LMFDB - Embedded newform 1512.2.t.c.289.10

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			289.10
Character	$\chi$	$=$	1512.289
Dual form			1512.2.t.c.361.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.79940 q^{5} +(2.59312 - 0.525101i) q^{7} +O(q^{10})$	$q+3.79940 q^{5} +(2.59312 - 0.525101i) q^{7} -4.51412 q^{11} +(0.588451 + 1.01923i) q^{13} +(2.95973 + 5.12641i) q^{17} +(2.55676 - 4.42844i) q^{19} +4.18164 q^{23} +9.43545 q^{25} +(-2.11164 + 3.65747i) q^{29} +(3.12141 - 5.40645i) q^{31} +(9.85230 - 1.99507i) q^{35} +(-3.87179 + 6.70614i) q^{37} +(-0.754693 - 1.30717i) q^{41} +(-5.01709 + 8.68986i) q^{43} +(-1.11832 - 1.93699i) q^{47} +(6.44854 - 2.72330i) q^{49} +(-6.49368 - 11.2474i) q^{53} -17.1510 q^{55} +(6.19609 - 10.7319i) q^{59} +(-0.729171 - 1.26296i) q^{61} +(2.23576 + 3.87245i) q^{65} +(-0.813192 + 1.40849i) q^{67} -8.48517 q^{71} +(3.72984 + 6.46027i) q^{73} +(-11.7057 + 2.37037i) q^{77} +(0.920926 + 1.59509i) q^{79} +(0.307606 - 0.532789i) q^{83} +(11.2452 + 19.4773i) q^{85} +(1.25572 - 2.17496i) q^{89} +(2.06112 + 2.33398i) q^{91} +(9.71417 - 16.8254i) q^{95} +(2.36751 - 4.10064i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 - q^7	$ 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	3.79940			1.69914			0.849572	−	0.527473i	$-0.176860\pi$
$5$	3.79940			1.69914			0.849572	+	0.527473i	$0.176860\pi$
$6$		0			0
$7$	2.59312	−	0.525101i	0.980107	−	0.198470i
$7$	2.59312	−	0.525101i	0.980107	−	0.198470i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.51412			−1.36106			−0.680529	−	0.732721i	$-0.738250\pi$
$11$	−4.51412			−1.36106			−0.680529	+	0.732721i	$0.738250\pi$
$12$		0			0
$13$	0.588451	+	1.01923i	0.163207	+	0.282683i	0.936017	−	0.351955i	$-0.114483\pi$
$13$	0.588451	+	1.01923i	0.163207	+	0.282683i	−0.772810	+	0.634637i	$0.781150\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.95973	+	5.12641i	0.717841	+	1.24334i	0.961853	+	0.273565i	$0.0882029\pi$
$17$	2.95973	+	5.12641i	0.717841	+	1.24334i	−0.244012	+	0.969772i	$0.578464\pi$
$18$		0			0
$19$	2.55676	−	4.42844i	0.586562	−	1.01595i	−0.408117	−	0.912930i	$-0.633815\pi$
$19$	2.55676	−	4.42844i	0.586562	−	1.01595i	0.994679	−	0.103025i	$-0.0328521\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.18164			0.871931			0.435966	−	0.899963i	$-0.356407\pi$
$23$	4.18164			0.871931			0.435966	+	0.899963i	$0.356407\pi$
$24$		0			0
$25$	9.43545			1.88709
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.11164	+	3.65747i	−0.392122	+	0.679175i	−0.992729	−	0.120369i	$-0.961592\pi$
$29$	−2.11164	+	3.65747i	−0.392122	+	0.679175i	0.600607	+	0.799544i	$0.294925\pi$
$30$		0			0
$31$	3.12141	−	5.40645i	0.560622	−	0.971027i	−0.436820	−	0.899549i	$-0.643895\pi$
$31$	3.12141	−	5.40645i	0.560622	−	0.971027i	0.997442	−	0.0714776i	$-0.0227714\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.85230	−	1.99507i	1.66534	−	0.337229i
$36$		0			0
$37$	−3.87179	+	6.70614i	−0.636519	+	1.10248i	0.349672	+	0.936872i	$0.386293\pi$
$37$	−3.87179	+	6.70614i	−0.636519	+	1.10248i	−0.986191	+	0.165611i	$0.947040\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.754693	−	1.30717i	−0.117863	−	0.204145i	0.801057	−	0.598587i	$-0.204271\pi$
$41$	−0.754693	−	1.30717i	−0.117863	−	0.204145i	−0.918921	+	0.394442i	$0.870938\pi$
$42$		0			0
$43$	−5.01709	+	8.68986i	−0.765099	+	1.32519i	0.175095	+	0.984552i	$0.443977\pi$
$43$	−5.01709	+	8.68986i	−0.765099	+	1.32519i	−0.940194	+	0.340639i	$0.889357\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.11832	−	1.93699i	−0.163124	−	0.282539i	0.772863	−	0.634572i	$-0.218824\pi$
$47$	−1.11832	−	1.93699i	−0.163124	−	0.282539i	−0.935988	+	0.352033i	$0.885490\pi$
$48$		0			0
$49$	6.44854	−	2.72330i	0.921220	−	0.389043i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.49368	−	11.2474i	−0.891975	−	1.54495i	−0.837504	−	0.546431i	$-0.815986\pi$
$53$	−6.49368	−	11.2474i	−0.891975	−	1.54495i	−0.0544716	−	0.998515i	$-0.517347\pi$
$54$		0			0
$55$	−17.1510			−2.31263
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.19609	−	10.7319i	0.806662	−	1.39718i	−0.108501	−	0.994096i	$-0.534605\pi$
$59$	6.19609	−	10.7319i	0.806662	−	1.39718i	0.915163	−	0.403083i	$-0.132061\pi$
$60$		0			0
$61$	−0.729171	−	1.26296i	−0.0933608	−	0.161706i	0.815563	−	0.578669i	$-0.196428\pi$
$61$	−0.729171	−	1.26296i	−0.0933608	−	0.161706i	−0.908923	+	0.416963i	$0.863094\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.23576	+	3.87245i	0.277312	+	0.480318i
$66$		0			0
$67$	−0.813192	+	1.40849i	−0.0993472	+	0.172074i	−0.911415	−	0.411489i	$-0.865009\pi$
$67$	−0.813192	+	1.40849i	−0.0993472	+	0.172074i	0.812067	+	0.583564i	$0.198342\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.48517			−1.00700			−0.503502	−	0.863994i	$-0.667955\pi$
$71$	−8.48517			−1.00700			−0.503502	+	0.863994i	$0.667955\pi$
$72$		0			0
$73$	3.72984	+	6.46027i	0.436544	+	0.756117i	0.997420	−	0.0717827i	$-0.0228688\pi$
$73$	3.72984	+	6.46027i	0.436544	+	0.756117i	−0.560876	+	0.827900i	$0.689535\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.7057	+	2.37037i	−1.33398	+	0.270129i
$78$		0			0
$79$	0.920926	+	1.59509i	0.103612	+	0.179462i	0.913170	−	0.407578i	$-0.133627\pi$
$79$	0.920926	+	1.59509i	0.103612	+	0.179462i	−0.809558	+	0.587040i	$0.800293\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.307606	−	0.532789i	0.0337641	−	0.0584812i	−0.848650	−	0.528956i	$-0.822584\pi$
$83$	0.307606	−	0.532789i	0.0337641	−	0.0584812i	0.882414	+	0.470474i	$0.155917\pi$
$84$		0			0
$85$	11.2452	+	19.4773i	1.21972	+	2.11261i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.25572	−	2.17496i	0.133106	−	0.230546i	−0.791767	−	0.610824i	$-0.790838\pi$
$89$	1.25572	−	2.17496i	0.133106	−	0.230546i	0.924872	+	0.380278i	$0.124172\pi$
$90$		0			0
