LMFDB - Embedded newform 1512.2.t.d.361.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (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			361.6
Character	$\chi$	$=$	1512.361
Dual form			1512.2.t.d.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.481387 q^{5} +(2.53326 - 0.763277i) q^{7} +O(q^{10})$	$q+0.481387 q^{5} +(2.53326 - 0.763277i) q^{7} -3.38159 q^{11} +(-2.86067 + 4.95482i) q^{13} +(-2.75605 + 4.77362i) q^{17} +(2.18023 + 3.77626i) q^{19} -3.62585 q^{23} -4.76827 q^{25} +(-1.53131 - 2.65231i) q^{29} +(4.67459 + 8.09663i) q^{31} +(1.21948 - 0.367431i) q^{35} +(1.48552 + 2.57299i) q^{37} +(6.29558 - 10.9043i) q^{41} +(1.90827 + 3.30522i) q^{43} +(-1.88282 + 3.26114i) q^{47} +(5.83482 - 3.86716i) q^{49} +(-5.57860 + 9.66242i) q^{53} -1.62786 q^{55} +(4.21141 + 7.29438i) q^{59} +(3.64312 - 6.31007i) q^{61} +(-1.37709 + 2.38519i) q^{65} +(-1.28571 - 2.22692i) q^{67} +3.94304 q^{71} +(-0.862216 + 1.49340i) q^{73} +(-8.56646 + 2.58109i) q^{77} +(2.79980 - 4.84940i) q^{79} +(0.119494 + 0.206970i) q^{83} +(-1.32673 + 2.29796i) q^{85} +(-0.648116 - 1.12257i) q^{89} +(-3.46492 + 14.7353i) q^{91} +(1.04953 + 1.81784i) q^{95} +(-7.02669 - 12.1706i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) $ 22 * q + 6 * q^5 + 7 * q^7	$ 22 q + 6 q^{5} + 7 q^{7} - 6 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} + 4 q^{23} + 20 q^{25} - 9 q^{29} - 4 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} - 5 q^{47} - 15 q^{49} - 11 q^{53} + 22 q^{55} + 19 q^{59} - 13 q^{61} - 13 q^{65} + 26 q^{67} + 48 q^{71} - 35 q^{73} + 4 q^{77} + 10 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} - 12 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q + 6 * q^5 + 7 * q^7 - 6 * q^11 - 3 * q^13 - 7 * q^17 - q^19 + 4 * q^23 + 20 * q^25 - 9 * q^29 - 4 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 - 5 * q^47 - 15 * q^49 - 11 * q^53 + 22 * q^55 + 19 * q^59 - 13 * q^61 - 13 * q^65 + 26 * q^67 + 48 * q^71 - 35 * q^73 + 4 * q^77 + 10 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 - 12 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	0.481387			0.215283			0.107641	−	0.994190i	$-0.465670\pi$
$5$	0.481387			0.215283			0.107641	+	0.994190i	$0.465670\pi$
$6$		0			0
$7$	2.53326	−	0.763277i	0.957482	−	0.288491i
$7$	2.53326	−	0.763277i	0.957482	−	0.288491i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.38159			−1.01959			−0.509794	−	0.860296i	$-0.670279\pi$
$11$	−3.38159			−1.01959			−0.509794	+	0.860296i	$0.670279\pi$
$12$		0			0
$13$	−2.86067	+	4.95482i	−0.793406	+	1.37422i	0.130440	+	0.991456i	$0.458361\pi$
$13$	−2.86067	+	4.95482i	−0.793406	+	1.37422i	−0.923846	+	0.382764i	$0.874972\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.75605	+	4.77362i	−0.668440	+	1.15777i	0.309900	+	0.950769i	$0.399704\pi$
$17$	−2.75605	+	4.77362i	−0.668440	+	1.15777i	−0.978340	+	0.207003i	$0.933629\pi$
$18$		0			0
$19$	2.18023	+	3.77626i	0.500178	+	0.866334i	1.00000		0.000205746i	$6.54909e-5\pi$
$19$	2.18023	+	3.77626i	0.500178	+	0.866334i	−0.499822	+	0.866128i	$0.666601\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.62585			−0.756042			−0.378021	−	0.925797i	$-0.623395\pi$
$23$	−3.62585			−0.756042			−0.378021	+	0.925797i	$0.623395\pi$
$24$		0			0
$25$	−4.76827			−0.953653
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.53131	−	2.65231i	−0.284358	−	0.492522i	0.688095	−	0.725620i	$-0.258447\pi$
$29$	−1.53131	−	2.65231i	−0.284358	−	0.492522i	−0.972453	+	0.233098i	$0.925114\pi$
$30$		0			0
$31$	4.67459	+	8.09663i	0.839581	+	1.45420i	0.890245	+	0.455481i	$0.150533\pi$
$31$	4.67459	+	8.09663i	0.839581	+	1.45420i	−0.0506646	+	0.998716i	$0.516134\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.21948	−	0.367431i	0.206130	−	0.0621072i
$36$		0			0
$37$	1.48552	+	2.57299i	0.244218	+	0.422997i	0.961911	−	0.273361i	$-0.0881355\pi$
$37$	1.48552	+	2.57299i	0.244218	+	0.422997i	−0.717694	+	0.696359i	$0.754802\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.29558	−	10.9043i	0.983204	−	1.70296i	0.333545	−	0.942734i	$-0.391755\pi$
$41$	6.29558	−	10.9043i	0.983204	−	1.70296i	0.649659	−	0.760226i	$-0.274912\pi$
$42$		0			0
$43$	1.90827	+	3.30522i	0.291009	+	0.504042i	0.974049	−	0.226339i	$-0.0726758\pi$
$43$	1.90827	+	3.30522i	0.291009	+	0.504042i	−0.683040	+	0.730381i	$0.739342\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.88282	+	3.26114i	−0.274638	+	0.475687i	−0.970044	−	0.242930i	$-0.921891\pi$
$47$	−1.88282	+	3.26114i	−0.274638	+	0.475687i	0.695406	+	0.718617i	$0.255225\pi$
$48$		0			0
$49$	5.83482	−	3.86716i	0.833545	−	0.552451i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.57860	+	9.66242i	−0.766280	+	1.32724i	0.173287	+	0.984871i	$0.444561\pi$
$53$	−5.57860	+	9.66242i	−0.766280	+	1.32724i	−0.939567	+	0.342364i	$0.888772\pi$
$54$		0			0
$55$	−1.62786			−0.219500
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.21141	+	7.29438i	0.548279	+	0.949647i	0.998393	+	0.0566756i	$0.0180501\pi$
$59$	4.21141	+	7.29438i	0.548279	+	0.949647i	−0.450114	+	0.892971i	$0.648617\pi$
$60$		0			0
$61$	3.64312	−	6.31007i	0.466454	−	0.807922i	−0.532812	−	0.846234i	$-0.678865\pi$
$61$	3.64312	−	6.31007i	0.466454	−	0.807922i	0.999266	+	0.0383116i	$0.0121979\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.37709	+	2.38519i	−0.170807	+	0.295846i
$66$		0			0
$67$	−1.28571	−	2.22692i	−0.157075	−	0.272062i	0.776738	−	0.629824i	$-0.216873\pi$
$67$	−1.28571	−	2.22692i	−0.157075	−	0.272062i	−0.933813	+	0.357763i	$0.883540\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.94304			0.467953			0.233977	−	0.972242i	$-0.424826\pi$
$71$	3.94304			0.467953			0.233977	+	0.972242i	$0.424826\pi$
$72$		0			0
$73$	−0.862216	+	1.49340i	−0.100915	+	0.174790i	−0.912062	−	0.410053i	$-0.865510\pi$
$73$	−0.862216	+	1.49340i	−0.100915	+	0.174790i	0.811147	+	0.584842i	$0.198844\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.56646	+	2.58109i	−0.976238	+	0.294143i
