LMFDB - Embedded newform 1512.2.q.c.793.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(793,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.8
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.c.1369.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841578 + 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +O(q^{10})$	$q+(0.841578 + 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +(0.622490 - 1.07818i) q^{11} +(1.96039 - 3.39550i) q^{13} +(1.62691 + 2.81788i) q^{17} +(2.36192 - 4.09097i) q^{19} +(-0.199068 - 0.344795i) q^{23} +(1.08349 - 1.87667i) q^{25} +(3.19896 + 5.54076i) q^{29} -0.578367 q^{31} +(-1.61605 + 4.14963i) q^{35} +(2.72146 - 4.71371i) q^{37} +(-4.20216 + 7.27836i) q^{41} +(2.46299 + 4.26603i) q^{43} +0.425190 q^{47} +(-1.52179 + 6.83258i) q^{49} +(0.466315 + 0.807681i) q^{53} +2.09550 q^{55} -6.05054 q^{59} +10.2092 q^{61} +6.59930 q^{65} -9.41952 q^{67} -8.46617 q^{71} +(6.82340 + 11.8185i) q^{73} +(3.25582 - 0.499480i) q^{77} -5.53340 q^{79} +(8.03669 + 13.9199i) q^{83} +(-2.73833 + 4.74293i) q^{85} +(6.03776 - 10.4577i) q^{89} +(10.2535 - 1.57300i) q^{91} +7.95097 q^{95} +(-5.86046 - 10.1506i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 - 5 * q^7	$ 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	0.841578	+	1.45766i	0.376365	+	0.651883i	0.990530	−	0.137294i	$-0.0438405\pi$
$5$	0.841578	+	1.45766i	0.376365	+	0.651883i	−0.614165	+	0.789177i	$0.710507\pi$
$6$		0			0
$7$	1.65502	+	2.06419i	0.625540	+	0.780192i
$7$	1.65502	+	2.06419i	0.625540	+	0.780192i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.622490	−	1.07818i	0.187688	−	0.325085i	−0.756791	−	0.653657i	$-0.773234\pi$
$11$	0.622490	−	1.07818i	0.187688	−	0.325085i	0.944479	+	0.328572i	$0.106567\pi$
$12$		0			0
$13$	1.96039	−	3.39550i	0.543715	−	0.941743i	−0.454971	−	0.890506i	$-0.650350\pi$
$13$	1.96039	−	3.39550i	0.543715	−	0.941743i	0.998687	−	0.0512366i	$-0.0163162\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.62691	+	2.81788i	0.394582	+	0.683437i	0.993048	−	0.117712i	$-0.0375559\pi$
$17$	1.62691	+	2.81788i	0.394582	+	0.683437i	−0.598465	+	0.801149i	$0.704223\pi$
$18$		0			0
$19$	2.36192	−	4.09097i	0.541863	−	0.938534i	−0.456935	−	0.889500i	$-0.651053\pi$
$19$	2.36192	−	4.09097i	0.541863	−	0.938534i	0.998797	−	0.0490333i	$-0.0156140\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.199068	−	0.344795i	−0.0415085	−	0.0718948i	0.844525	−	0.535516i	$-0.179883\pi$
$23$	−0.199068	−	0.344795i	−0.0415085	−	0.0718948i	−0.886033	+	0.463622i	$0.846550\pi$
$24$		0			0
$25$	1.08349	−	1.87667i	0.216699	−	0.375333i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.19896	+	5.54076i	0.594032	+	1.02889i	0.993683	+	0.112226i	$0.0357979\pi$
$29$	3.19896	+	5.54076i	0.594032	+	1.02889i	−0.399651	+	0.916667i	$0.630869\pi$
$30$		0			0
$31$	−0.578367			−0.103878			−0.0519389	−	0.998650i	$-0.516540\pi$
$31$	−0.578367			−0.103878			−0.0519389	+	0.998650i	$0.516540\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.61605	+	4.14963i	−0.273163	+	0.701416i
$36$		0			0
$37$	2.72146	−	4.71371i	0.447405	−	0.774928i	−0.550811	−	0.834630i	$-0.685682\pi$
$37$	2.72146	−	4.71371i	0.447405	−	0.774928i	0.998216	+	0.0597015i	$0.0190149\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.20216	+	7.27836i	−0.656267	+	1.13669i	0.325307	+	0.945608i	$0.394532\pi$
$41$	−4.20216	+	7.27836i	−0.656267	+	1.13669i	−0.981574	+	0.191080i	$0.938801\pi$
$42$		0			0
$43$	2.46299	+	4.26603i	0.375603	+	0.650563i	0.990417	−	0.138109i	$-0.0441024\pi$
$43$	2.46299	+	4.26603i	0.375603	+	0.650563i	−0.614814	+	0.788672i	$0.710769\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.425190			0.0620203			0.0310101	−	0.999519i	$-0.490128\pi$
$47$	0.425190			0.0620203			0.0310101	+	0.999519i	$0.490128\pi$
$48$		0			0
$49$	−1.52179	+	6.83258i	−0.217399	+	0.976083i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.466315	+	0.807681i	0.0640533	+	0.110944i	0.896274	−	0.443501i	$-0.146264\pi$
$53$	0.466315	+	0.807681i	0.0640533	+	0.110944i	−0.832220	+	0.554445i	$0.812931\pi$
$54$		0			0
$55$	2.09550			0.282557
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.05054			−0.787713			−0.393856	−	0.919172i	$-0.628859\pi$
$59$	−6.05054			−0.787713			−0.393856	+	0.919172i	$0.628859\pi$
$60$		0			0
$61$	10.2092			1.30715			0.653575	−	0.756862i	$-0.273268\pi$
$61$	10.2092			1.30715			0.653575	+	0.756862i	$0.273268\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.59930			0.818542
$66$		0			0
$67$	−9.41952			−1.15078			−0.575389	−	0.817880i	$-0.695149\pi$
$67$	−9.41952			−1.15078			−0.575389	+	0.817880i	$0.695149\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.46617			−1.00475			−0.502375	−	0.864650i	$-0.667540\pi$
$71$	−8.46617			−1.00475			−0.502375	+	0.864650i	$0.667540\pi$
$72$		0			0
$73$	6.82340	+	11.8185i	0.798619	+	1.38325i	0.920516	+	0.390705i	$0.127769\pi$
$73$	6.82340	+	11.8185i	0.798619	+	1.38325i	−0.121897	+	0.992543i	$0.538898\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.25582	−	0.499480i	0.371035	−	0.0569211i
$78$		0			0
$79$	−5.53340			−0.622556			−0.311278	−	0.950319i	$-0.600757\pi$
$79$	−5.53340			−0.622556			−0.311278	+	0.950319i	$0.600757\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.03669	+	13.9199i	0.882141	+	1.52791i	0.848956	+	0.528463i	$0.177232\pi$
$83$	8.03669	+	13.9199i	0.882141	+	1.52791i	0.0331848	+	0.999449i	$0.489435\pi$
$84$		0			0
$85$	−2.73833	+	4.74293i	−0.297014	+	0.514444i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.03776	−	10.4577i	0.640001	−	1.10851i	−0.345431	−	0.938444i	$-0.612267\pi$
$89$	6.03776	−	10.4577i	0.640001	−	1.10851i	0.985432	−	0.170070i	$-0.0543993\pi$
$90$		0			0
$91$	10.2535	−	1.57300i	1.07486	−	0.164895i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.95097			0.815753
$96$		0			0
