LMFDB - Embedded newform 1512.2.q.d.793.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1512.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.9
Character	$\chi$	$=$	1512.793
Dual form			1512.2.q.d.1369.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38590 + 2.40045i) q^{5} +(1.74026 + 1.99286i) q^{7} +O(q^{10})$	$q+(1.38590 + 2.40045i) q^{5} +(1.74026 + 1.99286i) q^{7} +(-1.71972 + 2.97864i) q^{11} +(-0.429164 + 0.743335i) q^{13} +(0.405132 + 0.701710i) q^{17} +(0.750215 - 1.29941i) q^{19} +(3.82465 + 6.62449i) q^{23} +(-1.34143 + 2.32343i) q^{25} +(-3.99696 - 6.92294i) q^{29} -7.21156 q^{31} +(-2.37193 + 6.93931i) q^{35} +(0.458211 - 0.793644i) q^{37} +(-1.67577 + 2.90251i) q^{41} +(1.20465 + 2.08652i) q^{43} +0.615039 q^{47} +(-0.942983 + 6.93619i) q^{49} +(-6.31646 - 10.9404i) q^{53} -9.53342 q^{55} -1.46938 q^{59} +11.4327 q^{61} -2.37911 q^{65} +16.2012 q^{67} -14.4177 q^{71} +(-4.16893 - 7.22079i) q^{73} +(-8.92877 + 1.75645i) q^{77} -2.75171 q^{79} +(5.75814 + 9.97340i) q^{83} +(-1.12294 + 1.94500i) q^{85} +(5.11395 - 8.85763i) q^{89} +(-2.22822 + 0.438331i) q^{91} +4.15889 q^{95} +(3.82852 + 6.63119i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - q^5 + 5 * q^7	$ 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.38590	+	2.40045i	0.619793	+	1.07351i	0.989523	+	0.144373i	$0.0461167\pi$
$5$	1.38590	+	2.40045i	0.619793	+	1.07351i	−0.369731	+	0.929139i	$0.620550\pi$
$6$		0			0
$7$	1.74026	+	1.99286i	0.657757	+	0.753230i
$7$	1.74026	+	1.99286i	0.657757	+	0.753230i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.71972	+	2.97864i	−0.518515	+	0.898094i	0.481254	+	0.876581i	$0.340181\pi$
$11$	−1.71972	+	2.97864i	−0.518515	+	0.898094i	−0.999769	+	0.0215124i	$0.993152\pi$
$12$		0			0
$13$	−0.429164	+	0.743335i	−0.119029	+	0.206164i	−0.919383	−	0.393363i	$-0.871311\pi$
$13$	−0.429164	+	0.743335i	−0.119029	+	0.206164i	0.800354	+	0.599527i	$0.204645\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.405132	+	0.701710i	0.0982590	+	0.170190i	0.910964	−	0.412486i	$-0.135339\pi$
$17$	0.405132	+	0.701710i	0.0982590	+	0.170190i	−0.812705	+	0.582675i	$0.802006\pi$
$18$		0			0
$19$	0.750215	−	1.29941i	0.172111	−	0.298105i	−0.767047	−	0.641591i	$-0.778275\pi$
$19$	0.750215	−	1.29941i	0.172111	−	0.298105i	0.939158	+	0.343486i	$0.111608\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.82465	+	6.62449i	0.797495	+	1.38130i	0.921243	+	0.388988i	$0.127175\pi$
$23$	3.82465	+	6.62449i	0.797495	+	1.38130i	−0.123748	+	0.992314i	$0.539492\pi$
$24$		0			0
$25$	−1.34143	+	2.32343i	−0.268286	+	0.464685i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.99696	−	6.92294i	−0.742217	−	1.28556i	−0.951484	−	0.307700i	$-0.900441\pi$
$29$	−3.99696	−	6.92294i	−0.742217	−	1.28556i	0.209266	−	0.977859i	$-0.432893\pi$
$30$		0			0
$31$	−7.21156			−1.29524			−0.647618	−	0.761965i	$-0.724235\pi$
$31$	−7.21156			−1.29524			−0.647618	+	0.761965i	$0.724235\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.37193	+	6.93931i	−0.400929	+	1.17296i
$36$		0			0
$37$	0.458211	−	0.793644i	0.0753294	−	0.130474i	−0.825900	−	0.563817i	$-0.809333\pi$
$37$	0.458211	−	0.793644i	0.0753294	−	0.130474i	0.901229	+	0.433342i	$0.142666\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.67577	+	2.90251i	−0.261711	+	0.453297i	−0.966697	−	0.255925i	$-0.917620\pi$