$91$	2.06112	+	2.33398i	0.216064	+	0.244668i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9.71417	−	16.8254i	0.996652	−	1.72625i
$96$		0			0
$97$	2.36751	−	4.10064i	0.240384	−	0.416357i	−0.720440	−	0.693517i	$-0.756060\pi$
$97$	2.36751	−	4.10064i	0.240384	−	0.416357i	0.960824	+	0.277160i	$0.0893934\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	11.4216			1.13649			0.568247	−	0.822858i	$-0.307622\pi$
$101$	11.4216			1.13649			0.568247	+	0.822858i	$0.307622\pi$
$102$		0			0
$103$	−6.37505			−0.628152			−0.314076	−	0.949398i	$-0.601695\pi$
$103$	−6.37505			−0.628152			−0.314076	+	0.949398i	$0.601695\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.11999	+	1.93988i	−0.108274	+	0.187536i	−0.915071	−	0.403293i	$-0.867866\pi$
$107$	−1.11999	+	1.93988i	−0.108274	+	0.187536i	0.806797	+	0.590828i	$0.201199\pi$
$108$		0			0
$109$	−2.73089	−	4.73005i	−0.261572	−	0.453056i	0.705088	−	0.709120i	$-0.250908\pi$
$109$	−2.73089	−	4.73005i	−0.261572	−	0.453056i	−0.966660	+	0.256064i	$0.917574\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.45456	+	7.71553i	0.419050	+	0.725816i	0.995844	−	0.0910734i	$-0.0290298\pi$
$113$	4.45456	+	7.71553i	0.419050	+	0.725816i	−0.576794	+	0.816890i	$0.695696\pi$
$114$		0			0
$115$	15.8877			1.48154
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.3668	+	11.7392i	0.950326	+	1.07613i
$120$		0			0
$121$	9.37728			0.852480
$122$		0			0
$123$		0			0
$124$		0			0
$125$	16.8520			1.50729
$126$		0			0
$127$	0.434918			0.0385927			0.0192964	−	0.999814i	$-0.493857\pi$
$127$	0.434918			0.0385927			0.0192964	+	0.999814i	$0.493857\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.35265			0.467664			0.233832	−	0.972277i	$-0.424874\pi$
$131$	5.35265			0.467664			0.233832	+	0.972277i	$0.424874\pi$
$132$		0			0
$133$	4.30461	−	12.8260i	0.373257	−	1.11216i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.90242			−0.504278			−0.252139	−	0.967691i	$-0.581134\pi$
$137$	−5.90242			−0.504278			−0.252139	+	0.967691i	$0.581134\pi$
$138$		0			0
$139$	4.33649	+	7.51102i	0.367816	+	0.637077i	0.989224	−	0.146411i	$-0.0467721\pi$
$139$	4.33649	+	7.51102i	0.367816	+	0.637077i	−0.621407	+	0.783488i	$0.713439\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.65634	−	4.60091i	−0.222134	−	0.384747i
$144$		0			0
$145$	−8.02297	+	13.8962i	−0.666271	+	1.15402i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.7772			0.882903			0.441451	−	0.897285i	$-0.354464\pi$
$149$	10.7772			0.882903			0.441451	+	0.897285i	$0.354464\pi$
$150$		0			0
$151$	−16.8262			−1.36930			−0.684648	−	0.728873i	$-0.740044\pi$
$151$	−16.8262			−1.36930			−0.684648	+	0.728873i	$0.740044\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.8595	−	20.5413i	0.952578	−	1.64991i
$156$		0			0
$157$	−4.48068	+	7.76076i	−0.357597	+	0.619376i	−0.987559	−	0.157250i	$-0.949737\pi$
$157$	−4.48068	+	7.76076i	−0.357597	+	0.619376i	0.629962	+	0.776626i	$0.283071\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	10.8435	−	2.19578i	0.854586	−	0.173052i
$162$		0			0
$163$	−3.71319	+	6.43144i	−0.290840	+	0.503749i	−0.974009	−	0.226511i	$-0.927268\pi$
$163$	−3.71319	+	6.43144i	−0.290840	+	0.503749i	0.683169	+	0.730261i	$0.260601\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.13764	+	8.89866i	0.397563	+	0.688599i	0.993425	−	0.114488i	$-0.0365227\pi$
$167$	5.13764	+	8.89866i	0.397563	+	0.688599i	−0.595862	+	0.803087i	$0.703189\pi$
$168$		0			0
$169$	5.80745	−	10.0588i	0.446727	−	0.773754i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.10496	−	8.84205i	−0.388123	−	0.672249i	0.604074	−	0.796928i	$-0.293543\pi$
$173$	−5.10496	−	8.84205i	−0.388123	−	0.672249i	−0.992197	+	0.124679i	$0.960210\pi$
$174$		0			0
$175$	24.4672	−	4.95457i	1.84955	−	0.374530i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.62985	−	16.6794i	−0.719769	−	1.24668i	−0.961091	−	0.276231i	$-0.910915\pi$
$179$	−9.62985	−	16.6794i	−0.719769	−	1.24668i	0.241323	−	0.970445i	$-0.422419\pi$
$180$		0			0
$181$	−1.39163			−0.103439			−0.0517195	−	0.998662i	$-0.516470\pi$
$181$	−1.39163			−0.103439			−0.0517195	+	0.998662i	$0.516470\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−14.7105	+	25.4793i	−1.08154	+	1.87328i
$186$		0			0
$187$	−13.3606	−	23.1412i	−0.977024	−	1.69225i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.35741	−	2.35111i	−0.0982190	−	0.170120i	0.812728	−	0.582643i	$-0.197981\pi$
$191$	−1.35741	−	2.35111i	−0.0982190	−	0.170120i	−0.910948	+	0.412522i	$0.864648\pi$
$192$		0			0
$193$	−0.920846	+	1.59495i	−0.0662839	+	0.114807i	−0.897263	−	0.441497i	$-0.854448\pi$
$193$	−0.920846	+	1.59495i	−0.0662839	+	0.114807i	0.830979	+	0.556304i	$0.187781\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−21.9198			−1.56172			−0.780860	−	0.624706i	$-0.785219\pi$
$197$	−21.9198			−1.56172			−0.780860	+	0.624706i	$0.785219\pi$
$198$		0			0
$199$	−0.726101	−	1.25764i	−0.0514719	−	0.0891520i	0.839141	−	0.543913i	$-0.183058\pi$
$199$	−0.726101	−	1.25764i	−0.0514719	−	0.0891520i	−0.890613	+	0.454761i	$0.849725\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.55519	+	10.5931i	−0.249526	+	0.743488i
$204$		0			0
$205$	−2.86738	−	4.96645i	−0.200267	−	0.346872i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.5415	+	19.9905i	−0.798344	+	1.38277i
$210$		0			0
$211$	0.771347	+	1.33601i	0.0531017	+	0.0919749i	0.891354	−	0.453307i	$-0.149756\pi$
$211$	0.771347	+	1.33601i	0.0531017	+	0.0919749i	−0.838253	+	0.545282i	$0.816423\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−19.0619	+	33.0162i	−1.30001	+	2.25169i
$216$		0			0
$217$	5.25527	−	15.6586i	0.356751	−	1.06298i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.48332	+	6.03328i	−0.234313	+	0.405842i
$222$		0			0
$223$	−0.346045	+	0.599368i	−0.0231729	+	0.0401366i	−0.877379	−	0.479797i	$-0.840710\pi$