$97$	−5.86046	−	10.1506i	−0.595040	−	1.03064i	−0.993541	−	0.113472i	$-0.963803\pi$
$97$	−5.86046	−	10.1506i	−0.595040	−	1.03064i	0.398501	−	0.917168i	$-0.369530\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.70302	−	4.68177i	0.268961	−	0.465854i	−0.699633	−	0.714502i	$-0.746653\pi$
$101$	2.70302	−	4.68177i	0.268961	−	0.465854i	0.968594	+	0.248649i	$0.0799865\pi$
$102$		0			0
$103$	−7.31018	−	12.6616i	−0.720294	−	1.24759i	−0.960882	−	0.276958i	$-0.910674\pi$
$103$	−7.31018	−	12.6616i	−0.720294	−	1.24759i	0.240588	−	0.970627i	$-0.422660\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.40209	−	5.89259i	0.328892	−	0.569658i	−0.653400	−	0.757013i	$-0.726658\pi$
$107$	3.40209	−	5.89259i	0.328892	−	0.569658i	0.982292	+	0.187354i	$0.0599913\pi$
$108$		0			0
$109$	8.37636	+	14.5083i	0.802310	+	1.38964i	0.918092	+	0.396367i	$0.129729\pi$
$109$	8.37636	+	14.5083i	0.802310	+	1.38964i	−0.115783	+	0.993275i	$0.536938\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.77154	+	11.7287i	−0.637013	+	1.10334i	0.349072	+	0.937096i	$0.386497\pi$
$113$	−6.77154	+	11.7287i	−0.637013	+	1.10334i	−0.986085	+	0.166243i	$0.946836\pi$
$114$		0			0
$115$	0.335062	−	0.580344i	0.0312447	−	0.0541174i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.12409	+	8.02191i	−0.286385	+	0.735367i
$120$		0			0
$121$	4.72501	+	8.18396i	0.429547	+	0.743996i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0632			1.07896
$126$		0			0
$127$	10.5904			0.939748			0.469874	−	0.882734i	$-0.344299\pi$
$127$	10.5904			0.939748			0.469874	+	0.882734i	$0.344299\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−11.1819	−	19.3676i	−0.976968	−	1.69216i	−0.673282	−	0.739385i	$-0.735116\pi$
$131$	−11.1819	−	19.3676i	−0.976968	−	1.69216i	−0.303685	−	0.952772i	$-0.598217\pi$
$132$		0			0
$133$	12.3536	−	1.89519i	1.07119	−	0.164333i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.97700	−	15.5486i	0.766957	−	1.32841i	−0.172249	−	0.985053i	$-0.555104\pi$
$137$	8.97700	−	15.5486i	0.766957	−	1.32841i	0.939206	−	0.343354i	$-0.111563\pi$
$138$		0			0
$139$	0.570825	−	0.988699i	0.0484168	−	0.0838603i	−0.840801	−	0.541344i	$-0.817916\pi$
$139$	0.570825	−	0.988699i	0.0484168	−	0.0838603i	0.889218	+	0.457483i	$0.151249\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.44065	−	4.22733i	−0.204098	−	0.353507i
$144$		0			0
$145$	−5.38434	+	9.32596i	−0.447145	+	0.774479i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.82916	+	15.2925i	0.723313	+	1.25281i	0.959665	+	0.281147i	$0.0907148\pi$
$149$	8.82916	+	15.2925i	0.723313	+	1.25281i	−0.236352	+	0.971667i	$0.575952\pi$
$150$		0			0
$151$	7.61769	−	13.1942i	0.619919	−	1.07373i	−0.369581	−	0.929198i	$-0.620499\pi$
$151$	7.61769	−	13.1942i	0.619919	−	1.07373i	0.989500	−	0.144532i	$-0.0461678\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.486741	−	0.843060i	−0.0390960	−	0.0677162i
$156$		0			0
$157$	−13.6288			−1.08769			−0.543847	−	0.839184i	$-0.683033\pi$
$157$	−13.6288			−1.08769			−0.543847	+	0.839184i	$0.683033\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.382263	−	0.981559i	0.0301265	−	0.0773577i
$162$		0			0
$163$	−4.04726	+	7.01005i	−0.317006	+	0.549070i	−0.979862	−	0.199677i	$-0.936011\pi$
$163$	−4.04726	+	7.01005i	−0.317006	+	0.549070i	0.662856	+	0.748747i	$0.269344\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.07739	−	3.59814i	0.160753	−	0.278433i	−0.774386	−	0.632714i	$-0.781941\pi$
$167$	2.07739	−	3.59814i	0.160753	−	0.278433i	0.935139	+	0.354281i	$0.115274\pi$
$168$		0			0
$169$	−1.18629	−	2.05471i	−0.0912529	−	0.158055i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−13.8346			−1.05183			−0.525913	−	0.850539i	$-0.676276\pi$
$173$	−13.8346			−1.05183			−0.525913	+	0.850539i	$0.676276\pi$
$174$		0			0
$175$	5.66701	−	0.869385i	0.428386	−	0.0657193i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.71167	+	8.16084i	0.352166	+	0.609970i	0.986629	−	0.162984i	$-0.0521118\pi$
$179$	4.71167	+	8.16084i	0.352166	+	0.609970i	−0.634462	+	0.772954i	$0.718778\pi$
$180$		0			0
$181$	1.32133			0.0982136			0.0491068	−	0.998794i	$-0.484363\pi$
$181$	1.32133			0.0982136			0.0491068	+	0.998794i	$0.484363\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	9.16128			0.673551
$186$		0			0
$187$	4.05093			0.296233
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.2854			−1.17837			−0.589186	−	0.807997i	$-0.700551\pi$
$191$	−16.2854			−1.17837			−0.589186	+	0.807997i	$0.700551\pi$
$192$		0			0
$193$	2.56155			0.184384			0.0921921	−	0.995741i	$-0.470613\pi$
$193$	2.56155			0.184384			0.0921921	+	0.995741i	$0.470613\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−21.6916			−1.54546			−0.772730	−	0.634735i	$-0.781109\pi$
$197$	−21.6916			−1.54546			−0.772730	+	0.634735i	$0.781109\pi$
$198$		0			0
$199$	−5.59684	−	9.69402i	−0.396750	−	0.687191i	0.596573	−	0.802559i	$-0.296529\pi$
$199$	−5.59684	−	9.69402i	−0.396750	−	0.687191i	−0.993323	+	0.115368i	$0.963195\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.14285	+	15.7734i	−0.431143	+	1.10707i
$204$		0			0
$205$	−14.1458			−0.987985
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.94055	−	5.09318i	−0.203402	−	0.352303i
$210$		0			0
$211$	−14.1807	+	24.5616i	−0.976237	+	1.69089i	−0.300444	+	0.953799i	$0.597135\pi$
$211$	−14.1807	+	24.5616i	−0.976237	+	1.69089i	−0.675793	+	0.737092i	$0.736199\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.14560	+	7.18039i	−0.282728	+	0.489699i
$216$		0			0
$217$	−0.957211	−	1.19386i	−0.0649797	−	0.0810446i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	12.7575			0.858162
$222$		0			0
$223$	−12.6962	−	21.9905i	−0.850202	−	1.47259i	−0.881026	−	0.473068i	$-0.843147\pi$
$223$	−12.6962	−	21.9905i	−0.850202	−	1.47259i	0.0308242	−	0.999525i	$-0.490187\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.31430	−	4.00849i	0.153606	−	0.266053i	−0.778945	−	0.627092i	$-0.784245\pi$