$41$	−1.67577	+	2.90251i	−0.261711	+	0.453297i	0.704986	+	0.709221i	$0.250953\pi$
$42$		0			0
$43$	1.20465	+	2.08652i	0.183708	+	0.318191i	0.943140	−	0.332395i	$-0.107857\pi$
$43$	1.20465	+	2.08652i	0.183708	+	0.318191i	−0.759433	+	0.650586i	$0.774523\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.615039			0.0897127			0.0448564	−	0.998993i	$-0.485717\pi$
$47$	0.615039			0.0897127			0.0448564	+	0.998993i	$0.485717\pi$
$48$		0			0
$49$	−0.942983	+	6.93619i	−0.134712	+	0.990885i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.31646	−	10.9404i	−0.867633	−	1.50278i	−0.864409	−	0.502789i	$-0.832307\pi$
$53$	−6.31646	−	10.9404i	−0.867633	−	1.50278i	−0.00322332	−	0.999995i	$-0.501026\pi$
$54$		0			0
$55$	−9.53342			−1.28549
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.46938			−0.191297			−0.0956485	−	0.995415i	$-0.530492\pi$
$59$	−1.46938			−0.191297			−0.0956485	+	0.995415i	$0.530492\pi$
$60$		0			0
$61$	11.4327			1.46381			0.731904	−	0.681408i	$-0.238632\pi$
$61$	11.4327			1.46381			0.731904	+	0.681408i	$0.238632\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.37911			−0.295093
$66$		0			0
$67$	16.2012			1.97929			0.989647	−	0.143522i	$-0.0458427\pi$
$67$	16.2012			1.97929			0.989647	+	0.143522i	$0.0458427\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.4177			−1.71106			−0.855532	−	0.517749i	$-0.826770\pi$
$71$	−14.4177			−1.71106			−0.855532	+	0.517749i	$0.826770\pi$
$72$		0			0
$73$	−4.16893	−	7.22079i	−0.487936	−	0.845130i	0.511968	−	0.859005i	$-0.328917\pi$
$73$	−4.16893	−	7.22079i	−0.487936	−	0.845130i	−0.999904	+	0.0138749i	$0.995583\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.92877	+	1.75645i	−1.01753	+	0.200166i
$78$		0			0
$79$	−2.75171			−0.309592			−0.154796	−	0.987946i	$-0.549472\pi$
$79$	−2.75171			−0.309592			−0.154796	+	0.987946i	$0.549472\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.75814	+	9.97340i	0.632038	+	1.09472i	0.987134	+	0.159893i	$0.0511148\pi$
$83$	5.75814	+	9.97340i	0.632038	+	1.09472i	−0.355096	+	0.934830i	$0.615552\pi$
$84$		0			0
$85$	−1.12294	+	1.94500i	−0.121800	+	0.210965i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.11395	−	8.85763i	0.542078	−	0.938907i	−0.456707	−	0.889617i	$-0.650971\pi$
$89$	5.11395	−	8.85763i	0.542078	−	0.938907i	0.998785	−	0.0492892i	$-0.0156956\pi$
$90$		0			0
$91$	−2.22822	+	0.438331i	−0.233581	+	0.0459496i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.15889			0.426693
$96$		0			0
$97$	3.82852	+	6.63119i	0.388727	+	0.673296i	0.992279	−	0.124029i	$-0.0395814\pi$
$97$	3.82852	+	6.63119i	0.388727	+	0.673296i	−0.603551	+	0.797324i	$0.706248\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.84302	+	3.19220i	−0.183387	+	0.317635i	−0.943032	−	0.332703i	$-0.892039\pi$
$101$	−1.84302	+	3.19220i	−0.183387	+	0.317635i	0.759645	+	0.650338i	$0.225373\pi$
$102$		0			0
$103$	8.06026	+	13.9608i	0.794201	+	1.37560i	0.923346	+	0.383970i	$0.125443\pi$
$103$	8.06026	+	13.9608i	0.794201	+	1.37560i	−0.129145	+	0.991626i	$0.541223\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.16767	+	5.48656i	−0.306230	+	0.530405i	−0.977534	−	0.210776i	$-0.932401\pi$
$107$	−3.16767	+	5.48656i	−0.306230	+	0.530405i	0.671305	+	0.741182i	$0.265734\pi$
$108$		0			0
$109$	4.89477	+	8.47799i	0.468834	+	0.812044i	0.999365	−	0.0356213i	$-0.0113410\pi$