$78$		0			0
$79$	2.79980	−	4.84940i	0.315002	−	0.545600i	−0.664436	−	0.747345i	$-0.731328\pi$
$79$	2.79980	−	4.84940i	0.315002	−	0.545600i	0.979438	+	0.201746i	$0.0646614\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.119494	+	0.206970i	0.0131162	+	0.0227179i	0.872509	−	0.488598i	$-0.162492\pi$
$83$	0.119494	+	0.206970i	0.0131162	+	0.0227179i	−0.859393	+	0.511316i	$0.829158\pi$
$84$		0			0
$85$	−1.32673	+	2.29796i	−0.143904	+	0.249249i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.648116	−	1.12257i	−0.0687002	−	0.118992i	0.829629	−	0.558315i	$-0.188552\pi$
$89$	−0.648116	−	1.12257i	−0.0687002	−	0.118992i	−0.898329	+	0.439323i	$0.855219\pi$
$90$		0			0
$91$	−3.46492	+	14.7353i	−0.363222	+	1.54468i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.04953	+	1.81784i	0.107680	+	0.186507i
$96$		0			0
$97$	−7.02669	−	12.1706i	−0.713452	−	1.23574i	−0.963553	−	0.267516i	$-0.913797\pi$
$97$	−7.02669	−	12.1706i	−0.713452	−	1.23574i	0.250101	−	0.968220i	$-0.419536\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−10.6064			−1.05538			−0.527690	−	0.849437i	$-0.676942\pi$
$101$	−10.6064			−1.05538			−0.527690	+	0.849437i	$0.676942\pi$
$102$		0			0
$103$	−0.159416			−0.0157077			−0.00785385	−	0.999969i	$-0.502500\pi$
$103$	−0.159416			−0.0157077			−0.00785385	+	0.999969i	$0.502500\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.99030	+	6.91140i	0.385757	+	0.668150i	0.991874	−	0.127225i	$-0.0406071\pi$
$107$	3.99030	+	6.91140i	0.385757	+	0.668150i	−0.606117	+	0.795375i	$0.707274\pi$
$108$		0			0
$109$	−6.85612	+	11.8751i	−0.656697	+	1.13743i	0.324769	+	0.945793i	$0.394714\pi$
$109$	−6.85612	+	11.8751i	−0.656697	+	1.13743i	−0.981466	+	0.191639i	$0.938620\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−8.98656	+	15.5652i	−0.845384	+	1.46425i	0.0399031	+	0.999204i	$0.487295\pi$
$113$	−8.98656	+	15.5652i	−0.845384	+	1.46425i	−0.885287	+	0.465045i	$0.846038\pi$
$114$		0			0
$115$	−1.74544			−0.162763
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.33820	+	14.1964i	−0.306012	+	1.30139i
$120$		0			0
$121$	0.435176			0.0395615
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.70232			−0.420588
$126$		0			0
$127$	18.9684			1.68317			0.841587	−	0.540121i	$-0.181622\pi$
$127$	18.9684			1.68317			0.841587	+	0.540121i	$0.181622\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.88232			0.426570			0.213285	−	0.976990i	$-0.431584\pi$
$131$	4.88232			0.426570			0.213285	+	0.976990i	$0.431584\pi$
$132$		0			0
$133$	8.40541	+	7.90214i	0.728842	+	0.685203i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.47482			0.553181			0.276591	−	0.960988i	$-0.410795\pi$
$137$	6.47482			0.553181			0.276591	+	0.960988i	$0.410795\pi$
$138$		0			0
$139$	−11.3740	+	19.7003i	−0.964727	+	1.67096i	−0.254381	+	0.967104i	$0.581872\pi$
$139$	−11.3740	+	19.7003i	−0.964727	+	1.67096i	−0.710346	+	0.703852i	$0.751462\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.67362	−	16.7552i	0.808948	−	1.40114i
$144$		0			0
$145$	−0.737155	−	1.27679i	−0.0612174	−	0.106032i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	14.2046			1.16369			0.581843	−	0.813301i	$-0.302332\pi$
$149$	14.2046			1.16369			0.581843	+	0.813301i	$0.302332\pi$
$150$		0			0
$151$	2.52259			0.205285			0.102643	−	0.994718i	$-0.467270\pi$
$151$	2.52259			0.205285			0.102643	+	0.994718i	$0.467270\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.25029	+	3.89761i	0.180747	+	0.313064i
$156$		0			0
$157$	−8.74064	−	15.1392i	−0.697579	−	1.20824i	−0.969303	−	0.245867i	$-0.920927\pi$
$157$	−8.74064	−	15.1392i	−0.697579	−	1.20824i	0.271724	−	0.962375i	$-0.412406\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−9.18523	+	2.76753i	−0.723897	+	0.218112i
$162$		0			0
$163$	0.881184	+	1.52625i	0.0690196	+	0.119546i	0.898470	−	0.439035i	$-0.144680\pi$
$163$	0.881184	+	1.52625i	0.0690196	+	0.119546i	−0.829450	+	0.558580i	$0.811346\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.57220	−	6.18723i	0.276425	−	0.478782i	−0.694069	−	0.719909i	$-0.744184\pi$
$167$	3.57220	−	6.18723i	0.276425	−	0.478782i	0.970494	+	0.241127i	$0.0775169\pi$
$168$		0			0
$169$	−9.86684	−	17.0899i	−0.758988	−	1.31461i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.94691	−	8.56830i	0.376107	−	0.651436i	−0.614385	−	0.789006i	$-0.710596\pi$
$173$	4.94691	−	8.56830i	0.376107	−	0.651436i	0.990492	+	0.137570i	$0.0439293\pi$
$174$		0			0
$175$	−12.0793	+	3.63951i	−0.913106	+	0.275121i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.02967	+	3.51550i	−0.151705	+	0.262761i	−0.931854	−	0.362833i	$-0.881810\pi$
$179$	−2.02967	+	3.51550i	−0.151705	+	0.262761i	0.780149	+	0.625593i	$0.215143\pi$
$180$		0			0
$181$	4.58084			0.340491			0.170246	−	0.985402i	$-0.445544\pi$
$181$	4.58084			0.340491			0.170246	+	0.985402i	$0.445544\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.715109	+	1.23861i	0.0525759	+	0.0910641i
$186$		0			0
$187$	9.31984	−	16.1424i	0.681534	−	1.18045i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.59624	−	9.69298i	0.404930	−	0.701359i	−0.589383	−	0.807853i	$-0.700629\pi$
$191$	5.59624	−	9.69298i	0.404930	−	0.701359i	0.994313	+	0.106494i	$0.0339626\pi$
$192$		0			0
$193$	−8.14679	−	14.1106i	−0.586419	−	1.01571i	−0.994697	−	0.102849i	$-0.967204\pi$
$193$	−8.14679	−	14.1106i	−0.586419	−	1.01571i	0.408278	−	0.912857i	$-0.366129\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.17438			0.226165			0.113082	−	0.993586i	$-0.463928\pi$
$197$	3.17438			0.226165			0.113082	+	0.993586i	$0.463928\pi$
$198$		0			0
$199$	1.44140	−	2.49658i	0.102178	−	0.176978i	−0.810404	−	0.585872i	$-0.800752\pi$
$199$	1.44140	−	2.49658i	0.102178	−	0.176978i	0.912582	+	0.408894i	$0.134085\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.90367	−	5.55019i	−0.414356	−	0.389547i
$204$		0			0
$205$	3.03061	−	5.24917i	0.211667	−	0.366618i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.37264	−	12.7698i	−0.509976	−	0.883305i