$227$	2.31430	−	4.00849i	0.153606	−	0.266053i	0.932550	+	0.361040i	$0.117578\pi$
$228$		0			0
$229$	−1.16296	−	2.01431i	−0.0768506	−	0.133109i	0.825039	−	0.565076i	$-0.191153\pi$
$229$	−1.16296	−	2.01431i	−0.0768506	−	0.133109i	−0.901890	+	0.431967i	$0.857820\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.37989	−	11.0503i	0.417960	−	0.723929i	−0.577774	−	0.816197i	$-0.696078\pi$
$233$	6.37989	−	11.0503i	0.417960	−	0.723929i	0.995734	+	0.0922683i	$0.0294117\pi$
$234$		0			0
$235$	0.357830	+	0.619780i	0.0233423	+	0.0404300i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.0492	−	19.1378i	0.714714	−	1.23792i	−0.248355	−	0.968669i	$-0.579890\pi$
$239$	11.0492	−	19.1378i	0.714714	−	1.23792i	0.963070	−	0.269252i	$-0.0867766\pi$
$240$		0			0
$241$	−10.0088	+	17.3358i	−0.644726	+	1.11670i	0.339639	+	0.940556i	$0.389695\pi$
$241$	−10.0088	+	17.3358i	−0.644726	+	1.11670i	−0.984365	+	0.176142i	$0.943638\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.2403	+	3.53190i	−0.718114	+	0.225645i
$246$		0			0
$247$	−9.26060	−	16.0398i	−0.589238	−	1.02059i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.12390			0.134059			0.0670297	−	0.997751i	$-0.478648\pi$
$251$	2.12390			0.134059			0.0670297	+	0.997751i	$0.478648\pi$
$252$		0			0
$253$	−0.495671			−0.0311625
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.38150	−	11.0531i	−0.398067	−	0.689472i	0.595420	−	0.803414i	$-0.296986\pi$
$257$	−6.38150	−	11.0531i	−0.398067	−	0.689472i	−0.993487	+	0.113942i	$0.963652\pi$
$258$		0			0
$259$	14.2341	−	2.18367i	0.884463	−	0.135687i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.53432	+	9.58572i	−0.341261	+	0.591081i	−0.984667	−	0.174444i	$-0.944187\pi$
$263$	−5.53432	+	9.58572i	−0.341261	+	0.591081i	0.643406	+	0.765525i	$0.277521\pi$
$264$		0			0
$265$	−0.784881	+	1.35945i	−0.0482148	+	0.0835105i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.77479	+	3.07403i	0.108211	+	0.187427i	0.915046	−	0.403351i	$-0.132154\pi$
$269$	1.77479	+	3.07403i	0.108211	+	0.187427i	−0.806835	+	0.590777i	$0.798821\pi$
$270$		0			0
$271$	−0.687666	+	1.19107i	−0.0417727	+	0.0723525i	−0.886156	−	0.463387i	$-0.846634\pi$
$271$	−0.687666	+	1.19107i	−0.0417727	+	0.0723525i	0.844383	+	0.535740i	$0.179967\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.34893	−	2.33641i	−0.0813434	−	0.140891i
$276$		0			0
$277$	14.5809	−	25.2548i	0.876079	−	1.51741i	0.0204692	−	0.999790i	$-0.493484\pi$
$277$	14.5809	−	25.2548i	0.876079	−	1.51741i	0.855609	−	0.517622i	$-0.173183\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.29603	−	10.9050i	−0.375590	−	0.650540i	0.614826	−	0.788663i	$-0.289226\pi$
$281$	−6.29603	−	10.9050i	−0.375590	−	0.650540i	−0.990415	+	0.138123i	$0.955893\pi$
$282$		0			0
$283$	−9.46056			−0.562372			−0.281186	−	0.959653i	$-0.590728\pi$
$283$	−9.46056			−0.562372			−0.281186	+	0.959653i	$0.590728\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−21.9786	+	3.37178i	−1.29736	+	0.199030i
$288$		0			0
$289$	3.20636	−	5.55358i	0.188609	−	0.326681i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.32726	−	14.4232i	0.486484	−	0.842614i	−0.513396	−	0.858152i	$-0.671613\pi$
$293$	8.32726	−	14.4232i	0.486484	−	0.842614i	0.999879	+	0.0155376i	$0.00494598\pi$
$294$		0			0
$295$	−5.09200	−	8.81960i	−0.296468	−	0.513497i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.56100			−0.0902752
$300$		0			0
$301$	−4.72960	+	12.1445i	−0.272610	+	0.699996i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.59181	+	14.8815i	0.491966	+	0.852110i
$306$		0			0
$307$	−9.55966			−0.545599			−0.272799	−	0.962071i	$-0.587949\pi$
$307$	−9.55966			−0.545599			−0.272799	+	0.962071i	$0.587949\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−26.3702			−1.49532			−0.747658	−	0.664084i	$-0.768822\pi$
$311$	−26.3702			−1.49532			−0.747658	+	0.664084i	$0.768822\pi$
$312$		0			0
$313$	−12.7018			−0.717949			−0.358975	−	0.933347i	$-0.616874\pi$
$313$	−12.7018			−0.717949			−0.358975	+	0.933347i	$0.616874\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.0331536			−0.00186209			−0.000931047	−	1.00000i	$-0.500296\pi$
$317$	−0.0331536			−0.00186209			−0.000931047		1.00000i	$0.500296\pi$
$318$		0			0
$319$	7.96528			0.445970
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.3705			0.855238
$324$		0			0
$325$	−4.24815	−	7.35801i	−0.235645	−	0.408149i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.703699	+	0.877674i	0.0387962	+	0.0483877i
$330$		0			0
$331$	−4.85388			−0.266793			−0.133397	−	0.991063i	$-0.542588\pi$
$331$	−4.85388			−0.266793			−0.133397	+	0.991063i	$0.542588\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.92726	−	13.7304i	−0.433112	−	0.750173i
$336$		0			0
$337$	−4.32200	+	7.48592i	−0.235434	+	0.407784i	−0.959399	−	0.282053i	$-0.908985\pi$
$337$	−4.32200	+	7.48592i	−0.235434	+	0.407784i	0.723965	+	0.689837i	$0.242318\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.360028	+	0.623586i	−0.0194966	+	0.0337691i
$342$		0			0
$343$	−16.6224	+	8.16680i	−0.897524	+	0.440966i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	23.2232			1.24669			0.623344	−	0.781948i	$-0.285774\pi$
$347$	23.2232			1.24669			0.623344	+	0.781948i	$0.285774\pi$
$348$		0			0
$349$	−3.76025	−	6.51295i	−0.201282	−	0.348630i	0.747660	−	0.664082i	$-0.231177\pi$
$349$	−3.76025	−	6.51295i	−0.201282	−	0.348630i	−0.948942	+	0.315452i	$0.897844\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.459528	+	0.795925i	−0.0244582	+	0.0423628i	−0.877995	−	0.478669i	$-0.841119\pi$
$353$	−0.459528	+	0.795925i	−0.0244582	+	0.0423628i	0.853537	+	0.521032i	$0.174453\pi$
$354$		0			0
$355$	−7.12495	−	12.3408i	−0.378153	−	0.654980i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.24300	+	14.2773i	−0.435049	+	0.753527i	−0.997300	−	0.0734398i	$-0.976602\pi$