$109$	4.89477	+	8.47799i	0.468834	+	0.812044i	−0.530532	+	0.847665i	$0.678008\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.06963	+	7.04881i	−0.382839	+	0.663096i	−0.991467	−	0.130360i	$-0.958387\pi$
$113$	−4.06963	+	7.04881i	−0.382839	+	0.663096i	0.608628	+	0.793456i	$0.291720\pi$
$114$		0			0
$115$	−10.6012	+	18.3617i	−0.988563	+	1.71224i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.693374	+	2.02853i	−0.0635615	+	0.185955i
$120$		0			0
$121$	−0.414862	−	0.718563i	−0.0377148	−	0.0653239i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.42264			0.574459
$126$		0			0
$127$	−12.5658			−1.11504			−0.557518	−	0.830165i	$-0.688246\pi$
$127$	−12.5658			−1.11504			−0.557518	+	0.830165i	$0.688246\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.792752	+	1.37309i	0.0692631	+	0.119967i	0.898577	−	0.438816i	$-0.144602\pi$
$131$	0.792752	+	1.37309i	0.0692631	+	0.119967i	−0.829314	+	0.558783i	$0.811269\pi$
$132$		0			0
$133$	3.89511	−	0.766240i	0.337749	−	0.0664414i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.46394	−	4.26767i	0.210508	−	0.364611i	−0.741365	−	0.671102i	$-0.765821\pi$
$137$	2.46394	−	4.26767i	0.210508	−	0.364611i	0.951874	+	0.306490i	$0.0991547\pi$
$138$		0			0
$139$	4.12999	−	7.15336i	0.350301	−	0.606740i	−0.636001	−	0.771688i	$-0.719412\pi$
$139$	4.12999	−	7.15336i	0.350301	−	0.606740i	0.986302	+	0.164949i	$0.0527458\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.47608	−	2.55665i	−0.123436	−	0.213798i
$144$		0			0
$145$	11.0788	−	19.1890i	0.920042	−	1.59356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.95698	−	12.0498i	−0.569938	−	0.987161i	−0.996571	−	0.0827368i	$-0.973634\pi$
$149$	−6.95698	−	12.0498i	−0.569938	−	0.987161i	0.426634	−	0.904425i	$-0.359699\pi$
$150$		0			0
$151$	−11.4964	+	19.9123i	−0.935561	+	1.62044i	−0.161930	+	0.986802i	$0.551772\pi$
$151$	−11.4964	+	19.9123i	−0.935561	+	1.62044i	−0.773631	+	0.633637i	$0.781561\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.99450	−	17.3110i	−0.802777	−	1.39045i
$156$		0			0
$157$	18.5804			1.48288			0.741441	−	0.671019i	$-0.234143\pi$
$157$	18.5804			1.48288			0.741441	+	0.671019i	$0.234143\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.54579	+	19.1503i	−0.515880	+	1.50926i
$162$		0			0
$163$	−2.45194	+	4.24688i	−0.192050	+	0.332641i	−0.945930	−	0.324372i	$-0.894847\pi$
$163$	−2.45194	+	4.24688i	−0.192050	+	0.332641i	0.753879	+	0.657013i	$0.228180\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.47493	−	9.48286i	0.423663	−	0.733805i	−0.572632	−	0.819813i	$-0.694077\pi$
$167$	5.47493	−	9.48286i	0.423663	−	0.733805i	0.996295	+	0.0860073i	$0.0274108\pi$
$168$		0			0
$169$	6.13164	+	10.6203i	0.471664	+	0.816947i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	13.4054			1.01920			0.509598	−	0.860413i	$-0.329794\pi$
$173$	13.4054			1.01920			0.509598	+	0.860413i	$0.329794\pi$
$174$		0			0
$175$	−6.96470	+	1.37008i	−0.526482	+	0.103569i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.64888	+	11.5162i	0.496961	+	0.860761i	0.999994	−	0.00350600i	$-0.00111600\pi$
$179$	6.64888	+	11.5162i	0.496961	+	0.860761i	−0.503033	+	0.864267i	$0.667783\pi$
$180$		0			0
$181$	−10.9190			−0.811601			−0.405801	−	0.913962i	$-0.633007\pi$