$210$		0			0
$211$	−0.242718	+	0.420400i	−0.0167094	+	0.0289415i	−0.874259	−	0.485459i	$-0.838652\pi$
$211$	−0.242718	+	0.420400i	−0.0167094	+	0.0289415i	0.857550	+	0.514401i	$0.171986\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.918617	+	1.59109i	0.0626492	+	0.108512i
$216$		0			0
$217$	18.0219	+	16.9429i	1.22341	+	1.15016i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−15.7683	−	27.3115i	−1.06069	−	1.83717i
$222$		0			0
$223$	2.14795	+	3.72037i	0.143838	+	0.249134i	0.928939	−	0.370234i	$-0.120722\pi$
$223$	2.14795	+	3.72037i	0.143838	+	0.249134i	−0.785101	+	0.619368i	$0.787389\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.3827			1.15373			0.576866	−	0.816839i	$-0.304275\pi$
$227$	17.3827			1.15373			0.576866	+	0.816839i	$0.304275\pi$
$228$		0			0
$229$	7.33125			0.484463			0.242231	−	0.970218i	$-0.422121\pi$
$229$	7.33125			0.484463			0.242231	+	0.970218i	$0.422121\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.16624	+	3.75205i	0.141915	+	0.245805i	0.928218	−	0.372037i	$-0.121341\pi$
$233$	2.16624	+	3.75205i	0.141915	+	0.245805i	−0.786302	+	0.617842i	$0.788007\pi$
$234$		0			0
$235$	−0.906366	+	1.56987i	−0.0591248	+	0.102407i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.77960	+	3.08236i	−0.115113	+	0.199381i	−0.917825	−	0.396986i	$-0.870056\pi$
$239$	−1.77960	+	3.08236i	−0.115113	+	0.199381i	0.802712	+	0.596367i	$0.203390\pi$
$240$		0			0
$241$	16.0185			1.03184			0.515921	−	0.856636i	$-0.327450\pi$
$241$	16.0185			1.03184			0.515921	+	0.856636i	$0.327450\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.80881	−	1.86160i	0.179448	−	0.118933i
$246$		0			0
$247$	−24.9476			−1.58738
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.8007			0.807972			0.403986	−	0.914765i	$-0.367625\pi$
$251$	12.8007			0.807972			0.403986	+	0.914765i	$0.367625\pi$
$252$		0			0
$253$	12.2612			0.770852
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−16.4154			−1.02396			−0.511981	−	0.858997i	$-0.671088\pi$
$257$	−16.4154			−1.02396			−0.511981	+	0.858997i	$0.671088\pi$
$258$		0			0
$259$	5.72711	+	5.38420i	0.355865	+	0.334558i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−25.6528			−1.58182			−0.790910	−	0.611933i	$-0.790392\pi$
$263$	−25.6528			−1.58182			−0.790910	+	0.611933i	$0.790392\pi$
$264$		0			0
$265$	−2.68547	+	4.65136i	−0.164967	+	0.285731i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.35397	+	9.27335i	−0.326437	+	0.565406i	−0.981802	−	0.189906i	$-0.939182\pi$
$269$	−5.35397	+	9.27335i	−0.326437	+	0.565406i	0.655365	+	0.755313i	$0.272515\pi$
$270$		0			0
$271$	−12.7513	−	22.0859i	−0.774587	−	1.34162i	−0.935026	−	0.354578i	$-0.884624\pi$
$271$	−12.7513	−	22.0859i	−0.774587	−	1.34162i	0.160439	−	0.987046i	$-0.448709\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	16.1243			0.972334
$276$		0			0
$277$	−12.7825			−0.768023			−0.384012	−	0.923328i	$-0.625458\pi$
$277$	−12.7825			−0.768023			−0.384012	+	0.923328i	$0.625458\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.4763	+	18.1454i	0.624961	+	1.08246i	0.988548	+	0.150904i	$0.0482185\pi$
$281$	10.4763	+	18.1454i	0.624961	+	1.08246i	−0.363587	+	0.931560i	$0.618448\pi$
$282$		0			0
$283$	−7.53085	−	13.0438i	−0.447663	−	0.775374i	0.550571	−	0.834788i	$-0.314410\pi$
$283$	−7.53085	−	13.0438i	−0.447663	−	0.775374i	−0.998233	+	0.0594141i	$0.981077\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.62537	−	32.4286i	0.450112	−	1.91420i
$288$		0			0
$289$	−6.69162	−	11.5902i	−0.393625	−	0.681778i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.134459	+	0.232890i	−0.00785519	+	0.0136056i	−0.869926	−	0.493182i	$-0.835834\pi$
$293$	−0.134459	+	0.232890i	−0.00785519	+	0.0136056i	0.862071	+	0.506787i	$0.169167\pi$
$294$		0			0
$295$	2.02732	+	3.51142i	0.118035	+	0.204443i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.3724	−	17.9654i	0.599849	−	1.03897i
$300$		0			0
$301$	7.35695	+	6.91645i	0.424048	+	0.398658i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.75375	−	3.03759i	0.100420	−	0.173932i
$306$		0			0
$307$	−5.03514			−0.287371			−0.143685	−	0.989623i	$-0.545895\pi$
$307$	−5.03514			−0.287371			−0.143685	+	0.989623i	$0.545895\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.23815	+	3.87659i	0.126914	+	0.219821i	0.922479	−	0.386046i	$-0.126159\pi$
$311$	2.23815	+	3.87659i	0.126914	+	0.219821i	−0.795566	+	0.605868i	$0.792826\pi$
$312$		0			0
$313$	−5.48895	+	9.50715i	−0.310254	+	0.537376i	−0.978417	−	0.206639i	$-0.933747\pi$
$313$	−5.48895	+	9.50715i	−0.310254	+	0.537376i	0.668163	+	0.744015i	$0.267081\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.4826	−	21.6205i	0.701092	−	1.21433i	−0.266992	−	0.963699i	$-0.586030\pi$
$317$	12.4826	−	21.6205i	0.701092	−	1.21433i	0.968084	−	0.250628i	$-0.0806371\pi$
$318$		0			0
$319$	5.17828	+	8.96905i	0.289928	+	0.502170i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−24.0352			−1.33736
$324$		0			0
$325$	13.6404	−	23.6259i	0.756635	−	1.31053i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.28052	+	9.69844i	−0.125729	+	0.534692i
$330$		0			0
$331$	−6.01206	+	10.4132i	−0.330453	+	0.572361i	−0.982601	−	0.185731i	$-0.940535\pi$
$331$	−6.01206	+	10.4132i	−0.330453	+	0.572361i	0.652148	+	0.758092i	$0.273868\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.618925	−	1.07201i	−0.0338155	−	0.0585702i
$336$		0			0
$337$	−14.1286	+	24.4715i	−0.769636	+	1.33305i	0.168125	+	0.985766i	$0.446229\pi$
$337$	−14.1286	+	24.4715i	−0.769636	+	1.33305i	−0.937761	+	0.347282i	$0.887105\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.8076	−	27.3795i	−0.856027	−	1.48268i
$342$		0			0
$343$	11.8294	−	14.2501i	0.638728	−	0.769433i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.80293	+	16.9792i	0.526249	+	0.911490i	0.999532	+	0.0305797i	$0.00973535\pi$
$347$	9.80293	+	16.9792i	0.526249	+	0.911490i	−0.473283	+	0.880910i	$0.656931\pi$
$348$		0			0
$349$	−8.22904	−	14.2531i	−0.440490	−	0.762952i	0.557236	−	0.830354i	$-0.311862\pi$