$359$	−8.24300	+	14.2773i	−0.435049	+	0.753527i	0.562251	+	0.826967i	$0.309936\pi$
$360$		0			0
$361$	−1.65737	−	2.87066i	−0.0872302	−	0.151087i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−11.4848	+	19.8923i	−0.601144	+	1.04121i
$366$		0			0
$367$	6.33921	−	10.9798i	0.330904	−	0.573143i	−0.651785	−	0.758404i	$-0.725980\pi$
$367$	6.33921	−	10.9798i	0.330904	−	0.573143i	0.982689	+	0.185261i	$0.0593130\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.895448	+	2.29930i	−0.0464894	+	0.119373i
$372$		0			0
$373$	−11.3410	−	19.6433i	−0.587217	−	1.01709i	−0.994595	−	0.103830i	$-0.966890\pi$
$373$	−11.3410	−	19.6433i	−0.587217	−	1.01709i	0.407378	−	0.913259i	$-0.366443\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	25.0849			1.29194
$378$		0			0
$379$	19.0925			0.980717			0.490358	−	0.871521i	$-0.336866\pi$
$379$	19.0925			0.980717			0.490358	+	0.871521i	$0.336866\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.03963	−	5.26479i	−0.155318	−	0.269018i	0.777857	−	0.628441i	$-0.216307\pi$
$383$	−3.03963	−	5.26479i	−0.155318	−	0.269018i	−0.933175	+	0.359423i	$0.882973\pi$
$384$		0			0
$385$	3.46809	+	4.32551i	0.176750	+	0.220448i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.315781	+	0.546948i	−0.0160107	+	0.0277314i	−0.873920	−	0.486070i	$-0.838430\pi$
$389$	−0.315781	+	0.546948i	−0.0160107	+	0.0277314i	0.857909	+	0.513802i	$0.171763\pi$
$390$		0			0
$391$	0.647728	−	1.12190i	0.0327570	−	0.0567368i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.65679	−	8.06579i	−0.234308	−	0.405834i
$396$		0			0
$397$	−18.1830	+	31.4939i	−0.912578	+	1.58063i	−0.102170	+	0.994767i	$0.532579\pi$
$397$	−18.1830	+	31.4939i	−0.912578	+	1.58063i	−0.810408	+	0.585865i	$0.800755\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.8069	−	27.3783i	−0.789357	−	1.36721i	−0.926361	−	0.376636i	$-0.877081\pi$
$401$	−15.8069	−	27.3783i	−0.789357	−	1.36721i	0.137004	−	0.990571i	$-0.456253\pi$
$402$		0			0
$403$	−1.13383	+	1.96385i	−0.0564800	+	0.0978262i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.38816	−	5.86847i	−0.167945	−	0.290889i
$408$		0			0
$409$	20.1812			0.997896			0.498948	−	0.866632i	$-0.333720\pi$
$409$	20.1812			0.997896			0.498948	+	0.866632i	$0.333720\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.0138	−	12.4895i	−0.492746	−	0.614567i
$414$		0			0
$415$	−13.5270	+	23.4294i	−0.664014	+	1.15011i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.4159	−	21.5049i	0.606555	−	1.05058i	−0.385248	−	0.922813i	$-0.625884\pi$
$419$	12.4159	−	21.5049i	0.606555	−	1.05058i	0.991804	−	0.127772i	$-0.0407825\pi$
$420$		0			0
$421$	−5.71841	−	9.90458i	−0.278698	−	0.482720i	0.692363	−	0.721549i	$-0.256570\pi$
$421$	−5.71841	−	9.90458i	−0.278698	−	0.482720i	−0.971062	+	0.238829i	$0.923236\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.05096			0.342022
$426$		0			0
$427$	16.8964	+	21.0737i	0.817675	+	1.01983i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.80157	−	4.85246i	−0.134947	−	0.233735i	0.790630	−	0.612294i	$-0.209753\pi$
$431$	−2.80157	−	4.85246i	−0.134947	−	0.233735i	−0.925577	+	0.378559i	$0.876420\pi$
$432$		0			0
$433$	−4.22555			−0.203067			−0.101534	−	0.994832i	$-0.532375\pi$
$433$	−4.22555			−0.203067			−0.101534	+	0.994832i	$0.532375\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.88073			−0.0899676
$438$		0			0
$439$	−35.4631			−1.69256			−0.846281	−	0.532737i	$-0.821164\pi$
$439$	−35.4631			−1.69256			−0.846281	+	0.532737i	$0.821164\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	22.9315			1.08951			0.544755	−	0.838595i	$-0.316623\pi$
$443$	22.9315			1.08951			0.544755	+	0.838595i	$0.316623\pi$
$444$		0			0
$445$	20.3250			0.963496
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.4850			−0.966747			−0.483373	−	0.875414i	$-0.660589\pi$
$449$	−20.4850			−0.966747			−0.483373	+	0.875414i	$0.660589\pi$
$450$		0			0
$451$	5.23161	+	9.06141i	0.246347	+	0.426685i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.9220	+	13.6222i	0.512031	+	0.638620i
$456$		0			0
$457$	15.4535			0.722886			0.361443	−	0.932394i	$-0.382284\pi$
$457$	15.4535			0.722886			0.361443	+	0.932394i	$0.382284\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.0815	−	24.3898i	−0.655839	−	1.13595i	−0.981683	−	0.190523i	$-0.938982\pi$
$461$	−14.0815	−	24.3898i	−0.655839	−	1.13595i	0.325844	−	0.945424i	$-0.394352\pi$
$462$		0			0
$463$	−15.3193	+	26.5338i	−0.711948	+	1.23313i	0.252177	+	0.967681i	$0.418854\pi$
$463$	−15.3193	+	26.5338i	−0.711948	+	1.23313i	−0.964125	+	0.265449i	$0.914480\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.61798	−	11.4627i	0.306244	−	0.530429i	−0.671294	−	0.741191i	$-0.734261\pi$
$467$	6.61798	−	11.4627i	0.306244	−	0.530429i	0.977537	+	0.210762i	$0.0675945\pi$
$468$		0			0
$469$	−15.5895	−	19.4437i	−0.719857	−	0.897827i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6.13275			0.281984
$474$		0			0
$475$	−5.11826	−	8.86508i	−0.234842	−	0.406758i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.04358	−	12.1998i	0.321829	−	0.557425i	−0.659036	−	0.752111i	$-0.729036\pi$
$479$	7.04358	−	12.1998i	0.321829	−	0.557425i	0.980866	+	0.194687i	$0.0623690\pi$
$480$		0			0
$481$	−10.6703	−	18.4814i	−0.486522	−	0.842681i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.86407	−	17.0851i	0.447904	−	0.775793i
$486$		0			0
$487$	3.45654	+	5.98690i	0.156631	+	0.271292i	0.933652	−	0.358183i	$-0.116603\pi$
$487$	3.45654	+	5.98690i	0.156631	+	0.271292i	−0.777021	+	0.629475i	$0.783270\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	15.3481	−	26.5837i	0.692651	−	1.19971i	−0.278315	−	0.960490i	$-0.589776\pi$
$491$	15.3481	−	26.5837i	0.692651	−	1.19971i	0.970966	−	0.239217i	$-0.0768909\pi$
$492$		0			0
$493$	−10.4088	+	18.0286i	−0.468789	+	0.811966i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.0117	−	17.4758i	−0.628511	−	0.783898i
