.a.n.1.2		2	180.139	odd	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.31386 - 4.00772i) q^{5} +(6.05842 + 10.4935i) q^{7} +O(q^{10})\)	\(q+(2.31386 - 4.00772i) q^{5} +(6.05842 + 10.4935i) q^{7} +(-5.01087 - 8.67909i) q^{11} +(24.2921 - 42.0752i) q^{13} -75.3505 q^{17} +116.052 q^{19} +(19.0367 - 32.9725i) q^{23} +(51.7921 + 89.7066i) q^{25} +(-11.3139 - 19.5962i) q^{29} +(15.0584 - 26.0820i) q^{31} +56.0733 q^{35} +130.103 q^{37} +(173.742 - 300.930i) q^{41} +(13.3832 + 23.1803i) q^{43} +(-230.439 - 399.132i) q^{47} +(98.0910 - 169.899i) q^{49} +438.310 q^{53} -46.3778 q^{55} +(-4.18487 + 7.24841i) q^{59} +(41.0448 + 71.0916i) q^{61} +(-112.417 - 194.712i) q^{65} +(341.785 - 591.989i) q^{67} +1097.61 q^{71} +470.464 q^{73} +(60.7160 - 105.163i) q^{77} +(243.017 + 420.919i) q^{79} +(-49.5829 - 85.8802i) q^{83} +(-174.351 + 301.984i) q^{85} -8.80426 q^{89} +588.687 q^{91} +(268.527 - 465.103i) q^{95} +(-330.486 - 572.419i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 15 q^{5} + 7 q^{7}+O(q^{10}) \) 4 * q + 15 * q^5 + 7 * q^7	\( 4 q + 15 q^{5} + 7 q^{7} - 66 q^{11} + 11 q^{13} - 198 q^{17} + 154 q^{19} - 33 q^{23} + 121 q^{25} - 51 q^{29} + 43 q^{31} + 6 q^{35} - 100 q^{37} + 132 q^{41} + 88 q^{43} - 399 q^{47} + 513 q^{49} - 108 q^{53} - 1254 q^{55} - 798 q^{59} - 439 q^{61} + 165 q^{65} + 988 q^{67} + 2736 q^{71} - 910 q^{73} - 165 q^{77} - 803 q^{79} - 813 q^{83} - 594 q^{85} + 792 q^{89} + 1562 q^{91} + 132 q^{95} - 736 q^{97}+O(q^{100}) \) 4 * q + 15 * q^5 + 7 * q^7 - 66 * q^11 + 11 * q^13 - 198 * q^17 + 154 * q^19 - 33 * q^23 + 121 * q^25 - 51 * q^29 + 43 * q^31 + 6 * q^35 - 100 * q^37 + 132 * q^41 + 88 * q^43 - 399 * q^47 + 513 * q^49 - 108 * q^53 - 1254 * q^55 - 798 * q^59 - 439 * q^61 + 165 * q^65 + 988 * q^67 + 2736 * q^71 - 910 * q^73 - 165 * q^77 - 803 * q^79 - 813 * q^83 - 594 * q^85 + 792 * q^89 + 1562 * q^91 + 132 * q^95 - 736 * q^97

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