$349$	−8.22904	−	14.2531i	−0.440490	−	0.762952i	−0.997726	+	0.0674029i	$0.978529\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	27.3709			1.45680			0.728402	−	0.685150i	$-0.240263\pi$
$353$	27.3709			1.45680			0.728402	+	0.685150i	$0.240263\pi$
$354$		0			0
$355$	1.89813			0.100742
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.88714	−	13.6609i	−0.416267	−	0.720996i	0.579293	−	0.815119i	$-0.303329\pi$
$359$	−7.88714	−	13.6609i	−0.416267	−	0.720996i	−0.995561	+	0.0941231i	$0.969995\pi$
$360$		0			0
$361$	−0.00677168	+	0.0117289i	−0.000356404	+	0.000617310i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.415060	+	0.718905i	−0.0217252	+	0.0376292i
$366$		0			0
$367$	18.8137			0.982066			0.491033	−	0.871141i	$-0.336619\pi$
$367$	18.8137			0.982066			0.491033	+	0.871141i	$0.336619\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.75695	+	28.7355i	−0.350803	+	1.49187i
$372$		0			0
$373$	−17.5737			−0.909934			−0.454967	−	0.890508i	$-0.650349\pi$
$373$	−17.5737			−0.909934			−0.454967	+	0.890508i	$0.650349\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	17.5223			0.902446
$378$		0			0
$379$	34.4618			1.77018			0.885091	−	0.465419i	$-0.154096\pi$
$379$	34.4618			1.77018			0.885091	+	0.465419i	$0.154096\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	22.7410			1.16201			0.581005	−	0.813900i	$-0.302660\pi$
$383$	22.7410			1.16201			0.581005	+	0.813900i	$0.302660\pi$
$384$		0			0
$385$	−4.12378	+	1.24250i	−0.210167	+	0.0633239i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.7638			−0.799255			−0.399628	−	0.916678i	$-0.630861\pi$
$389$	−15.7638			−0.799255			−0.399628	+	0.916678i	$0.630861\pi$
$390$		0			0
$391$	9.99303	−	17.3084i	0.505369	−	0.875325i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.34779	−	2.33444i	0.0678145	−	0.117458i
$396$		0			0
$397$	−5.39875	−	9.35091i	−0.270955	−	0.469308i	0.698151	−	0.715950i	$-0.254006\pi$
$397$	−5.39875	−	9.35091i	−0.270955	−	0.469308i	−0.969107	+	0.246642i	$0.920673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.3295			−0.615704			−0.307852	−	0.951434i	$-0.599610\pi$
$401$	−12.3295			−0.615704			−0.307852	+	0.951434i	$0.599610\pi$
$402$		0			0
$403$	−53.4898			−2.66452
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.02342	−	8.70082i	−0.249002	−	0.431284i
$408$		0			0
$409$	−9.31771	−	16.1387i	−0.460731	−	0.798010i	0.538266	−	0.842775i	$-0.319079\pi$
$409$	−9.31771	−	16.1387i	−0.460731	−	0.798010i	−0.998998	+	0.0447650i	$0.985746\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.2362	+	15.2641i	0.798932	+	0.751096i
$414$		0			0
$415$	0.0575230	+	0.0996328i	0.00282369	+	0.00489078i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.90976	−	10.2360i	0.288711	−	0.500062i	−0.684791	−	0.728739i	$-0.740107\pi$
$419$	5.90976	−	10.2360i	0.288711	−	0.500062i	0.973502	+	0.228677i	$0.0734400\pi$
$420$		0			0
$421$	4.81800	+	8.34503i	0.234815	+	0.406712i	0.959219	−	0.282664i	$-0.0912182\pi$
$421$	4.81800	+	8.34503i	0.234815	+	0.406712i	−0.724404	+	0.689376i	$0.757885\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	13.1416	−	22.7619i	0.637460	−	1.10411i
$426$		0			0
$427$	4.41265	−	18.7658i	0.213543	−	0.908139i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.2913	−	31.6815i	0.881062	−	1.52604i	0.0309004	−	0.999522i	$-0.490163\pi$
$431$	18.2913	−	31.6815i	0.881062	−	1.52604i	0.850162	−	0.526522i	$-0.176504\pi$
$432$		0			0
$433$	−7.69388			−0.369744			−0.184872	−	0.982763i	$-0.559187\pi$
$433$	−7.69388			−0.369744			−0.184872	+	0.982763i	$0.559187\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.90518	−	13.6922i	−0.378156	−	0.654985i
$438$		0			0
$439$	10.2717	−	17.7911i	0.490241	−	0.849122i	−0.509696	−	0.860355i	$-0.670242\pi$
$439$	10.2717	−	17.7911i	0.490241	−	0.849122i	0.999937	+	0.0112324i	$0.00357545\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−16.8401	+	29.1679i	−0.800098	+	1.38581i	0.119454	+	0.992840i	$0.461886\pi$
$443$	−16.8401	+	29.1679i	−0.800098	+	1.38581i	−0.919551	+	0.392970i	$0.871448\pi$
$444$		0			0
$445$	−0.311995	−	0.540391i	−0.0147900	−	0.0256170i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.5141			1.06250			0.531252	−	0.847214i	$-0.321722\pi$
$449$	22.5141			1.06250			0.531252	+	0.847214i	$0.321722\pi$
$450$		0			0
$451$	−21.2891	+	36.8738i	−1.00246	+	1.73632i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.66797	+	7.09340i	−0.0781955	+	0.332544i
$456$		0			0
$457$	11.8559	−	20.5349i	0.554594	−	0.960584i	−0.443342	−	0.896353i	$-0.646207\pi$
$457$	11.8559	−	20.5349i	0.554594	−	0.960584i	0.997935	−	0.0642314i	$-0.0204596\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.57340	+	9.65342i	0.259579	+	0.449605i	0.966129	−	0.258059i	$-0.0830828\pi$
$461$	5.57340	+	9.65342i	0.259579	+	0.449605i	−0.706550	+	0.707663i	$0.749749\pi$
$462$		0			0
$463$	10.3208	−	17.8761i	0.479647	−	0.830773i	−0.520080	−	0.854117i	$-0.674098\pi$
$463$	10.3208	−	17.8761i	0.479647	−	0.830773i	0.999727	+	0.0233441i	$0.00743133\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.68477	+	15.0425i	0.401883	+	0.696082i	0.993953	−	0.109804i	$-0.0350224\pi$
$467$	8.68477	+	15.0425i	0.401883	+	0.696082i	−0.592070	+	0.805887i	$0.701689\pi$
$468$		0			0
$469$	−4.95680	−	4.66001i	−0.228884	−	0.215179i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.45300	−	11.1769i	−0.296709	−	0.513916i
$474$		0			0
$475$	−10.3959	−	18.0062i	−0.476997	−	0.826182i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.09033			0.186892			0.0934461	−	0.995624i	$-0.470212\pi$
$479$	4.09033			0.186892			0.0934461	+	0.995624i	$0.470212\pi$
$480$		0			0
$481$	−16.9983			−0.775056
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.38256	−	5.85876i	−0.153594	−	0.266033i
$486$		0			0
$487$	−0.843065	+	1.46023i	−0.0382029	+	0.0661694i	−0.884495	−	0.466550i	$-0.845497\pi$