$498$		0			0
$499$	11.0186	+	19.0847i	0.493259	+	0.854350i	0.999970	−	0.00776631i	$-0.00247212\pi$
$499$	11.0186	+	19.0847i	0.493259	+	0.854350i	−0.506711	+	0.862116i	$0.669139\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−38.9653			−1.73737			−0.868687	−	0.495361i	$-0.835036\pi$
$503$	−38.9653			−1.73737			−0.868687	+	0.495361i	$0.835036\pi$
$504$		0			0
$505$	9.09922			0.404910
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.1471	−	24.5034i	−0.627058	−	1.08610i	−0.988139	−	0.153561i	$-0.950926\pi$
$509$	−14.1471	−	24.5034i	−0.627058	−	1.08610i	0.361082	−	0.932534i	$-0.382408\pi$
$510$		0			0
$511$	−13.1027	+	33.6447i	−0.579631	+	1.48835i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.3042	−	21.3115i	0.542187	−	0.939095i
$516$		0			0
$517$	0.264676	−	0.458433i	0.0116405	−	0.0201619i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.98150	+	10.3603i	0.262054	+	0.453892i	0.966788	−	0.255581i	$-0.0822667\pi$
$521$	5.98150	+	10.3603i	0.262054	+	0.453892i	−0.704733	+	0.709472i	$0.748933\pi$
$522$		0			0
$523$	−3.15056	+	5.45693i	−0.137764	+	0.238615i	−0.926650	−	0.375925i	$-0.877325\pi$
$523$	−3.15056	+	5.45693i	−0.137764	+	0.238615i	0.788886	+	0.614540i	$0.210658\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.940948	−	1.62977i	−0.0409884	−	0.0709939i
$528$		0			0
$529$	11.4207	−	19.7813i	0.496554	−	0.860057i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	16.4758	+	28.5369i	0.713645	+	1.23607i
$534$		0			0
$535$	11.4525			0.495135
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.41948	+	5.89399i	0.276507	+	0.253872i
$540$		0			0
$541$	9.88191	−	17.1160i	0.424857	−	0.735873i	−0.571550	−	0.820567i	$-0.693658\pi$
$541$	9.88191	−	17.1160i	0.424857	−	0.735873i	0.996407	+	0.0846937i	$0.0269912\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.0987	+	24.4197i	−0.603923	+	1.04602i
$546$		0			0
$547$	21.6125	+	37.4340i	0.924085	+	1.60056i	0.793026	+	0.609188i	$0.208504\pi$
$547$	21.6125	+	37.4340i	0.924085	+	1.60056i	0.131059	+	0.991375i	$0.458162\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	30.2228			1.28753
$552$		0			0
$553$	−9.15791	−	11.4220i	−0.389434	−	0.485713i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.0838	+	24.3938i	0.596748	+	1.03360i	0.993298	+	0.115584i	$0.0368740\pi$
$557$	14.0838	+	24.3938i	0.596748	+	1.03360i	−0.396550	+	0.918013i	$0.629793\pi$
$558$		0			0
$559$	19.3137			0.816884
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−25.6944			−1.08289			−0.541445	−	0.840736i	$-0.682122\pi$
$563$	−25.6944			−1.08289			−0.541445	+	0.840736i	$0.682122\pi$
$564$		0			0
$565$	−22.7951			−0.958998
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−35.4881			−1.48774			−0.743870	−	0.668324i	$-0.767012\pi$
$569$	−35.4881			−1.48774			−0.743870	+	0.668324i	$0.767012\pi$
$570$		0			0
$571$	21.6824			0.907378			0.453689	−	0.891160i	$-0.350108\pi$
$571$	21.6824			0.907378			0.453689	+	0.891160i	$0.350108\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.862754			−0.0359793
$576$		0			0
$577$	−7.60727	−	13.1762i	−0.316695	−	0.548531i	0.663102	−	0.748529i	$-0.269240\pi$
$577$	−7.60727	−	13.1762i	−0.316695	−	0.548531i	−0.979796	+	0.199998i	$0.935906\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−15.4326	+	39.6271i	−0.640251	+	1.64401i
$582$		0			0
$583$	1.16111			0.0480881
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.1924	+	33.2423i	0.792157	+	1.37206i	0.924629	+	0.380869i	$0.124375\pi$
$587$	19.1924	+	33.2423i	0.792157	+	1.37206i	−0.132472	+	0.991187i	$0.542292\pi$
$588$		0			0
$589$	−1.36606	+	2.36608i	−0.0562875	+	0.0974928i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.25559	−	16.0311i	0.380081	−	0.658320i	−0.610992	−	0.791637i	$-0.709229\pi$
$593$	9.25559	−	16.0311i	0.380081	−	0.658320i	0.991074	+	0.133316i	$0.0425626\pi$
$594$		0			0
$595$	−14.3223	+	2.19721i	−0.587159	+	0.0900770i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	21.6825			0.885924			0.442962	−	0.896540i	$-0.353928\pi$
$599$	21.6825			0.885924			0.442962	+	0.896540i	$0.353928\pi$
$600$		0			0
$601$	3.95776	+	6.85505i	0.161441	+	0.279623i	0.935386	−	0.353630i	$-0.115053\pi$
$601$	3.95776	+	6.85505i	0.161441	+	0.279623i	−0.773945	+	0.633253i	$0.781719\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.95293	+	13.7749i	−0.323333	+	0.560029i
$606$		0			0
$607$	−17.9623	−	31.1117i	−0.729068	−	1.26278i	−0.957277	−	0.289171i	$-0.906620\pi$
$607$	−17.9623	−	31.1117i	−0.729068	−	1.26278i	0.228209	−	0.973612i	$-0.426713\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.833539	−	1.44373i	0.0337214	−	0.0584072i
$612$		0			0
$613$	−1.60252	−	2.77565i	−0.0647253	−	0.112108i	0.831847	−	0.555005i	$-0.187284\pi$
$613$	−1.60252	−	2.77565i	−0.0647253	−	0.112108i	−0.896572	+	0.442898i	$0.853950\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.9357	+	27.6015i	−0.641549	+	1.11120i	0.343538	+	0.939139i	$0.388374\pi$
$617$	−15.9357	+	27.6015i	−0.641549	+	1.11120i	−0.985087	+	0.172056i	$0.944959\pi$
$618$		0			0
$619$	10.4863	−	18.1628i	0.421480	−	0.730024i	−0.574605	−	0.818431i	$-0.694844\pi$
$619$	10.4863	−	18.1628i	0.421480	−	0.730024i	0.996084	+	0.0884070i	$0.0281776\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	31.5793	−	4.84464i	1.26520	−	0.194096i
$624$		0			0
$625$	4.73462	+	8.20060i	0.189385	+	0.328024i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	17.7102			0.706153
$630$		0			0
$631$	26.4435			1.05270			0.526349	−	0.850268i	$-0.323560\pi$
$631$	26.4435			1.05270			0.526349	+	0.850268i	$0.323560\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.91266	+	15.4372i	0.353688	+	0.612606i
$636$		0			0
$637$	20.2167	+	18.5618i	0.801016	+	0.735445i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−13.9809	+	24.2157i	−0.552213	+	0.956461i	0.445901	+	0.895082i	$0.352883\pi$