$181$	−10.9190			−0.811601			−0.405801	+	0.913962i	$0.633007\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.54013			0.186754
$186$		0			0
$187$	−2.78685			−0.203795
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.6111			1.34665			0.673325	−	0.739347i	$-0.264866\pi$
$191$	18.6111			1.34665			0.673325	+	0.739347i	$0.264866\pi$
$192$		0			0
$193$	2.92940			0.210863			0.105431	−	0.994427i	$-0.466378\pi$
$193$	2.92940			0.210863			0.105431	+	0.994427i	$0.466378\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.5050			1.31843			0.659214	−	0.751956i	$-0.270889\pi$
$197$	18.5050			1.31843			0.659214	+	0.751956i	$0.270889\pi$
$198$		0			0
$199$	0.793836	+	1.37496i	0.0562736	+	0.0974687i	0.892790	−	0.450473i	$-0.148745\pi$
$199$	0.793836	+	1.37496i	0.0562736	+	0.0974687i	−0.836516	+	0.547942i	$0.815411\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.84070	−	20.0131i	0.480123	−	1.40465i
$204$		0			0
$205$	−9.28977			−0.648826
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.58032	+	4.46924i	0.178484	+	0.309144i
$210$		0			0
$211$	12.3436	−	21.3798i	0.849770	−	1.47184i	−0.0316443	−	0.999499i	$-0.510074\pi$
$211$	12.3436	−	21.3798i	0.849770	−	1.47184i	0.881414	−	0.472345i	$-0.156592\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.33905	+	5.78340i	−0.227721	+	0.394425i
$216$		0			0
$217$	−12.5500	−	14.3716i	−0.851950	−	0.975611i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.695474			−0.0467826
$222$		0			0
$223$	−9.78468	−	16.9476i	−0.655231	−	1.13489i	−0.981836	−	0.189732i	$-0.939238\pi$
$223$	−9.78468	−	16.9476i	−0.655231	−	1.13489i	0.326605	−	0.945161i	$-0.394095\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.32404	−	7.48945i	0.286996	−	0.497092i	−0.686095	−	0.727512i	$-0.740677\pi$
$227$	4.32404	−	7.48945i	0.286996	−	0.497092i	0.973091	+	0.230420i	$0.0740099\pi$
$228$		0			0
$229$	−5.77136	−	9.99630i	−0.381382	−	0.660574i	0.609878	−	0.792496i	$-0.291219\pi$
$229$	−5.77136	−	9.99630i	−0.381382	−	0.660574i	−0.991260	+	0.131922i	$0.957885\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.12745	−	14.0772i	0.532447	−	0.922225i	−0.466835	−	0.884344i	$-0.654606\pi$
$233$	8.12745	−	14.0772i	0.532447	−	0.922225i	0.999282	−	0.0378811i	$-0.0120608\pi$
$234$		0			0
$235$	0.852382	+	1.47637i	0.0556033	+	0.0963077i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.4336	+	21.5355i	−0.804260	+	1.39302i	0.112530	+	0.993648i	$0.464105\pi$
$239$	−12.4336	+	21.5355i	−0.804260	+	1.39302i	−0.916790	+	0.399371i	$0.869229\pi$
$240$		0			0
$241$	9.51814	−	16.4859i	0.613117	−	1.06195i	−0.377595	−	0.925971i	$-0.623249\pi$
$241$	9.51814	−	16.4859i	0.613117	−	1.06195i	0.990712	−	0.135979i	$-0.0434180\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.9568	+	7.34928i	−1.14722	+	0.469528i
$246$		0			0
$247$	0.643931	+	1.11532i	0.0409724	+	0.0709662i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.980433			0.0618844			0.0309422	−	0.999521i	$-0.490149\pi$
$251$	0.980433			0.0618844			0.0309422	+	0.999521i	$0.490149\pi$
$252$		0			0
$253$	−26.3093			−1.65405
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.18362	+	3.78215i	0.136211	+	0.235924i	0.926059	−	0.377378i	$-0.123174\pi$
$257$	2.18362	+	3.78215i	0.136211	+	0.235924i	−0.789849	+	0.613302i	$0.789841\pi$
$258$		0			0