$487$	−0.843065	+	1.46023i	−0.0382029	+	0.0661694i	0.846292	+	0.532720i	$0.178830\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.85070	+	11.8658i	−0.309168	+	0.535494i	−0.978181	−	0.207757i	$-0.933384\pi$
$491$	−6.85070	+	11.8658i	−0.309168	+	0.535494i	0.669013	+	0.743251i	$0.266717\pi$
$492$		0			0
$493$	16.8815			0.760305
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.98875	−	3.00963i	0.448057	−	0.135000i
$498$		0			0
$499$	−6.55655			−0.293511			−0.146756	−	0.989173i	$-0.546883\pi$
$499$	−6.55655			−0.293511			−0.146756	+	0.989173i	$0.546883\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−26.8584			−1.19756			−0.598779	−	0.800914i	$-0.704347\pi$
$503$	−26.8584			−1.19756			−0.598779	+	0.800914i	$0.704347\pi$
$504$		0			0
$505$	−5.10580			−0.227205
$506$		0			0
$507$		0			0
$508$		0			0
$509$	39.7337			1.76117			0.880584	−	0.473891i	$-0.157151\pi$
$509$	39.7337			1.76117			0.880584	+	0.473891i	$0.157151\pi$
$510$		0			0
$511$	−1.04434	+	4.44129i	−0.0461989	+	0.196471i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.0767406			−0.00338160
$516$		0			0
$517$	6.36694	−	11.0279i	0.280018	−	0.485005i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−11.7585	+	20.3663i	−0.515148	+	0.892262i	0.484698	+	0.874682i	$0.338930\pi$
$521$	−11.7585	+	20.3663i	−0.515148	+	0.892262i	−0.999845	+	0.0175802i	$0.994404\pi$
$522$		0			0
$523$	−10.9289	−	18.9294i	−0.477887	−	0.827725i	0.521791	−	0.853073i	$-0.325264\pi$
$523$	−10.9289	−	18.9294i	−0.477887	−	0.827725i	−0.999679	+	0.0253481i	$0.991931\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−51.5336			−2.24484
$528$		0			0
$529$	−9.85320			−0.428400
$530$		0			0
$531$		0			0
$532$		0			0
$533$	36.0191	+	62.3869i	1.56016	+	2.70228i
$534$		0			0
$535$	1.92088	+	3.32706i	0.0830468	+	0.143841i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.7310	+	13.0772i	−0.849874	+	0.563273i
$540$		0			0
$541$	14.0063	+	24.2596i	0.602178	+	1.04300i	0.992491	+	0.122320i	$0.0390334\pi$
$541$	14.0063	+	24.2596i	0.602178	+	1.04300i	−0.390313	+	0.920682i	$0.627633\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.30045	+	5.71654i	−0.141376	+	0.244870i
$546$		0			0
$547$	−2.02714	−	3.51112i	−0.0866744	−	0.150124i	0.819429	−	0.573181i	$-0.194291\pi$
$547$	−2.02714	−	3.51112i	−0.0866744	−	0.150124i	−0.906103	+	0.423056i	$0.860957\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.67722	−	11.5653i	0.284459	−	0.492698i
$552$		0			0
$553$	3.39119	−	14.4218i	0.144208	−	0.613278i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.926620	−	1.60495i	0.0392621	−	0.0680040i	−0.845727	−	0.533616i	$-0.820833\pi$
$557$	0.926620	−	1.60495i	0.0392621	−	0.0680040i	0.884989	+	0.465612i	$0.154166\pi$
$558$		0			0
$559$	−21.8357			−0.923553
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.2331	+	38.5088i	0.937013	+	1.62295i	0.771005	+	0.636830i	$0.219755\pi$
$563$	22.2331	+	38.5088i	0.937013	+	1.62295i	0.166008	+	0.986124i	$0.446912\pi$
$564$		0			0
$565$	−4.32601	+	7.49287i	−0.181997	+	0.315227i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.63116	−	13.2176i	0.319915	−	0.554109i	−0.660555	−	0.750778i	$-0.729679\pi$
$569$	7.63116	−	13.2176i	0.319915	−	0.554109i	0.980470	+	0.196669i	$0.0630124\pi$
$570$		0			0
$571$	12.7634	+	22.1068i	0.534130	+	0.925140i	0.999205	+	0.0398690i	$0.0126940\pi$
$571$	12.7634	+	22.1068i	0.534130	+	0.925140i	−0.465075	+	0.885271i	$0.653973\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	17.2890			0.721002
$576$		0			0
$577$	−3.26981	+	5.66348i	−0.136124	+	0.235774i	−0.926026	−	0.377459i	$-0.876798\pi$
$577$	−3.26981	+	5.66348i	−0.136124	+	0.235774i	0.789902	+	0.613233i	$0.210131\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.460686	+	0.433102i	0.0191125	+	0.0179681i
$582$		0			0
$583$	18.8646	−	32.6744i	0.781291	−	1.35323i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.2055	−	26.3366i	−0.627597	−	1.08703i	−0.988033	−	0.154245i	$-0.950705\pi$
$587$	−15.2055	−	26.3366i	−0.627597	−	1.08703i	0.360436	−	0.932784i	$-0.382628\pi$
$588$		0			0
$589$	−20.3833	+	35.3049i	−0.839880	+	1.45471i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	21.3291	+	36.9432i	0.875883	+	1.51707i	0.855819	+	0.517275i	$0.173053\pi$
$593$	21.3291	+	36.9432i	0.875883	+	1.51707i	0.0200633	+	0.999799i	$0.493613\pi$
$594$		0			0
$595$	−1.60697	+	6.83399i	−0.0658792	+	0.280166i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−22.2787	−	38.5879i	−0.910284	−	1.57666i	−0.813663	−	0.581337i	$-0.802530\pi$
$599$	−22.2787	−	38.5879i	−0.910284	−	1.57666i	−0.0966209	−	0.995321i	$-0.530803\pi$
$600$		0			0
$601$	14.1961	+	24.5884i	0.579071	+	1.00298i	0.995586	+	0.0938518i	$0.0299180\pi$
$601$	14.1961	+	24.5884i	0.579071	+	1.00298i	−0.416515	+	0.909129i	$0.636749\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.209488			0.00851691
$606$		0			0
$607$	14.0278			0.569372			0.284686	−	0.958621i	$-0.408111\pi$
$607$	14.0278			0.569372			0.284686	+	0.958621i	$0.408111\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.7723	−	18.6581i	−0.435799	−	0.754826i
$612$		0			0
$613$	−9.97062	+	17.2696i	−0.402709	+	0.697513i	−0.994052	−	0.108907i	$-0.965265\pi$
$613$	−9.97062	+	17.2696i	−0.402709	+	0.697513i	0.591342	+	0.806421i	$0.298598\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.51584	−	2.62551i	0.0610254	−	0.105699i	−0.833899	−	0.551918i	$-0.813896\pi$
$617$	1.51584	−	2.62551i	0.0610254	−	0.105699i	0.894924	+	0.446219i	$0.147230\pi$
$618$		0			0
$619$	2.55431			0.102666			0.0513331	−	0.998682i	$-0.483653\pi$
$619$	2.55431			0.102666			0.0513331	+	0.998682i	$0.483653\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.49868	−	2.34907i	−0.100107	−	0.0941136i
$624$		0			0
$625$	21.5777			0.863108
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16.3766			−0.652980
$630$		0			0
$631$	37.1162			1.47757			0.738786	−	0.673941i	$-0.235400\pi$
$631$	37.1162			1.47757			0.738786	+	0.673941i	$0.235400\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.13115			0.362358