$641$	−13.9809	+	24.2157i	−0.552213	+	0.956461i	−0.998115	+	0.0613792i	$0.980450\pi$
$642$		0			0
$643$	−6.12936	+	10.6164i	−0.241718	+	0.418669i	−0.961204	−	0.275839i	$-0.911044\pi$
$643$	−6.12936	+	10.6164i	−0.241718	+	0.418669i	0.719485	+	0.694508i	$0.244378\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.49923	−	7.79290i	−0.176883	−	0.306371i	0.763928	−	0.645301i	$-0.223268\pi$
$647$	−4.49923	−	7.79290i	−0.176883	−	0.306371i	−0.940811	+	0.338931i	$0.889935\pi$
$648$		0			0
$649$	−3.76640	+	6.52360i	−0.147844	+	0.256074i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.3950	−	19.7368i	−0.445922	−	0.772359i	0.552194	−	0.833716i	$-0.313791\pi$
$653$	−11.3950	−	19.7368i	−0.445922	−	0.772359i	−0.998116	+	0.0613562i	$0.980457\pi$
$654$		0			0
$655$	18.8209	−	32.5987i	0.735393	−	1.27374i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.3311	+	33.4824i	0.753033	+	1.30429i	0.946347	+	0.323154i	$0.104743\pi$
$659$	19.3311	+	33.4824i	0.753033	+	1.30429i	−0.193314	+	0.981137i	$0.561924\pi$
$660$		0			0
$661$	−11.5080			−0.447609			−0.223804	−	0.974634i	$-0.571848\pi$
$661$	−11.5080			−0.447609			−0.223804	+	0.974634i	$0.571848\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	13.1590	+	16.4124i	0.510286	+	0.636444i
$666$		0			0
$667$	1.27362	−	2.20597i	0.0493147	−	0.0854156i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.35511	−	11.0074i	0.245336	−	0.424935i
$672$		0			0
$673$	−10.6642	−	18.4709i	−0.411075	−	0.712002i	0.583933	−	0.811802i	$-0.301513\pi$
$673$	−10.6642	−	18.4709i	−0.411075	−	0.712002i	−0.995008	+	0.0997997i	$0.968180\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−27.7599			−1.06690			−0.533449	−	0.845832i	$-0.679104\pi$
$677$	−27.7599			−1.06690			−0.533449	+	0.845832i	$0.679104\pi$
$678$		0			0
$679$	11.2536	−	28.8966i	0.431875	−	1.10895i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.66854	+	15.0143i	0.331692	+	0.574508i	0.982844	−	0.184440i	$-0.0590471\pi$
$683$	8.66854	+	15.0143i	0.331692	+	0.574508i	−0.651151	+	0.758948i	$0.725714\pi$
$684$		0			0
$685$	30.2194			1.15462
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.65664			0.139307
$690$		0			0
$691$	39.6046			1.50663			0.753315	−	0.657660i	$-0.228453\pi$
$691$	39.6046			1.50663			0.753315	+	0.657660i	$0.228453\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.92158			0.0728895
$696$		0			0
$697$	−27.3461			−1.03581
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7.28469			−0.275139			−0.137570	−	0.990492i	$-0.543929\pi$
$701$	−7.28469			−0.275139			−0.137570	+	0.990492i	$0.543929\pi$
$702$		0			0
$703$	−12.8558	−	22.2668i	−0.484864	−	0.839809i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	14.1377	−	2.16888i	0.531701	−	0.0815691i
$708$		0			0
$709$	12.0108			0.451075			0.225538	−	0.974234i	$-0.427586\pi$
$709$	12.0108			0.451075			0.225538	+	0.974234i	$0.427586\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.115134	+	0.199418i	0.00431181	+	0.00746827i
$714$		0			0
$715$	4.10800	−	7.11526i	0.153630	−	0.266096i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.15819	−	3.73809i	0.0804868	−	0.139407i	−0.822972	−	0.568081i	$-0.807686\pi$
$719$	2.15819	−	3.73809i	0.0804868	−	0.139407i	0.903459	+	0.428674i	$0.141019\pi$
$720$		0			0
$721$	14.0375	−	36.0449i	0.522783	−	1.34238i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.8642			0.514903
$726$		0			0
$727$	10.2483	+	17.7506i	0.380090	+	0.658334i	0.991075	−	0.133308i	$-0.0425598\pi$
$727$	10.2483	+	17.7506i	0.380090	+	0.658334i	−0.610985	+	0.791642i	$0.709226\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.01411	+	13.8808i	−0.296413	+	0.513402i
$732$		0			0
$733$	−12.6661	−	21.9383i	−0.467833	−	0.810310i	0.531491	−	0.847064i	$-0.321632\pi$
$733$	−12.6661	−	21.9383i	−0.467833	−	0.810310i	−0.999324	+	0.0367533i	$0.988298\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.86356	+	10.1560i	−0.215987	+	0.374100i
$738$		0			0
$739$	−6.63391	−	11.4903i	−0.244032	−	0.422676i	0.717827	−	0.696222i	$-0.245137\pi$
$739$	−6.63391	−	11.4903i	−0.244032	−	0.422676i	−0.961859	+	0.273545i	$0.911804\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.6116	+	39.1644i	−0.829538	+	1.43680i	0.0688624	+	0.997626i	$0.478063\pi$
$743$	−22.6116	+	39.1644i	−0.829538	+	1.43680i	−0.898401	+	0.439176i	$0.855270\pi$
$744$		0			0
$745$	−14.8608	+	25.7397i	−0.544459	+	0.943031i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	17.7940	−	2.72981i	0.650178	−	0.0997449i
$750$		0			0
$751$	14.1898	+	24.5775i	0.517795	+	0.896847i	0.999786	+	0.0206709i	$0.00658022\pi$
$751$	14.1898	+	24.5775i	0.517795	+	0.896847i	−0.481992	+	0.876176i	$0.660086\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	25.6435			0.933263
$756$		0			0
$757$	5.08483			0.184811			0.0924056	−	0.995721i	$-0.470544\pi$
$757$	5.08483			0.184811			0.0924056	+	0.995721i	$0.470544\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.8612	+	32.6686i	0.683720	+	1.18424i	0.973837	+	0.227246i	$0.0729722\pi$
$761$	18.8612	+	32.6686i	0.683720	+	1.18424i	−0.290118	+	0.956991i	$0.593694\pi$
$762$		0			0
$763$	−16.0848	+	41.3020i	−0.582310	+	1.49523i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.8614	+	20.5446i	−0.428292	+	0.741823i
$768$		0			0
$769$	11.8729	−	20.5644i	0.428147	−	0.741572i	−0.568562	−	0.822641i	$-0.692500\pi$
$769$	11.8729	−	20.5644i	0.428147	−	0.741572i	0.996709	+	0.0810688i	$0.0258333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.5347	−	33.8351i	−0.702614	−	1.21696i	−0.967546	−	0.252696i	$-0.918683\pi$
$773$	−19.5347	−	33.8351i	−0.702614	−	1.21696i	0.264932	−	0.964267i	$-0.414650\pi$
$774$		0			0
$775$	−0.626657	+	1.08540i	−0.0225102	+	0.0389888i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	19.8504	+	34.3819i	0.711214	+	1.23186i
$780$		0			0