$223$	−0.346045	+	0.599368i	−0.0231729	+	0.0401366i	0.854206	+	0.519934i	$0.174043\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18.4159			−1.22231			−0.611155	−	0.791511i	$-0.709295\pi$
$227$	−18.4159			−1.22231			−0.611155	+	0.791511i	$0.709295\pi$
$228$		0			0
$229$	−5.39392			−0.356440			−0.178220	−	0.983991i	$-0.557034\pi$
$229$	−5.39392			−0.356440			−0.178220	+	0.983991i	$0.557034\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.27352	−	14.3302i	0.542016	−	0.938800i	−0.456772	−	0.889584i	$-0.650994\pi$
$233$	8.27352	−	14.3302i	0.542016	−	0.938800i	0.998788	−	0.0492161i	$-0.0156723\pi$
$234$		0			0
$235$	−4.24896	−	7.35941i	−0.277171	−	0.480075i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.56724	+	2.71454i	0.101376	+	0.175589i	0.912252	−	0.409630i	$-0.134342\pi$
$239$	1.56724	+	2.71454i	0.101376	+	0.175589i	−0.810876	+	0.585219i	$0.801009\pi$
$240$		0			0
$241$	−16.4746			−1.06122			−0.530611	−	0.847615i	$-0.678038\pi$
$241$	−16.4746			−1.06122			−0.530611	+	0.847615i	$0.678038\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	24.5006	−	10.3469i	1.56528	−	0.661040i
$246$		0			0
$247$	6.01811			0.382923
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.8939			−0.813858			−0.406929	−	0.913460i	$-0.633400\pi$
$251$	−12.8939			−0.813858			−0.406929	+	0.913460i	$0.633400\pi$
$252$		0			0
$253$	−18.8764			−1.18675
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.6089			−1.28555			−0.642774	−	0.766055i	$-0.722217\pi$
$257$	−20.6089			−1.28555			−0.642774	+	0.766055i	$0.722217\pi$
$258$		0			0
$259$	−6.51862	+	19.4229i	−0.405047	+	1.20688i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.13233			−0.563123			−0.281562	−	0.959543i	$-0.590852\pi$
$263$	−9.13233			−0.563123			−0.281562	+	0.959543i	$0.590852\pi$
$264$		0			0
$265$	−24.6721	−	42.7333i	−1.51559	−	2.62509i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.4387	+	21.5445i	0.758401	+	1.31359i	0.943666	+	0.330900i	$0.107352\pi$
$269$	12.4387	+	21.5445i	0.758401	+	1.31359i	−0.185265	+	0.982689i	$0.559314\pi$
$270$		0			0
$271$	5.70814	−	9.88679i	0.346745	−	0.600580i	−0.638924	−	0.769270i	$-0.720620\pi$
$271$	5.70814	−	9.88679i	0.346745	−	0.600580i	0.985669	+	0.168690i	$0.0539536\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−42.5927			−2.56844
$276$		0			0
$277$	30.9876			1.86186			0.930932	−	0.365192i	$-0.118997\pi$
$277$	30.9876			1.86186			0.930932	+	0.365192i	$0.118997\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.40910	−	12.8329i	0.441990	−	0.765549i	−0.555847	−	0.831285i	$-0.687606\pi$
$281$	7.40910	−	12.8329i	0.441990	−	0.765549i	0.997837	+	0.0657354i	$0.0209393\pi$
$282$		0			0
$283$	−12.8715	+	22.2942i	−0.765134	+	1.32525i	0.175042	+	0.984561i	$0.443994\pi$
$283$	−12.8715	+	22.2942i	−0.765134	+	1.32525i	−0.940176	+	0.340689i	$0.889340\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.64340	−	2.99335i	−0.156035	−	0.176692i
$288$		0			0
$289$	−9.02006	+	15.6232i	−0.530592	+	0.919012i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.41185	−	14.5697i	−0.491425	−	0.851174i	0.508526	−	0.861047i	$-0.330191\pi$
$293$	−8.41185	−	14.5697i	−0.491425	−	0.851174i	−0.999951	+	0.00987288i	$0.996857\pi$
$294$		0			0
$295$	23.5414	−	40.7749i	1.37063	−	2.37401i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.46069	+	4.26203i	0.142305	+	0.246480i
$300$		0			0
$301$	−8.44686	+	25.1683i	−0.486869	+	1.45068i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.77041	−	4.79849i	−0.158633	−	0.274761i
$306$		0			0
$307$	−28.2972			−1.61501			−0.807504	−	0.589862i	$-0.799182\pi$
$307$	−28.2972			−1.61501			−0.807504	+	0.589862i	$0.799182\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.93477	−	17.2075i	0.563349	−	0.975750i	−0.433852	−	0.900984i	$-0.642846\pi$
$311$	9.93477	−	17.2075i	0.563349	−	0.975750i	0.997201	−	0.0747654i	$-0.0238208\pi$
$312$		0			0
$313$	9.14293	+	15.8360i	0.516789	+	0.895105i	0.999810	+	0.0194961i	$0.00620619\pi$
$313$	9.14293	+	15.8360i	0.516789	+	0.895105i	−0.483021	+	0.875609i	$0.660460\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.97401	+	12.0793i	0.391700	+	0.678444i	0.992674	−	0.120825i	$-0.0385539\pi$
$317$	6.97401	+	12.0793i	0.391700	+	0.678444i	−0.600974	+	0.799268i	$0.705221\pi$
$318$		0			0
$319$	9.53220	−	16.5103i	0.533701	−	0.924397i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	30.2694			1.68423
$324$		0			0
$325$	5.55230	+	9.61686i	0.307986	+	0.533447i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.91706	−	4.43562i	−0.215955	−	0.244544i
$330$		0			0
$331$	−10.4200	−	18.0479i	−0.572733	−	0.992003i	−0.996284	−	0.0861302i	$-0.972550\pi$
$331$	−10.4200	−	18.0479i	−0.572733	−	0.992003i	0.423551	−	0.905872i	$-0.360783\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.08964	+	5.35142i	−0.168805	+	0.292379i
$336$		0			0
$337$	15.4376	+	26.7387i	0.840939	+	1.45655i	0.889101	+	0.457710i	$0.151330\pi$
$337$	15.4376	+	26.7387i	0.840939	+	1.45655i	−0.0481619	+	0.998840i	$0.515336\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.0904	+	24.4054i	−0.763040	+	1.32162i
$342$		0			0
$343$	15.2918	−	10.4480i	0.825681	−	0.564138i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.13427	+	8.89281i	−0.275622	+	0.477391i	−0.970292	−	0.241938i	$-0.922217\pi$
$347$	−5.13427	+	8.89281i	−0.275622	+	0.477391i	0.694670	+	0.719329i	$0.255550\pi$
$348$		0			0
$349$	4.61262	−	7.98930i	0.246908	−	0.427657i	−0.715758	−	0.698348i	$-0.753919\pi$
$349$	4.61262	−	7.98930i	0.246908	−	0.427657i	0.962666	+	0.270691i	$0.0872521\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.17321			−0.435016			−0.217508	−	0.976059i	$-0.569793\pi$
$353$	−8.17321			−0.435016			−0.217508	+	0.976059i	$0.569793\pi$
$354$		0			0
$355$	−32.2386			−1.71104
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.35957	+	11.0151i	−0.335645	+	0.581355i	−0.983609	−	0.180317i	$-0.942288\pi$