$636$		0			0
$637$	2.46960	+	39.9731i	0.0978491	+	1.58379i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.0968			−0.833275			−0.416638	−	0.909073i	$-0.636792\pi$
$641$	−21.0968			−0.833275			−0.416638	+	0.909073i	$0.636792\pi$
$642$		0			0
$643$	9.31948	−	16.1418i	0.367524	−	0.636571i	−0.621654	−	0.783292i	$-0.713539\pi$
$643$	9.31948	−	16.1418i	0.367524	−	0.636571i	0.989178	+	0.146722i	$0.0468722\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.78509	+	8.28801i	−0.188121	+	0.325835i	−0.944624	−	0.328155i	$-0.893573\pi$
$647$	−4.78509	+	8.28801i	−0.188121	+	0.325835i	0.756503	+	0.653991i	$0.226906\pi$
$648$		0			0
$649$	−14.2413	−	24.6666i	−0.559019	−	0.968249i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	32.8560			1.28575			0.642877	−	0.765970i	$-0.277741\pi$
$653$	32.8560			1.28575			0.642877	+	0.765970i	$0.277741\pi$
$654$		0			0
$655$	2.35028			0.0918332
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.8011	−	42.9568i	−0.966114	−	1.67336i	−0.706593	−	0.707620i	$-0.749769\pi$
$659$	−24.8011	−	42.9568i	−0.966114	−	1.67336i	−0.259521	−	0.965738i	$-0.583565\pi$
$660$		0			0
$661$	1.65895	+	2.87338i	0.0645255	+	0.111761i	0.896483	−	0.443077i	$-0.146113\pi$
$661$	1.65895	+	2.87338i	0.0645255	+	0.111761i	−0.831958	+	0.554839i	$0.812780\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.04626	+	3.80399i	0.156907	+	0.147512i
$666$		0			0
$667$	5.55232	+	9.61690i	0.214987	+	0.372368i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.3196	+	21.3381i	−0.475591	+	0.823748i
$672$		0			0
$673$	21.8005	+	37.7597i	0.840349	+	1.45553i	0.889600	+	0.456741i	$0.150983\pi$
$673$	21.8005	+	37.7597i	0.840349	+	1.45553i	−0.0492503	+	0.998786i	$0.515683\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.14039	+	15.8316i	−0.351294	+	0.608459i	−0.986476	−	0.163903i	$-0.947591\pi$
$677$	−9.14039	+	15.8316i	−0.351294	+	0.608459i	0.635183	+	0.772362i	$0.280925\pi$
$678$		0			0
$679$	−27.0900	−	25.4680i	−1.03962	−	0.977371i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−22.5380	+	39.0369i	−0.862391	+	1.49371i	0.00722317	+	0.999974i	$0.497701\pi$
$683$	−22.5380	+	39.0369i	−0.862391	+	1.49371i	−0.869614	+	0.493732i	$0.835633\pi$
$684$		0			0
$685$	3.11689			0.119090
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−31.9171	−	55.2820i	−1.21594	−	2.10608i
$690$		0			0
$691$	−20.8977	+	36.1960i	−0.794988	+	1.37696i	0.127859	+	0.991792i	$0.459189\pi$
$691$	−20.8977	+	36.1960i	−0.794988	+	1.37696i	−0.922847	+	0.385167i	$0.874144\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.47528	+	9.48346i	−0.207689	+	0.359728i
$696$		0			0
$697$	34.7019	+	60.1054i	1.31443	+	2.27665i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.3967			−0.732604			−0.366302	−	0.930496i	$-0.619376\pi$
$701$	−19.3967			−0.732604			−0.366302	+	0.930496i	$0.619376\pi$
$702$		0			0
$703$	−6.47753	+	11.2194i	−0.244305	+	0.423148i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26.8689	+	8.09565i	−1.01051	+	0.304468i
$708$		0			0
$709$	8.61542	−	14.9223i	0.323559	−	0.560420i	−0.657661	−	0.753314i	$-0.728454\pi$
$709$	8.61542	−	14.9223i	0.323559	−	0.560420i	0.981220	+	0.192894i	$0.0617873\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−16.9494	−	29.3572i	−0.634759	−	1.09943i
$714$		0			0
$715$	4.65675	−	8.06573i	0.174153	−	0.301641i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.08444	−	8.80650i	−0.189617	−	0.328427i	0.755505	−	0.655143i	$-0.227391\pi$
$719$	−5.08444	−	8.80650i	−0.189617	−	0.328427i	−0.945123	+	0.326715i	$0.894058\pi$
$720$		0			0
$721$	−0.403841	+	0.121678i	−0.0150398	+	0.00453153i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.30172	+	12.6469i	0.271179	+	0.469696i
$726$		0			0
$727$	−0.0914356	−	0.158371i	−0.00339116	−	0.00587366i	0.864325	−	0.502934i	$-0.167746\pi$
$727$	−0.0914356	−	0.158371i	−0.00339116	−	0.00587366i	−0.867716	+	0.497060i	$0.834413\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.0372			−0.778088
$732$		0			0
$733$	41.9343			1.54888			0.774440	−	0.632647i	$-0.218032\pi$
$733$	41.9343			1.54888			0.774440	+	0.632647i	$0.218032\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.34776	+	7.53054i	0.160152	+	0.277391i
$738$		0			0
$739$	−11.8013	+	20.4404i	−0.434116	+	0.751911i	−0.997223	−	0.0744729i	$-0.976273\pi$
$739$	−11.8013	+	20.4404i	−0.434116	+	0.751911i	0.563107	+	0.826384i	$0.309606\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.1821	−	19.3680i	0.410233	−	0.710544i	−0.584682	−	0.811263i	$-0.698781\pi$
$743$	11.1821	−	19.3680i	0.410233	−	0.710544i	0.994915	+	0.100718i	$0.0321141\pi$
$744$		0			0
$745$	6.83791			0.250522
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.3838	+	14.4627i	0.562111	+	0.528454i
$750$		0			0
$751$	31.0462			1.13289			0.566445	−	0.824099i	$-0.308318\pi$
$751$	31.0462			1.13289			0.566445	+	0.824099i	$0.308318\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.21434			0.0441943
$756$		0			0
$757$	−44.0639			−1.60153			−0.800764	−	0.598980i	$-0.795573\pi$
$757$	−44.0639			−1.60153			−0.800764	+	0.598980i	$0.795573\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.74941			−0.208416			−0.104208	−	0.994556i	$-0.533231\pi$
$761$	−5.74941			−0.208416			−0.104208	+	0.994556i	$0.533231\pi$
$762$		0			0
$763$	−8.30431	+	35.3159i	−0.300636	+	1.27852i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−48.1898			−1.74003
$768$		0			0
$769$	−7.48401	+	12.9627i	−0.269880	+	0.467446i	−0.968831	−	0.247724i	$-0.920317\pi$
$769$	−7.48401	+	12.9627i	−0.269880	+	0.467446i	0.698950	+	0.715170i	$0.253651\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.0605	−	17.4253i	0.361850	−	0.626743i	−0.626415	−	0.779490i	$-0.715479\pi$
$773$	10.0605	−	17.4253i	0.361850	−	0.626743i	0.988265	+	0.152747i	$0.0488119\pi$
$774$		0			0
$775$	−22.2897	−	38.6069i	−0.800669	−	1.38680i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	54.9031			1.96711
$780$		0			0
$781$	−13.3338			−0.477120