$781$	−5.27011	+	9.12810i	−0.188579	+	0.326629i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.4697	−	19.8661i	−0.409370	−	0.709050i
$786$		0			0
$787$	3.80915			0.135782			0.0678908	−	0.997693i	$-0.478373\pi$
$787$	3.80915			0.135782			0.0678908	+	0.997693i	$0.478373\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−35.4173	+	5.43342i	−1.25929	+	0.193190i
$792$		0			0
$793$	20.0140	−	34.6653i	0.710718	−	1.23100i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.8239	−	18.7476i	0.383404	−	0.664075i	−0.608143	−	0.793828i	$-0.708085\pi$
$797$	10.8239	−	18.7476i	0.383404	−	0.664075i	0.991546	+	0.129753i	$0.0414184\pi$
$798$		0			0
$799$	0.691743	+	1.19813i	0.0244721	+	0.0423870i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	16.9900			0.599564
$804$		0			0
$805$	1.75248	−	0.268851i	0.0617667	−	0.00947574i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.5128	+	32.0652i	0.650877	+	1.12735i	0.982910	+	0.184084i	$0.0589319\pi$
$809$	18.5128	+	32.0652i	0.650877	+	1.12735i	−0.332034	+	0.943268i	$0.607735\pi$
$810$		0			0
$811$	5.37416			0.188712			0.0943561	−	0.995539i	$-0.469921\pi$
$811$	5.37416			0.188712			0.0943561	+	0.995539i	$0.469921\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−13.6243			−0.477239
$816$		0			0
$817$	23.2696			0.814101
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.22239			−0.0775619			−0.0387809	−	0.999248i	$-0.512347\pi$
$821$	−2.22239			−0.0775619			−0.0387809	+	0.999248i	$0.512347\pi$
$822$		0			0
$823$	37.1073			1.29348			0.646740	−	0.762710i	$-0.276132\pi$
$823$	37.1073			1.29348			0.646740	+	0.762710i	$0.276132\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−19.4790			−0.677351			−0.338676	−	0.940903i	$-0.609979\pi$
$827$	−19.4790			−0.677351			−0.338676	+	0.940903i	$0.609979\pi$
$828$		0			0
$829$	0.137129	+	0.237514i	0.00476267	+	0.00824919i	0.868397	−	0.495870i	$-0.165151\pi$
$829$	0.137129	+	0.237514i	0.00476267	+	0.00824919i	−0.863634	+	0.504119i	$0.831817\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−21.7292	+	6.82772i	−0.752873	+	0.236566i
$834$		0			0
$835$	6.99314			0.242007
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.0711	−	36.4962i	−0.727455	−	1.25999i	−0.957956	−	0.286917i	$-0.907370\pi$
$839$	−21.0711	−	36.4962i	−0.727455	−	1.25999i	0.230501	−	0.973072i	$-0.425964\pi$
$840$		0			0
$841$	−5.96666	+	10.3346i	−0.205747	+	0.356364i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.99671	−	3.45840i	0.0686888	−	0.118973i
$846$		0			0
$847$	−9.07328	+	23.2980i	−0.311762	+	0.800528i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.16702			−0.0742844
$852$		0			0
$853$	22.3086	+	38.6397i	0.763833	+	1.32300i	0.940862	+	0.338791i	$0.110018\pi$
$853$	22.3086	+	38.6397i	0.763833	+	1.32300i	−0.177029	+	0.984206i	$0.556649\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.66614	+	6.34993i	−0.125233	+	0.216910i	−0.921824	−	0.387609i	$-0.873301\pi$
$857$	−3.66614	+	6.34993i	−0.125233	+	0.216910i	0.796591	+	0.604518i	$0.206634\pi$
$858$		0			0
$859$	1.35073	+	2.33953i	0.0460863	+	0.0798238i	0.888148	−	0.459557i	$-0.151992\pi$
$859$	1.35073	+	2.33953i	0.0460863	+	0.0798238i	−0.842062	+	0.539381i	$0.818658\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.40188	+	12.8204i	−0.251963	+	0.436413i	−0.964066	−	0.265662i	$-0.914409\pi$
$863$	−7.40188	+	12.8204i	−0.251963	+	0.436413i	0.712103	+	0.702075i	$0.247743\pi$
$864$		0			0
$865$	−11.6429	−	20.1661i	−0.395870	−	0.685668i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.44449	+	5.96603i	−0.116846	+	0.202384i
$870$		0			0
$871$	−18.4660	+	31.9840i	−0.625695	+	1.08374i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	19.9648	+	24.9007i	0.674934	+	0.841797i
$876$		0			0
$877$	5.54807	+	9.60954i	0.187345	+	0.324491i	0.944364	−	0.328902i	$-0.106678\pi$
$877$	5.54807	+	9.60954i	0.187345	+	0.324491i	−0.757019	+	0.653393i	$0.773345\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−15.0536			−0.507168			−0.253584	−	0.967313i	$-0.581609\pi$
$881$	−15.0536			−0.507168			−0.253584	+	0.967313i	$0.581609\pi$
$882$		0			0
$883$	2.39418			0.0805704			0.0402852	−	0.999188i	$-0.487173\pi$
$883$	2.39418			0.0805704			0.0402852	+	0.999188i	$0.487173\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.46697	−	4.27292i	−0.0828328	−	0.143471i	0.821633	−	0.570017i	$-0.193063\pi$
$887$	−2.46697	−	4.27292i	−0.0828328	−	0.143471i	−0.904466	+	0.426546i	$0.859730\pi$
$888$		0			0
$889$	17.5274	+	21.8607i	0.587850	+	0.733184i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.00427	−	1.73944i	0.0336065	−	0.0582081i
$894$		0			0
$895$	−7.93047	+	13.7360i	−0.265086	+	0.459143i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.85017	−	3.20459i	−0.0617067	−	0.106879i
$900$		0			0
$901$	−1.51730	+	2.62804i	−0.0505486	+	0.0875527i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.11200	+	1.92604i	0.0369642	+	0.0640238i
$906$		0			0
$907$	1.69815	−	2.94129i	0.0563863	−	0.0976639i	−0.836454	−	0.548036i	$-0.815376\pi$
$907$	1.69815	−	2.94129i	0.0563863	−	0.0976639i	0.892841	+	0.450373i	$0.148709\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.65142	−	8.05649i	−0.154108	−	0.266924i	0.778626	−	0.627489i	$-0.215917\pi$
$911$	−4.65142	−	8.05649i	−0.154108	−	0.266924i	−0.932734	+	0.360565i	$0.882584\pi$
$912$		0			0
$913$	20.0110			0.662268
$914$		0			0
$915$		0			0
$916$		0			0
$917$	21.4722	−	55.1355i	0.709076	−	1.82073i
$918$		0			0
$919$	8.92656	−	15.4613i	0.294460	−	0.510020i	−0.680399	−	0.732842i	$-0.738194\pi$
$919$	8.92656	−	15.4613i	0.294460	−	0.510020i	0.974859	+	0.222822i	$0.0715268\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−16.5970	+	28.7469i	−0.546298	+	0.946216i
$924$		0			0
$925$	−5.89737	−	10.2145i	−0.193904	−	0.335852i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	47.2861			1.55141			0.775703	−	0.631098i	$-0.217395\pi$