$359$	−6.35957	+	11.0151i	−0.335645	+	0.581355i	0.647963	+	0.761672i	$0.275621\pi$
$360$		0			0
$361$	−3.57407	−	6.19047i	−0.188109	−	0.325814i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	14.1711	+	24.5452i	0.741752	+	1.28475i
$366$		0			0
$367$	−21.8861			−1.14245			−0.571224	−	0.820794i	$-0.693531\pi$
$367$	−21.8861			−1.14245			−0.571224	+	0.820794i	$0.693531\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−22.7449	−	25.7560i	−1.18086	−	1.33718i
$372$		0			0
$373$	−13.4625			−0.697063			−0.348531	−	0.937297i	$-0.613320\pi$
$373$	−13.4625			−0.697063			−0.348531	+	0.937297i	$0.613320\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.97038			−0.255988
$378$		0			0
$379$	−11.2180			−0.576231			−0.288115	−	0.957596i	$-0.593029\pi$
$379$	−11.2180			−0.576231			−0.288115	+	0.957596i	$0.593029\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.00660			0.409118			0.204559	−	0.978854i	$-0.434424\pi$
$383$	8.00660			0.409118			0.204559	+	0.978854i	$0.434424\pi$
$384$		0			0
$385$	−44.4745	+	9.00599i	−2.26663	+	0.458988i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−28.7862			−1.45952			−0.729759	−	0.683705i	$-0.760368\pi$
$389$	−28.7862			−1.45952			−0.729759	+	0.683705i	$0.760368\pi$
$390$		0			0
$391$	12.3765	+	21.4368i	0.625908	+	1.08410i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.49897	+	6.06039i	0.176052	+	0.304931i
$396$		0			0
$397$	10.8138	−	18.7301i	0.542731	−	0.940037i	−0.456015	−	0.889972i	$-0.650724\pi$
$397$	10.8138	−	18.7301i	0.542731	−	0.940037i	0.998746	−	0.0500651i	$-0.0159429\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−26.9932			−1.34797			−0.673987	−	0.738743i	$-0.735420\pi$
$401$	−26.9932			−1.34797			−0.673987	+	0.738743i	$0.735420\pi$
$402$		0			0
$403$	7.34719			0.365990
$404$		0			0
$405$		0			0
$406$		0			0
$407$	17.4777	−	30.2723i	0.866339	−	1.50054i
$408$		0			0
$409$	10.4737	−	18.1409i	0.517889	−	0.897010i	−0.481895	−	0.876229i	$-0.660051\pi$
$409$	10.4737	−	18.1409i	0.517889	−	0.897010i	0.999784	−	0.0207814i	$-0.00661539\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.4318	−	31.0828i	0.513317	−	1.52948i
$414$		0			0
$415$	1.16872	−	2.02428i	0.0573701	−	0.0993680i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.91450	−	11.9763i	−0.337795	−	0.585079i	0.646222	−	0.763149i	$-0.276348\pi$
$419$	−6.91450	−	11.9763i	−0.337795	−	0.585079i	−0.984018	+	0.178070i	$0.943015\pi$
$420$		0			0
$421$	−6.86872	+	11.8970i	−0.334761	+	0.579823i	−0.983439	−	0.181240i	$-0.941989\pi$
$421$	−6.86872	+	11.8970i	−0.334761	+	0.579823i	0.648678	+	0.761063i	$0.275322\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	27.9264	+	48.3700i	1.35463	+	2.34629i
$426$		0			0
$427$	−2.55401	−	2.89212i	−0.123597	−	0.139959i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.20392	+	15.9417i	0.443337	+	0.767882i	0.997935	−	0.0642362i	$-0.0204611\pi$
$431$	9.20392	+	15.9417i	0.443337	+	0.767882i	−0.554598	+	0.832119i	$0.687128\pi$
$432$		0			0
$433$	24.3558			1.17047			0.585233	−	0.810865i	$-0.301003\pi$
$433$	24.3558			1.17047			0.585233	+	0.810865i	$0.301003\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.6914	−	18.5181i	0.511441	−	0.885842i
$438$		0			0
$439$	2.91828	+	5.05460i	0.139282	+	0.241243i	0.927225	−	0.374505i	$-0.122187\pi$
$439$	2.91828	+	5.05460i	0.139282	+	0.241243i	−0.787943	+	0.615748i	$0.788854\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.42002	+	12.8518i	0.352536	+	0.610610i	0.986693	−	0.162594i	$-0.0519862\pi$
$443$	7.42002	+	12.8518i	0.352536	+	0.610610i	−0.634157	+	0.773204i	$0.718653\pi$
$444$		0			0
$445$	4.77097	−	8.26356i	0.226166	−	0.391730i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.26289			0.201178			0.100589	−	0.994928i	$-0.467927\pi$
$449$	4.26289			0.201178			0.100589	+	0.994928i	$0.467927\pi$
$450$		0			0
$451$	3.40677	+	5.90070i	0.160419	+	0.277853i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.83102	+	8.86772i	0.367124	+	0.415725i
$456$		0			0
$457$	−19.8730	−	34.4210i	−0.929618	−	1.61015i	−0.783961	−	0.620810i	$-0.786804\pi$
$457$	−19.8730	−	34.4210i	−0.929618	−	1.61015i	−0.145657	−	0.989335i	$-0.546530\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.68671	−	4.65353i	0.125133	−	0.216736i	−0.796652	−	0.604438i	$-0.793398\pi$
$461$	2.68671	−	4.65353i	0.125133	−	0.216736i	0.921785	+	0.387702i	$0.126731\pi$
$462$		0			0
$463$	19.8205	+	34.3301i	0.921136	+	1.59545i	0.797661	+	0.603106i	$0.206070\pi$
$463$	19.8205	+	34.3301i	0.921136	+	1.59545i	0.123474	+	0.992348i	$0.460596\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.43069	+	16.3344i	−0.436400	+	0.755867i	−0.997409	−	0.0719427i	$-0.977080\pi$
$467$	−9.43069	+	16.3344i	−0.436400	+	0.755867i	0.561009	+	0.827810i	$0.310413\pi$
$468$		0			0
$469$	−1.36910	+	4.07939i	−0.0632193	+	0.188369i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	22.6477	−	39.2270i	1.04134	−	1.80366i
$474$		0			0
$475$	24.1242	−	41.7843i	1.10689	−	1.91720i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−19.0057			−0.868395			−0.434197	−	0.900818i	$-0.642968\pi$
$479$	−19.0057			−0.868395			−0.434197	+	0.900818i	$0.642968\pi$
$480$		0			0
$481$	−9.11344			−0.415537
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.99511	−	15.5800i	0.408447	−	0.707451i
$486$		0			0
$487$	−5.21626	−	9.03482i	−0.236371	−	0.409407i	0.723299	−	0.690535i	$-0.242625\pi$
$487$	−5.21626	−	9.03482i	−0.236371	−	0.409407i	−0.959670	+	0.281128i	$0.909291\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	14.3311	+	24.8221i	0.646752	+	1.12021i	0.983894	+	0.178753i	$0.0572063\pi$
$491$	14.3311	+	24.8221i	0.646752	+	1.12021i	−0.337142	+	0.941454i	$0.609460\pi$
$492$		0			0
$493$	−24.9996			−1.12592
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−22.0031	+	4.45557i	−0.986972	+	0.199860i