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.20763	−	7.28783i	−0.150177	−	0.260114i
$786$		0			0
$787$	12.0572	+	20.8837i	0.429794	+	0.744425i	0.996855	−	0.0792508i	$-0.0252528\pi$
$787$	12.0572	+	20.8837i	0.429794	+	0.744425i	−0.567061	+	0.823676i	$0.691919\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.8848	+	46.2899i	−0.387017	+	1.64588i
$792$		0			0
$793$	20.8435	+	36.1021i	0.740175	+	1.28202i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.54611	−	2.67794i	0.0547661	−	0.0948576i	−0.837343	−	0.546678i	$-0.815892\pi$
$797$	1.54611	−	2.67794i	0.0547661	−	0.0948576i	0.892109	+	0.451821i	$0.149225\pi$
$798$		0			0
$799$	−10.3783	−	17.9758i	−0.367158	−	0.635936i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.91567	−	5.05008i	0.102892	−	0.178213i
$804$		0			0
$805$	−4.42165	+	1.33225i	−0.155843	+	0.0469557i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.32067	−	5.75157i	0.116749	−	0.202215i	−0.801729	−	0.597688i	$-0.796086\pi$
$809$	3.32067	−	5.75157i	0.116749	−	0.202215i	0.918477	+	0.395473i	$0.129419\pi$
$810$		0			0
$811$	−23.7806			−0.835049			−0.417525	−	0.908666i	$-0.637102\pi$
$811$	−23.7806			−0.835049			−0.417525	+	0.908666i	$0.637102\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.424190	+	0.734719i	0.0148587	+	0.0257361i
$816$		0			0
$817$	−8.32093	+	14.4123i	−0.291112	+	0.504222i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.9151	+	43.1543i	−0.869544	+	1.50609i	−0.00708033	+	0.999975i	$0.502254\pi$
$821$	−24.9151	+	43.1543i	−0.869544	+	1.50609i	−0.862464	+	0.506119i	$0.831080\pi$
$822$		0			0
$823$	4.72691	+	8.18726i	0.164770	+	0.285390i	0.936574	−	0.350471i	$-0.113979\pi$
$823$	4.72691	+	8.18726i	0.164770	+	0.285390i	−0.771804	+	0.635861i	$0.780645\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.95385			0.276582			0.138291	−	0.990392i	$-0.455839\pi$
$827$	7.95385			0.276582			0.138291	+	0.990392i	$0.455839\pi$
$828$		0			0
$829$	6.22333	−	10.7791i	0.216145	−	0.374374i	−0.737481	−	0.675368i	$-0.763985\pi$
$829$	6.22333	−	10.7791i	0.216145	−	0.374374i	0.953626	+	0.300993i	$0.0973182\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.37928	+	38.5113i	0.0824373	+	1.33434i
$834$		0			0
$835$	1.71961	−	2.97845i	0.0595096	−	0.103074i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	22.5163	+	38.9994i	0.777350	+	1.34641i	0.933464	+	0.358671i	$0.116770\pi$
$839$	22.5163	+	38.9994i	0.777350	+	1.34641i	−0.156114	+	0.987739i	$0.549897\pi$
$840$		0			0
$841$	9.81015	−	16.9917i	0.338281	−	0.585920i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.74977	−	8.22684i	−0.163397	−	0.283012i
$846$		0			0
$847$	1.10242	−	0.332160i	0.0378794	−	0.0114131i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.38627	−	9.32929i	−0.184639	−	0.319804i
$852$		0			0
$853$	−1.15007	−	1.99198i	−0.0393777	−	0.0682042i	0.845665	−	0.533714i	$-0.179204\pi$
$853$	−1.15007	−	1.99198i	−0.0393777	−	0.0682042i	−0.885043	+	0.465510i	$0.845871\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.6695			−0.432780			−0.216390	−	0.976307i	$-0.569428\pi$
$857$	−12.6695			−0.432780			−0.216390	+	0.976307i	$0.569428\pi$
$858$		0			0
$859$	47.4748			1.61982			0.809910	−	0.586554i	$-0.199516\pi$
$859$	47.4748			1.61982			0.809910	+	0.586554i	$0.199516\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.1445	+	27.9630i	0.549564	+	0.951873i	0.998304	+	0.0582109i	$0.0185396\pi$
$863$	16.1445	+	27.9630i	0.549564	+	0.951873i	−0.448740	+	0.893662i	$0.648127\pi$
$864$		0			0
$865$	2.38138	−	4.12467i	0.0809693	−	0.140243i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.46779	+	16.3987i	−0.321173	+	0.556287i
$870$		0			0
$871$	14.7120			0.498497
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.9122	+	3.58917i	−0.402706	+	0.121336i
$876$		0			0
$877$	27.7589			0.937352			0.468676	−	0.883370i	$-0.344731\pi$
$877$	27.7589			0.937352			0.468676	+	0.883370i	$0.344731\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22.7696			0.767126			0.383563	−	0.923515i	$-0.374697\pi$
$881$	22.7696			0.767126			0.383563	+	0.923515i	$0.374697\pi$
$882$		0			0
$883$	4.65312			0.156590			0.0782950	−	0.996930i	$-0.475052\pi$
$883$	4.65312			0.156590			0.0782950	+	0.996930i	$0.475052\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	47.2867			1.58773			0.793866	−	0.608093i	$-0.208065\pi$
$887$	47.2867			1.58773			0.793866	+	0.608093i	$0.208065\pi$
$888$		0			0
$889$	48.0519	−	14.4781i	1.61161	−	0.485581i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−16.4199			−0.549471
$894$		0			0
$895$	−0.977058	+	1.69231i	−0.0326595	+	0.0565678i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	14.3165	−	24.7970i	0.477483	−	0.827025i
$900$		0			0
$901$	−30.7498	−	53.2602i	−1.02442	−	1.77436i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.20516			0.0733019
$906$		0			0
$907$	−6.06612			−0.201422			−0.100711	−	0.994916i	$-0.532112\pi$
$907$	−6.06612			−0.201422			−0.100711	+	0.994916i	$0.532112\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.3223	−	19.6109i	−0.375126	−	0.649737i	0.615220	−	0.788356i	$-0.289067\pi$
$911$	−11.3223	−	19.6109i	−0.375126	−	0.649737i	−0.990346	+	0.138618i	$0.955734\pi$
$912$		0			0
$913$	−0.404081	−	0.699889i	−0.0133731	−	0.0231630i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.3682	−	3.72656i	0.408433	−	0.123062i
$918$		0			0
$919$	−22.3902	−	38.7810i	−0.738585	−	1.27927i	−0.953133	−	0.302553i	$-0.902161\pi$
$919$	−22.3902	−	38.7810i	−0.738585	−	1.27927i	0.214548	−	0.976713i	$-0.431172\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−11.2797	+	19.5371i	−0.371277	+	0.643071i
$924$		0			0
$925$	−7.08335	−	12.2687i	−0.232899	−	0.403393i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.552620	+	0.957166i	−0.0181309	+	0.0314036i	−0.874948	−	0.484216i	$-0.839105\pi$
$929$	−0.552620	+	0.957166i	−0.0181309	+	0.0314036i	0.856818	+	0.515620i	$0.172438\pi$
$930$		0			0