$929$	47.2861			1.55141			0.775703	+	0.631098i	$0.217395\pi$
$930$		0			0
$931$	24.3575	+	22.3637i	0.798286	+	0.732939i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.40917	+	5.90486i	0.111492	+	0.193110i
$936$		0			0
$937$	21.2493			0.694183			0.347092	−	0.937831i	$-0.387169\pi$
$937$	21.2493			0.694183			0.347092	+	0.937831i	$0.387169\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	60.0810			1.95858			0.979292	−	0.202455i	$-0.0648920\pi$
$941$	60.0810			1.95858			0.979292	+	0.202455i	$0.0648920\pi$
$942$		0			0
$943$	3.34606			0.108963
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.66935			−0.119238			−0.0596189	−	0.998221i	$-0.518989\pi$
$947$	−3.66935			−0.119238			−0.0596189	+	0.998221i	$0.518989\pi$
$948$		0			0
$949$	53.5062			1.73688
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.837421			−0.0271267			−0.0135634	−	0.999908i	$-0.504317\pi$
$953$	−0.837421			−0.0271267			−0.0135634	+	0.999908i	$0.504317\pi$
$954$		0			0
$955$	−13.7055	−	23.7385i	−0.443498	−	0.768161i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	46.9525	−	7.20306i	1.51618	−	0.232599i
$960$		0			0
$961$	−30.6655			−0.989209
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.15574	+	3.73386i	0.0693958	+	0.120197i
$966$		0			0
$967$	21.8856	−	37.9070i	0.703795	−	1.21901i	−0.263330	−	0.964706i	$-0.584821\pi$
$967$	21.8856	−	37.9070i	0.703795	−	1.21901i	0.967125	−	0.254302i	$-0.0818458\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.3059	−	35.1709i	0.651648	−	1.12869i	−0.331075	−	0.943605i	$-0.607411\pi$
$971$	20.3059	−	35.1709i	0.651648	−	1.12869i	0.982723	−	0.185083i	$-0.0592554\pi$
$972$		0			0
$973$	2.98560	−	0.458025i	0.0957138	−	0.0146836i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−57.4959			−1.83946			−0.919728	−	0.392556i	$-0.871591\pi$
$977$	−57.4959			−1.83946			−0.919728	+	0.392556i	$0.871591\pi$
$978$		0			0
$979$	−7.51689	−	13.0196i	−0.240241	−	0.416109i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.72971	+	11.6562i	−0.214644	+	0.371775i	−0.953162	−	0.302459i	$-0.902193\pi$
$983$	−6.72971	+	11.6562i	−0.214644	+	0.371775i	0.738518	+	0.674234i	$0.235526\pi$
$984$		0			0
$985$	−18.2551	−	31.6188i	−0.581657	−	1.00746i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.980604	−	1.69846i	0.0311814	−	0.0540078i
$990$		0			0
$991$	−17.7821	−	30.7995i	−0.564867	−	0.978379i	−0.997062	−	0.0765983i	$-0.975594\pi$
$991$	−17.7821	−	30.7995i	−0.564867	−	0.978379i	0.432195	−	0.901780i	$-0.357739\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.42036	−	16.3165i	0.298645	−	0.517269i
$996$		0			0
$997$	−16.3644	+	28.3440i	−0.518267	+	0.897665i	0.481508	+	0.876442i	$0.340089\pi$
$997$	−16.3644	+	28.3440i	−0.518267	+	0.897665i	−0.999775	+	0.0212228i	$0.993244\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.c.793.8		22
3.2	odd	2		504.2.q.d.121.1	yes	22
4.3	odd	2		3024.2.q.k.2305.8		22
7.4	even	3		1512.2.t.d.361.4		22
9.2	odd	6		504.2.t.d.457.6	yes	22
9.7	even	3		1512.2.t.d.289.4		22
12.11	even	2		1008.2.q.k.625.11		22
21.11	odd	6		504.2.t.d.193.6	yes	22
28.11	odd	6		3024.2.t.l.1873.4		22
36.7	odd	6		3024.2.t.l.289.4		22
36.11	even	6		1008.2.t.k.961.6		22
63.11	odd	6		504.2.q.d.25.1	✓	22
63.25	even	3	inner	1512.2.q.c.1369.8		22
84.11	even	6		1008.2.t.k.193.6		22
252.11	even	6		1008.2.q.k.529.11		22
252.151	odd	6		3024.2.q.k.2881.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.1	✓	22	63.11	odd	6
504.2.q.d.121.1	yes	22	3.2	odd	2
504.2.t.d.193.6	yes	22	21.11	odd	6
504.2.t.d.457.6	yes	22	9.2	odd	6
1008.2.q.k.529.11		22	252.11	even	6
1008.2.q.k.625.11		22	12.11	even	2
1008.2.t.k.193.6		22	84.11	even	6
1008.2.t.k.961.6		22	36.11	even	6
1512.2.q.c.793.8		22	1.1	even	1	trivial
1512.2.q.c.1369.8		22	63.25	even	3	inner
1512.2.t.d.289.4		22	9.7	even	3
1512.2.t.d.361.4		22	7.4	even	3
3024.2.q.k.2305.8		22	4.3	odd	2
3024.2.q.k.2881.8		22	252.151	odd	6
3024.2.t.l.289.4		22	36.7	odd	6
3024.2.t.l.1873.4		22	28.11	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.841578 + 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +O(q^{10})\)	\(q+(0.841578 + 1.45766i) q^{5} +(1.65502 + 2.06419i) q^{7} +(0.622490 - 1.07818i) q^{11} +(1.96039 - 3.39550i) q^{13} +(1.62691 + 2.81788i) q^{17} +(2.36192 - 4.09097i) q^{19} +(-0.199068 - 0.344795i) q^{23} +(1.08349 - 1.87667i) q^{25} +(3.19896 + 5.54076i) q^{29} -0.578367 q^{31} +(-1.61605 + 4.14963i) q^{35} +(2.72146 - 4.71371i) q^{37} +(-4.20216 + 7.27836i) q^{41} +(2.46299 + 4.26603i) q^{43} +0.425190 q^{47} +(-1.52179 + 6.83258i) q^{49} +(0.466315 + 0.807681i) q^{53} +2.09550 q^{55} -6.05054 q^{59} +10.2092 q^{61} +6.59930 q^{65} -9.41952 q^{67} -8.46617 q^{71} +(6.82340 + 11.8185i) q^{73} +(3.25582 - 0.499480i) q^{77} -5.53340 q^{79} +(8.03669 + 13.9199i) q^{83} +(-2.73833 + 4.74293i) q^{85} +(6.03776 - 10.4577i) q^{89} +(10.2535 - 1.57300i) q^{91} +7.95097 q^{95} +(-5.86046 - 10.1506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 - 5 * q^7	\( 22 q - 3 q^{5} - 5 q^{7} + 3 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} - 2 q^{23} - 10 q^{25} - 9 q^{29} + 8 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} + 10 q^{47} + 15 q^{49} - 11 q^{53} + 22 q^{55} - 38 q^{59} + 26 q^{61} + 26 q^{65} - 52 q^{67} + 48 q^{71} - 35 q^{73} - 17 q^{77} - 20 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} + 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 - 5 * q^7 + 3 * q^11 - 3 * q^13 - 7 * q^17 - q^19 - 2 * q^23 - 10 * q^25 - 9 * q^29 + 8 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 + 10 * q^47 + 15 * q^49 - 11 * q^53 + 22 * q^55 - 38 * q^59 + 26 * q^61 + 26 * q^65 - 52 * q^67 + 48 * q^71 - 35 * q^73 - 17 * q^77 - 20 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 + 24 * q^95 - 29 * q^97

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