$498$		0			0
$499$	−33.0793			−1.48083			−0.740416	−	0.672149i	$-0.765372\pi$
$499$	−33.0793			−1.48083			−0.740416	+	0.672149i	$0.765372\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	28.9523			1.29092			0.645460	−	0.763794i	$-0.276666\pi$
$503$	28.9523			1.29092			0.645460	+	0.763794i	$0.276666\pi$
$504$		0			0
$505$	43.3953			1.93107
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−31.7641			−1.40792			−0.703959	−	0.710241i	$-0.748586\pi$
$509$	−31.7641			−1.40792			−0.703959	+	0.710241i	$0.748586\pi$
$510$		0			0
$511$	13.0642	+	14.7937i	0.577927	+	0.654435i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−24.2214			−1.06732
$516$		0			0
$517$	5.04825	+	8.74382i	0.222022	+	0.384553i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.87897	+	4.98652i	0.126130	+	0.218463i	0.922174	−	0.386775i	$-0.126411\pi$
$521$	2.87897	+	4.98652i	0.126130	+	0.218463i	−0.796044	+	0.605239i	$0.793078\pi$
$522$		0			0
$523$	−22.3123	+	38.6461i	−0.975650	+	1.68987i	−0.297875	+	0.954605i	$0.596278\pi$
$523$	−22.3123	+	38.6461i	−0.975650	+	1.68987i	−0.677774	+	0.735270i	$0.737055\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	36.9542			1.60975
$528$		0			0
$529$	−5.51392			−0.239736
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.888199	−	1.53841i	0.0384722	−	0.0666357i
$534$		0			0
$535$	−4.25530	+	7.37040i	−0.183973	+	0.318650i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−29.1095	+	12.2933i	−1.25383	+	0.529510i
$540$		0			0
$541$	15.6719	−	27.1445i	0.673786	−	1.16703i	−0.303036	−	0.952979i	$-0.598000\pi$
$541$	15.6719	−	27.1445i	0.673786	−	1.16703i	0.976822	−	0.214053i	$-0.0686665\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−10.3758	−	17.9713i	−0.444449	−	0.769808i
$546$		0			0
$547$	1.37567	−	2.38273i	0.0588195	−	0.101878i	−0.835116	−	0.550073i	$-0.814600\pi$
$547$	1.37567	−	2.38273i	0.0588195	−	0.101878i	0.893936	+	0.448195i	$0.147933\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.7979	+	18.7026i	0.460007	+	0.796756i
$552$		0			0
$553$	3.22565	+	3.65268i	0.137169	+	0.155328i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.42197	−	5.92703i	−0.144994	−	0.251136i	0.784377	−	0.620284i	$-0.212983\pi$
$557$	−3.42197	−	5.92703i	−0.144994	−	0.251136i	−0.929371	+	0.369148i	$0.879650\pi$
$558$		0			0
$559$	−11.8092			−0.499478
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.55007	−	13.0771i	0.318197	−	0.551134i	−0.661915	−	0.749579i	$-0.730256\pi$
$563$	7.55007	−	13.0771i	0.318197	−	0.551134i	0.980112	+	0.198445i	$0.0635892\pi$
$564$		0			0
$565$	16.9247	+	29.3144i	0.712027	+	1.23327i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.7638	−	23.8396i	−0.577008	−	0.999408i	−0.995820	−	0.0913346i	$-0.970887\pi$
$569$	−13.7638	−	23.8396i	−0.577008	−	0.999408i	0.418812	−	0.908073i	$-0.362447\pi$
$570$		0			0
$571$	19.4377	−	33.6672i	0.813444	−	1.40893i	−0.0969950	−	0.995285i	$-0.530923\pi$
$571$	19.4377	−	33.6672i	0.813444	−	1.40893i	0.910439	−	0.413642i	$-0.135744\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	39.4556			1.64541
$576$		0			0
$577$	−9.84330	−	17.0491i	−0.409782	−	0.709763i	0.585083	−	0.810973i	$-0.301062\pi$
$577$	−9.84330	−	17.0491i	−0.409782	−	0.709763i	−0.994865	+	0.101210i	$0.967729\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.517891	−	1.54311i	0.0214857	−	0.0640190i
$582$		0			0
$583$	29.3132	+	50.7720i	1.21403	+	2.10276i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.14068	+	5.43982i	−0.129630	+	0.224525i	−0.923533	−	0.383519i	$-0.874712\pi$
$587$	−3.14068	+	5.43982i	−0.129630	+	0.224525i	0.793903	+	0.608044i	$0.208046\pi$
$588$		0			0
$589$	−15.9614	−	27.6460i	−0.657679	−	1.13913i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.79280	+	13.4975i	−0.320012	+	0.554277i	−0.980490	−	0.196568i	$-0.937020\pi$
$593$	−7.79280	+	13.4975i	−0.320012	+	0.554277i	0.660478	+	0.750845i	$0.270354\pi$
$594$		0			0
$595$	39.3877	+	44.6021i	1.61474	+	1.82851i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.527783	−	0.914146i	0.0215646	−	0.0373510i	−0.855042	−	0.518559i	$-0.826469\pi$
$599$	0.527783	−	0.914146i	0.0215646	−	0.0373510i	0.876606	+	0.481208i	$0.159802\pi$
$600$		0			0
$601$	−12.1622	+	21.0656i	−0.496107	+	0.859283i	−0.999990	−	0.00448941i	$-0.998571\pi$
$601$	−12.1622	+	21.0656i	−0.496107	+	0.859283i	0.503883	+	0.863772i	$0.331904\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	35.6280			1.44849
$606$		0			0
$607$	4.33005			0.175751			0.0878756	−	0.996131i	$-0.471992\pi$
$607$	4.33005			0.175751			0.0878756	+	0.996131i	$0.471992\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.31616	−	2.27965i	0.0532460	−	0.0922247i
$612$		0			0
$613$	−24.3556	−	42.1852i	−0.983714	−	1.70384i	−0.647518	−	0.762050i	$-0.724193\pi$
$613$	−24.3556	−	42.1852i	−0.983714	−	1.70384i	−0.336196	−	0.941792i	$-0.609140\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.6366	−	25.3514i	−0.589249	−	1.02061i	−0.994331	−	0.106329i	$-0.966090\pi$
$617$	−14.6366	−	25.3514i	−0.589249	−	1.02061i	0.405082	−	0.914280i	$-0.367243\pi$
$618$		0			0
$619$	−36.4762			−1.46610			−0.733050	−	0.680174i	$-0.761904\pi$
$619$	−36.4762			−1.46610			−0.733050	+	0.680174i	$0.761904\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.11414	−	6.29932i	0.0847014	−	0.252377i
$624$		0			0
$625$	16.8505			0.674018
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−45.8379			−1.82768
$630$		0			0
$631$	0.501625			0.0199694			0.00998468	−	0.999950i	$-0.496822\pi$
$631$	0.501625			0.0199694			0.00998468	+	0.999950i	$0.496822\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.65243			0.0655746
$636$		0			0
$637$	6.57031	+	4.96999i	0.260325	+	0.196918i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	35.0224			1.38330			0.691651	−	0.722232i	$-0.256884\pi$