$931$	27.3246	+	13.6025i	0.895528	+	0.445805i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.48645	−	7.77076i	0.146723	−	0.254131i
$936$		0			0
$937$	44.7012			1.46033			0.730163	−	0.683273i	$-0.239444\pi$
$937$	44.7012			1.46033			0.730163	+	0.683273i	$0.239444\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.749661	−	1.29845i	−0.0244383	−	0.0423283i	0.853548	−	0.521015i	$-0.174446\pi$
$941$	−0.749661	−	1.29845i	−0.0244383	−	0.0423283i	−0.877986	+	0.478687i	$0.841113\pi$
$942$		0			0
$943$	−22.8268	+	39.5372i	−0.743344	+	1.28751i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.75447	−	8.23498i	0.154499	−	0.267601i	−0.778377	−	0.627797i	$-0.783957\pi$
$947$	4.75447	−	8.23498i	0.154499	−	0.267601i	0.932877	+	0.360196i	$0.117290\pi$
$948$		0			0
$949$	−4.93303	−	8.54426i	−0.160133	−	0.277358i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−15.2064			−0.492585			−0.246292	−	0.969196i	$-0.579212\pi$
$953$	−15.2064			−0.492585			−0.246292	+	0.969196i	$0.579212\pi$
$954$		0			0
$955$	2.69396	−	4.66607i	0.0871745	−	0.150991i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	16.4024	−	4.94208i	0.529661	−	0.159588i
$960$		0			0
$961$	−28.2036	+	48.8500i	−0.909792	+	1.57581i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.92176	−	6.79268i	−0.126246	−	0.218664i
$966$		0			0
$967$	−17.9319	+	31.0589i	−0.576649	+	0.998786i	0.419211	+	0.907889i	$0.362307\pi$
$967$	−17.9319	+	31.0589i	−0.576649	+	0.998786i	−0.995860	+	0.0908973i	$0.971027\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.72746	+	6.45615i	0.119620	+	0.207188i	0.919617	−	0.392816i	$-0.128499\pi$
$971$	3.72746	+	6.45615i	0.119620	+	0.207188i	−0.799997	+	0.600004i	$0.795166\pi$
$972$		0			0
$973$	−13.7765	+	58.5874i	−0.441653	+	1.87823i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.9756	−	34.5988i	−0.639076	−	1.10691i	−0.985636	−	0.168885i	$-0.945983\pi$
$977$	−19.9756	−	34.5988i	−0.639076	−	1.10691i	0.346559	−	0.938028i	$-0.387350\pi$
$978$		0			0
$979$	2.19167	+	3.79608i	0.0700460	+	0.121323i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−8.38416			−0.267413			−0.133707	−	0.991021i	$-0.542688\pi$
$983$	−8.38416			−0.267413			−0.133707	+	0.991021i	$0.542688\pi$
$984$		0			0
$985$	1.52810			0.0486894
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.91911	−	11.9843i	−0.220015	−	0.381077i
$990$		0			0
$991$	−21.2345	+	36.7792i	−0.674536	+	1.16833i	0.302068	+	0.953286i	$0.402323\pi$
$991$	−21.2345	+	36.7792i	−0.674536	+	1.16833i	−0.976604	+	0.215044i	$0.931010\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.693871	−	1.20182i	0.0219972	−	0.0381003i
$996$		0			0
$997$	−30.9632			−0.980613			−0.490306	−	0.871550i	$-0.663115\pi$
$997$	−30.9632			−0.980613			−0.490306	+	0.871550i	$0.663115\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.d.361.6		22
3.2	odd	2		504.2.t.d.193.3	yes	22
4.3	odd	2		3024.2.t.l.1873.6		22
7.2	even	3		1512.2.q.c.793.6		22
9.2	odd	6		504.2.q.d.25.5	✓	22
9.7	even	3		1512.2.q.c.1369.6		22
12.11	even	2		1008.2.t.k.193.9		22
21.2	odd	6		504.2.q.d.121.5	yes	22
28.23	odd	6		3024.2.q.k.2305.6		22
36.7	odd	6		3024.2.q.k.2881.6		22
36.11	even	6		1008.2.q.k.529.7		22
63.2	odd	6		504.2.t.d.457.3	yes	22
63.16	even	3	inner	1512.2.t.d.289.6		22
84.23	even	6		1008.2.q.k.625.7		22
252.79	odd	6		3024.2.t.l.289.6		22
252.191	even	6		1008.2.t.k.961.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.5	✓	22	9.2	odd	6
504.2.q.d.121.5	yes	22	21.2	odd	6
504.2.t.d.193.3	yes	22	3.2	odd	2
504.2.t.d.457.3	yes	22	63.2	odd	6
1008.2.q.k.529.7		22	36.11	even	6
1008.2.q.k.625.7		22	84.23	even	6
1008.2.t.k.193.9		22	12.11	even	2
1008.2.t.k.961.9		22	252.191	even	6
1512.2.q.c.793.6		22	7.2	even	3
1512.2.q.c.1369.6		22	9.7	even	3
1512.2.t.d.289.6		22	63.16	even	3	inner
1512.2.t.d.361.6		22	1.1	even	1	trivial
3024.2.q.k.2305.6		22	28.23	odd	6
3024.2.q.k.2881.6		22	36.7	odd	6
3024.2.t.l.289.6		22	252.79	odd	6
3024.2.t.l.1873.6		22	4.3	odd	2

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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.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.481387 q^{5} +(2.53326 - 0.763277i) q^{7} +O(q^{10})\)	\(q+0.481387 q^{5} +(2.53326 - 0.763277i) q^{7} -3.38159 q^{11} +(-2.86067 + 4.95482i) q^{13} +(-2.75605 + 4.77362i) q^{17} +(2.18023 + 3.77626i) q^{19} -3.62585 q^{23} -4.76827 q^{25} +(-1.53131 - 2.65231i) q^{29} +(4.67459 + 8.09663i) q^{31} +(1.21948 - 0.367431i) q^{35} +(1.48552 + 2.57299i) q^{37} +(6.29558 - 10.9043i) q^{41} +(1.90827 + 3.30522i) q^{43} +(-1.88282 + 3.26114i) q^{47} +(5.83482 - 3.86716i) q^{49} +(-5.57860 + 9.66242i) q^{53} -1.62786 q^{55} +(4.21141 + 7.29438i) q^{59} +(3.64312 - 6.31007i) q^{61} +(-1.37709 + 2.38519i) q^{65} +(-1.28571 - 2.22692i) q^{67} +3.94304 q^{71} +(-0.862216 + 1.49340i) q^{73} +(-8.56646 + 2.58109i) q^{77} +(2.79980 - 4.84940i) q^{79} +(0.119494 + 0.206970i) q^{83} +(-1.32673 + 2.29796i) q^{85} +(-0.648116 - 1.12257i) q^{89} +(-3.46492 + 14.7353i) q^{91} +(1.04953 + 1.81784i) q^{95} +(-7.02669 - 12.1706i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) \) 22 * q + 6 * q^5 + 7 * q^7	\( 22 q + 6 q^{5} + 7 q^{7} - 6 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} + 4 q^{23} + 20 q^{25} - 9 q^{29} - 4 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} - 5 q^{47} - 15 q^{49} - 11 q^{53} + 22 q^{55} + 19 q^{59} - 13 q^{61} - 13 q^{65} + 26 q^{67} + 48 q^{71} - 35 q^{73} + 4 q^{77} + 10 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} - 12 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q + 6 * q^5 + 7 * q^7 - 6 * q^11 - 3 * q^13 - 7 * q^17 - q^19 + 4 * q^23 + 20 * q^25 - 9 * q^29 - 4 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 - 5 * q^47 - 15 * q^49 - 11 * q^53 + 22 * q^55 + 19 * q^59 - 13 * q^61 - 13 * q^65 + 26 * q^67 + 48 * q^71 - 35 * q^73 + 4 * q^77 + 10 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 - 12 * q^95 - 29 * q^97

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