$641$	35.0224			1.38330			0.691651	+	0.722232i	$0.256884\pi$
$642$		0			0
$643$	7.29049	+	12.6275i	0.287509	+	0.497980i	0.973215	−	0.229899i	$-0.0738396\pi$
$643$	7.29049	+	12.6275i	0.287509	+	0.497980i	−0.685706	+	0.727879i	$0.740506\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.6503	+	20.1790i	0.458022	+	0.793318i	0.998856	−	0.0478116i	$-0.0152247\pi$
$647$	11.6503	+	20.1790i	0.458022	+	0.793318i	−0.540834	+	0.841129i	$0.681891\pi$
$648$		0			0
$649$	−27.9699	+	48.4453i	−1.09791	+	1.90164i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.53559			0.334023			0.167012	−	0.985955i	$-0.446588\pi$
$653$	8.53559			0.334023			0.167012	+	0.985955i	$0.446588\pi$
$654$		0			0
$655$	20.3369			0.794628
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.81616	−	3.14568i	0.0707476	−	0.122538i	−0.828482	−	0.560016i	$-0.810795\pi$
$659$	1.81616	−	3.14568i	0.0707476	−	0.122538i	0.899229	+	0.437478i	$0.144128\pi$
$660$		0			0
$661$	15.5116	−	26.8668i	0.603330	−	1.04500i	−0.388983	−	0.921245i	$-0.627173\pi$
$661$	15.5116	−	26.8668i	0.603330	−	1.04500i	0.992313	−	0.123753i	$-0.0394932\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	16.3549	−	48.7313i	0.634217	−	1.88972i
$666$		0			0
$667$	−8.83011	+	15.2942i	−0.341903	+	0.592194i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.29156	+	5.70116i	0.127069	+	0.220091i
$672$		0			0
$673$	0.291838	−	0.505478i	0.0112495	−	0.0194848i	−0.860346	−	0.509711i	$-0.829752\pi$
$673$	0.291838	−	0.505478i	0.0112495	−	0.0194848i	0.871595	+	0.490226i	$0.163086\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.8666	−	29.2138i	−0.648237	−	1.12278i	−0.983544	−	0.180670i	$-0.942173\pi$
$677$	−16.8666	−	29.2138i	−0.648237	−	1.12278i	0.335307	−	0.942109i	$-0.391160\pi$
$678$		0			0
$679$	3.98597	−	11.8766i	0.152968	−	0.455783i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.60312	+	2.77668i	0.0613417	+	0.106247i	0.895065	−	0.445935i	$-0.147129\pi$
$683$	1.60312	+	2.77668i	0.0613417	+	0.106247i	−0.833724	+	0.552182i	$0.813795\pi$
$684$		0			0
$685$	−22.4257			−0.856841
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.64242	−	13.2371i	0.291153	−	0.504292i
$690$		0			0
$691$	16.1837	+	28.0310i	0.615657	+	1.06635i	0.990269	+	0.139168i	$0.0444428\pi$
$691$	16.1837	+	28.0310i	0.615657	+	1.06635i	−0.374611	+	0.927182i	$0.622224\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	16.4761	+	28.5374i	0.624973	+	1.08249i
$696$		0			0
$697$	4.46738	−	7.73773i	0.169214	−	0.293087i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−21.2591			−0.802943			−0.401472	−	0.915871i	$-0.631501\pi$
$701$	−21.2591			−0.802943			−0.401472	+	0.915871i	$0.631501\pi$
$702$		0			0
$703$	19.7985	+	34.2920i	0.746715	+	1.29335i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	29.6176	−	5.99751i	1.11389	−	0.225560i
$708$		0			0
$709$	−15.8272	−	27.4135i	−0.594402	−	1.02953i	−0.993631	−	0.112684i	$-0.964055\pi$
$709$	−15.8272	−	27.4135i	−0.594402	−	1.02953i	0.399229	−	0.916851i	$-0.369278\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	13.0526	−	22.6078i	0.488824	−	0.846669i
$714$		0			0
$715$	−10.0925	−	17.4807i	−0.377438	−	0.653741i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.9776	−	25.9420i	0.558571	−	0.967473i	−0.439045	−	0.898465i	$-0.644683\pi$
$719$	14.9776	−	25.9420i	0.558571	−	0.967473i	0.997616	−	0.0690079i	$-0.0219834\pi$
$720$		0			0
$721$	−16.5313	+	3.34755i	−0.615656	+	0.124669i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−19.9243	+	34.5099i	−0.739969	+	1.28166i
$726$		0			0
$727$	−13.6310	+	23.6095i	−0.505544	+	0.875629i	0.494435	+	0.869215i	$0.335375\pi$
$727$	−13.6310	+	23.6095i	−0.505544	+	0.875629i	−0.999979	+	0.00641398i	$0.997958\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−59.3970			−2.19688
$732$		0			0
$733$	−22.5434			−0.832660			−0.416330	−	0.909214i	$-0.636684\pi$
$733$	−22.5434			−0.832660			−0.416330	+	0.909214i	$0.636684\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.67085	−	6.35809i	0.135217	−	0.234203i
$738$		0			0
$739$	−8.82742	−	15.2895i	−0.324722	−	0.562435i	0.656734	−	0.754122i	$-0.271937\pi$
$739$	−8.82742	−	15.2895i	−0.324722	−	0.562435i	−0.981456	+	0.191687i	$0.938604\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.31474	+	5.74130i	0.121606	+	0.210628i	0.920401	−	0.390975i	$-0.127862\pi$
$743$	3.31474	+	5.74130i	0.121606	+	0.210628i	−0.798795	+	0.601603i	$0.794529\pi$
$744$		0			0
$745$	40.9469			1.50018
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.88564	+	5.61846i	−0.0688997	+	0.205294i
$750$		0			0
$751$	7.87441			0.287341			0.143671	−	0.989626i	$-0.454109\pi$
$751$	7.87441			0.287341			0.143671	+	0.989626i	$0.454109\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−63.9295			−2.32663
$756$		0			0
$757$	−37.1503			−1.35025			−0.675125	−	0.737703i	$-0.735910\pi$
$757$	−37.1503			−1.35025			−0.675125	+	0.737703i	$0.735910\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	32.4545			1.17648			0.588238	−	0.808688i	$-0.299822\pi$
$761$	32.4545			1.17648			0.588238	+	0.808688i	$0.299822\pi$
$762$		0			0
$763$	−9.56529	−	10.8316i	−0.346287	−	0.392129i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.5844			0.526611
$768$		0			0
$769$	11.4992	+	19.9172i	0.414671	+	0.718232i	0.995394	−	0.0958699i	$-0.0305633\pi$
$769$	11.4992	+	19.9172i	0.414671	+	0.718232i	−0.580723	+	0.814101i	$0.697230\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−13.2117	−	22.8834i	−0.475194	−	0.823059i	0.524403	−	0.851470i	$-0.324289\pi$
$773$	−13.2117	−	22.8834i	−0.475194	−	0.823059i	−0.999596	+	0.0284109i	$0.990955\pi$
$774$		0			0
$775$	29.4519	−	51.0123i	1.05794	−	1.83241i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.71828			−0.276536
$780$		0			0
$781$	38.3031			1.37059
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−17.0239	+	29.4862i	−0.607609	+	1.05241i
$786$		0			0
$787$	4.55650	−	7.89209i	0.162422	−	0.281323i	−0.773315	−	0.634022i	$-0.781403\pi$
$787$	4.55650	−	7.89209i	0.162422	−	0.281323i	0.935737	+	0.352699i	$0.114736\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.6027	+	17.6682i	0.554767	+	0.628209i
$792$		0			0
$793$	0.858162	−	1.48638i	0.0304742	−	0.0527829i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	27.5330	+	47.6886i	0.975270	+	1.68922i	0.679042	+	0.734099i	$0.262395\pi$
$797$	27.5330	+	47.6886i	0.975270	+	1.68922i	0.296228	+	0.955117i	$0.404271\pi$
$798$		0			0
$799$	6.61988	−	11.4660i	0.234195	−	0.405637i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−16.8369	−	29.1624i	−0.594163	−	1.02912i
$804$		0			0
$805$	41.1987	−	8.34266i	1.45206	−	0.294040i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.0961	−	19.2191i	−0.390119	−	0.675707i	0.602346	−	0.798235i	$-0.294233\pi$
$809$	−11.0961	−	19.2191i	−0.390119	−	0.675707i	−0.992465	+	0.122529i	$0.960900\pi$
$810$		0			0
$811$	52.0941			1.82927			0.914636	−	0.404279i	$-0.132478\pi$
$811$	52.0941			1.82927			0.914636	+	0.404279i	$0.132478\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−14.1079	+	24.4356i	−0.494179	+	0.855943i
$816$		0			0
$817$	25.6550	+	44.4358i	0.897555	+	1.55461i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.8054	+	34.3039i	0.691212	+	1.19721i	0.971441	+	0.237282i	$0.0762564\pi$
$821$	19.8054	+	34.3039i	0.691212	+	1.19721i	−0.280229	+	0.959933i	$0.590410\pi$
$822$		0			0
$823$	16.1735	−	28.0134i	0.563773	−	0.976484i	−0.433389	−	0.901207i	$-0.642682\pi$
$823$	16.1735	−	28.0134i	0.563773	−	0.976484i	0.997163	−	0.0752773i	$-0.0239842\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	38.1724			1.32738			0.663692	−	0.748006i	$-0.268988\pi$
$827$	38.1724			1.32738			0.663692	+	0.748006i	$0.268988\pi$
$828$		0			0
$829$	27.7372	+	48.0422i	0.963353	+	1.66858i	0.713977	+	0.700169i	$0.246892\pi$
$829$	27.7372	+	48.0422i	0.963353	+	1.66858i	0.249375	+	0.968407i	$0.419775\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	33.0467	+	24.9976i	1.14500	+	0.866116i
$834$		0			0
$835$	19.5200	+	33.8096i	0.675516	+	1.17003i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.35256	+	4.07475i	−0.0812193	+	0.140676i	−0.903774	−	0.428010i	$-0.859215\pi$
$839$	−2.35256	+	4.07475i	−0.0812193	+	0.140676i	0.822555	+	0.568686i	$0.192548\pi$
$840$		0			0
$841$	5.58195	+	9.66822i	0.192481	+	0.333387i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	22.0648	−	38.2174i	0.759054	−	1.31472i
$846$		0			0
$847$	24.3164	−	4.92402i	0.835522	−	0.169191i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.1904	+	28.0426i	−0.555001	+	0.961289i
$852$		0			0
$853$	1.87889	−	3.25434i	0.0643321	−	0.111426i	−0.832065	−	0.554678i	$-0.812842\pi$
$853$	1.87889	−	3.25434i	0.0643321	−	0.111426i	0.896398	+	0.443251i	$0.146175\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	53.1561			1.81578			0.907888	−	0.419212i	$-0.137694\pi$
$857$	53.1561			1.81578			0.907888	+	0.419212i	$0.137694\pi$
$858$		0			0
$859$	−52.9776			−1.80757			−0.903786	−	0.427985i	$-0.859224\pi$
$859$	−52.9776			−1.80757			−0.903786	+	0.427985i	$0.859224\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.57834	+	16.5902i	−0.326051	+	0.564736i	−0.981724	−	0.190308i	$-0.939051\pi$
$863$	−9.57834	+	16.5902i	−0.326051	+	0.564736i	0.655674	+	0.755044i	$0.272385\pi$
$864$		0			0
$865$	−19.3958	−	33.5945i	−0.659477	−	1.14225i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.15717	−	7.20043i	−0.141022	−	0.244258i
$870$		0			0
$871$	−1.91409			−0.0648566
$872$		0			0
$873$		0			0
$874$		0			0
$875$	43.6994	−	8.84904i	1.47731	−	0.299152i
$876$		0			0
$877$	3.67730			0.124174			0.0620868	−	0.998071i	$-0.480224\pi$
$877$	3.67730			0.124174			0.0620868	+	0.998071i	$0.480224\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	14.8862			0.501529			0.250765	−	0.968048i	$-0.419318\pi$
$881$	14.8862			0.501529			0.250765	+	0.968048i	$0.419318\pi$
$882$		0			0
$883$	39.9262			1.34362			0.671811	−	0.740722i	$-0.265517\pi$
$883$	39.9262			1.34362			0.671811	+	0.740722i	$0.265517\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.50247			0.285485			0.142743	−	0.989760i	$-0.454408\pi$
$887$	8.50247			0.285485			0.142743	+	0.989760i	$0.454408\pi$
$888$		0			0
$889$	1.12779	−	0.228376i	0.0378250	−	0.00765949i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−11.4371			−0.382730
$894$		0			0
$895$	−36.5877	−	63.3717i	−1.22299	−	2.11828i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	13.1826	+	22.8329i	0.439665	+	0.761521i
$900$		0			0
$901$	38.4391	−	66.5785i	1.28059	−	2.21805i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.28736			−0.175758
$906$		0			0
$907$	−3.19089			−0.105952			−0.0529758	−	0.998596i	$-0.516871\pi$
$907$	−3.19089			−0.105952			−0.0529758	+	0.998596i	$0.516871\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.63889	+	13.2309i	−0.253088	+	0.438361i	−0.964374	−	0.264541i	$-0.914779\pi$
$911$	−7.63889	+	13.2309i	−0.253088	+	0.438361i	0.711287	+	0.702902i	$0.248113\pi$
$912$		0			0
$913$	−1.38857	+	2.40507i	−0.0459550	+	0.0795963i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.8801	−	2.81069i	0.458360	−	0.0928170i
$918$		0			0
$919$	25.2681	−	43.7656i	0.833516	−	1.44369i	−0.0617164	−	0.998094i	$-0.519657\pi$
$919$	25.2681	−	43.7656i	0.833516	−	1.44369i	0.895233	−	0.445599i	$-0.147009\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.99310	−	8.64831i	−0.164350	−	0.284662i
$924$		0			0
$925$	−36.5321	+	63.2755i	−1.20117	+	2.08048i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.9890	+	41.5502i	0.787055	+	1.36322i	0.927764	+	0.373168i	$0.121729\pi$
$929$	23.9890	+	41.5502i	0.787055	+	1.36322i	−0.140709	+	0.990051i	$0.544938\pi$
$930$		0			0
$931$	4.42739	−	35.5198i	0.145102	−	1.16411i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−50.7623	−	87.9228i	−1.66010	−	2.87538i
$936$		0			0
$937$	20.5226			0.670443			0.335222	−	0.942139i	$-0.391189\pi$
$937$	20.5226			0.670443			0.335222	+	0.942139i	$0.391189\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.97793	+	8.62203i	−0.162276	+	0.281070i	−0.935685	−	0.352838i	$-0.885217\pi$
$941$	−4.97793	+	8.62203i	−0.162276	+	0.281070i	0.773409	+	0.633908i	$0.218550\pi$
$942$		0			0
$943$	−3.15585	−	5.46609i	−0.102769	−	0.178000i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.6107	−	18.3782i	−0.344800	−	0.597212i	0.640517	−	0.767944i	$-0.278720\pi$
$947$	−10.6107	−	18.3782i	−0.344800	−	0.597212i	−0.985317	+	0.170732i	$0.945387\pi$
$948$		0			0
$949$	−4.38965	+	7.60310i	−0.142494	+	0.246807i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	35.9191			1.16353			0.581767	−	0.813355i	$-0.302361\pi$
$953$	35.9191			1.16353			0.581767	+	0.813355i	$0.302361\pi$
$954$		0			0
$955$	−5.15736	−	8.93281i	−0.166888	−	0.289059i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−15.3057	+	3.09937i	−0.494246	+	0.100084i
$960$		0			0
$961$	−3.98645	−	6.90473i	−0.128595	−	0.222733i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.49866	+	6.05986i	−0.112626	+	0.195074i
$966$		0			0
$967$	15.9559	+	27.6365i	0.513108	+	0.888729i	0.999884	+	0.0152023i	$0.00483924\pi$
$967$	15.9559	+	27.6365i	0.513108	+	0.888729i	−0.486777	+	0.873526i	$0.661827\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	28.6645	−	49.6483i	0.919886	−	1.59329i	0.120301	−	0.992737i	$-0.461614\pi$
$971$	28.6645	−	49.6483i	0.919886	−	1.59329i	0.799585	−	0.600553i	$-0.205053\pi$
$972$		0			0
$973$	15.1891	+	17.1999i	0.486940	+	0.551403i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.29227	−	7.43444i	0.137322	−	0.237849i	−0.789160	−	0.614188i	$-0.789484\pi$
$977$	4.29227	−	7.43444i	0.137322	−	0.237849i	0.926482	+	0.376339i	$0.122817\pi$
$978$		0			0
$979$	−5.66845	+	9.81805i	−0.181164	+	0.313786i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.5009			0.717667			0.358834	−	0.933402i	$-0.383175\pi$
$983$	22.5009			0.717667			0.358834	+	0.933402i	$0.383175\pi$
$984$		0			0
$985$	−83.2821			−2.65359
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−20.9796	+	36.3378i	−0.667114	+	1.15548i
$990$		0			0
$991$	19.3652	+	33.5415i	0.615156	+	1.06548i	0.990357	+	0.138538i	$0.0442405\pi$
$991$	19.3652	+	33.5415i	0.615156	+	1.06548i	−0.375201	+	0.926944i	$0.622426\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.75875	−	4.77829i	−0.0874582	−	0.151482i
$996$		0			0
$997$	36.7909			1.16518			0.582590	−	0.812766i	$-0.302039\pi$
$997$	36.7909			1.16518			0.582590	+	0.812766i	$0.302039\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.c.289.10		22
3.2	odd	2		504.2.t.c.457.10	yes	22
4.3	odd	2		3024.2.t.k.289.10		22
7.4	even	3		1512.2.q.d.1369.2		22
9.4	even	3		1512.2.q.d.793.2		22
9.5	odd	6		504.2.q.c.121.3	yes	22
12.11	even	2		1008.2.t.l.961.2		22
21.11	odd	6		504.2.q.c.25.3	✓	22
28.11	odd	6		3024.2.q.l.2881.2		22
36.23	even	6		1008.2.q.l.625.9		22
36.31	odd	6		3024.2.q.l.2305.2		22
63.4	even	3	inner	1512.2.t.c.361.10		22
63.32	odd	6		504.2.t.c.193.10	yes	22
84.11	even	6		1008.2.q.l.529.9		22
252.67	odd	6		3024.2.t.k.1873.10		22
252.95	even	6		1008.2.t.l.193.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.3	✓	22	21.11	odd	6
504.2.q.c.121.3	yes	22	9.5	odd	6
504.2.t.c.193.10	yes	22	63.32	odd	6
504.2.t.c.457.10	yes	22	3.2	odd	2
1008.2.q.l.529.9		22	84.11	even	6
1008.2.q.l.625.9		22	36.23	even	6
1008.2.t.l.193.2		22	252.95	even	6
1008.2.t.l.961.2		22	12.11	even	2
1512.2.q.d.793.2		22	9.4	even	3
1512.2.q.d.1369.2		22	7.4	even	3
1512.2.t.c.289.10		22	1.1	even	1	trivial
1512.2.t.c.361.10		22	63.4	even	3	inner
3024.2.q.l.2305.2		22	36.31	odd	6
3024.2.q.l.2881.2		22	28.11	odd	6
3024.2.t.k.289.10		22	4.3	odd	2
3024.2.t.k.1873.10		22	252.67	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.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.79940 q^{5} +(2.59312 - 0.525101i) q^{7} +O(q^{10})\)	\(q+3.79940 q^{5} +(2.59312 - 0.525101i) q^{7} -4.51412 q^{11} +(0.588451 + 1.01923i) q^{13} +(2.95973 + 5.12641i) q^{17} +(2.55676 - 4.42844i) q^{19} +4.18164 q^{23} +9.43545 q^{25} +(-2.11164 + 3.65747i) q^{29} +(3.12141 - 5.40645i) q^{31} +(9.85230 - 1.99507i) q^{35} +(-3.87179 + 6.70614i) q^{37} +(-0.754693 - 1.30717i) q^{41} +(-5.01709 + 8.68986i) q^{43} +(-1.11832 - 1.93699i) q^{47} +(6.44854 - 2.72330i) q^{49} +(-6.49368 - 11.2474i) q^{53} -17.1510 q^{55} +(6.19609 - 10.7319i) q^{59} +(-0.729171 - 1.26296i) q^{61} +(2.23576 + 3.87245i) q^{65} +(-0.813192 + 1.40849i) q^{67} -8.48517 q^{71} +(3.72984 + 6.46027i) q^{73} +(-11.7057 + 2.37037i) q^{77} +(0.920926 + 1.59509i) q^{79} +(0.307606 - 0.532789i) q^{83} +(11.2452 + 19.4773i) q^{85} +(1.25572 - 2.17496i) q^{89} +(2.06112 + 2.33398i) q^{91} +(9.71417 - 16.8254i) q^{95} +(2.36751 - 4.10064i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 - q^7	\( 22 q + 2 q^{5} - q^{7} + 6 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} + 44 q^{25} + 7 q^{29} + 6 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} - 17 q^{47} + 29 q^{49} - q^{53} + 2 q^{55} + 21 q^{59} + 31 q^{61} + 3 q^{65} - 26 q^{67} + 32 q^{71} + 17 q^{73} + 4 q^{77} - 16 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} + 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 - q^7 + 6 * q^11 + 7 * q^13 + q^17 + 13 * q^19 + 44 * q^25 + 7 * q^29 + 6 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 - 17 * q^47 + 29 * q^49 - q^53 + 2 * q^55 + 21 * q^59 + 31 * q^61 + 3 * q^65 - 26 * q^67 + 32 * q^71 + 17 * q^73 + 4 * q^77 - 16 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 + 24 * q^95 + 19 * q^97

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