$259$	2.37903	−	0.467998i	0.147826	−	0.0290800i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.24212	+	10.8117i	−0.384905	+	0.666676i	−0.991756	−	0.128140i	$-0.959099\pi$
$263$	−6.24212	+	10.8117i	−0.384905	+	0.666676i	0.606851	+	0.794816i	$0.292433\pi$
$264$		0			0
$265$	17.5079	−	30.3247i	1.07550	−	1.86283i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.29270	−	14.3634i	−0.505615	−	0.875750i	−0.999979	−	0.00649532i	$-0.997932\pi$
$269$	−8.29270	−	14.3634i	−0.505615	−	0.875750i	0.494364	−	0.869255i	$-0.335401\pi$
$270$		0			0
$271$	12.9814	−	22.4845i	0.788566	−	1.36584i	−0.138279	−	0.990393i	$-0.544157\pi$
$271$	12.9814	−	22.4845i	0.788566	−	1.36584i	0.926845	−	0.375444i	$-0.122510\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.61376	−	7.99127i	−0.278220	−	0.481892i
$276$		0			0
$277$	0.980373	−	1.69806i	0.0589049	−	0.102026i	−0.835069	−	0.550145i	$-0.814572\pi$
$277$	0.980373	−	1.69806i	0.0589049	−	0.102026i	0.893974	+	0.448119i	$0.147906\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.42057	−	16.3169i	−0.561984	−	0.973385i	−0.997323	−	0.0731185i	$-0.976705\pi$
$281$	−9.42057	−	16.3169i	−0.561984	−	0.973385i	0.435339	−	0.900267i	$-0.356628\pi$
$282$		0			0
$283$	−23.4844			−1.39600			−0.698002	−	0.716095i	$-0.745928\pi$
$283$	−23.4844			−1.39600			−0.698002	+	0.716095i	$0.745928\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.70058	+	1.71156i	−0.513579	+	0.101030i
$288$		0			0
$289$	8.17174	−	14.1539i	0.480690	−	0.832580i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.00384	−	1.73871i	0.0586452	−	0.101576i	−0.835212	−	0.549928i	$-0.814655\pi$
$293$	1.00384	−	1.73871i	0.0586452	−	0.101576i	0.893857	+	0.448351i	$0.147989\pi$
$294$		0			0
$295$	−2.03641	−	3.52717i	−0.118564	−	0.205360i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.56561			−0.379699
$300$		0			0
$301$	−2.06173	+	6.03179i	−0.118836	+	0.347666i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.8446	+	27.4436i	0.907257	+	1.57142i
$306$		0			0
$307$	32.7633			1.86990			0.934951	−	0.354777i	$-0.115443\pi$
$307$	32.7633			1.86990			0.934951	+	0.354777i	$0.115443\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	14.0996			0.799514			0.399757	−	0.916621i	$-0.369094\pi$
$311$	14.0996			0.799514			0.399757	+	0.916621i	$0.369094\pi$
$312$		0			0
$313$	−34.1539			−1.93049			−0.965245	−	0.261345i	$-0.915834\pi$
$313$	−34.1539			−1.93049			−0.965245	+	0.261345i	$0.915834\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.58117			0.0888074			0.0444037	−	0.999014i	$-0.485861\pi$
$317$	1.58117			0.0888074			0.0444037	+	0.999014i	$0.485861\pi$
$318$		0			0
$319$	27.4946			1.53940
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.21575			0.0676459
$324$		0			0
$325$	−1.15139	−	1.99426i	−0.0638675	−	0.110622i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.07033	+	1.22569i	0.0590092	+	0.0675743i
$330$		0			0
$331$	13.7372			0.755067			0.377533	−	0.925996i	$-0.376772\pi$
$331$	13.7372			0.755067			0.377533	+	0.925996i	$0.376772\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	22.4533	+	38.8902i	1.22675	+	2.12480i
$336$		0			0
$337$	−8.72318	+	15.1090i	−0.475182	+	0.823039i	−0.999596	−	0.0284243i	$-0.990951\pi$
$337$	−8.72318	+	15.1090i	−0.475182	+	0.823039i	0.524414	+	0.851463i	$0.324284\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.4019	−	21.4807i	0.671598	−	1.16324i
$342$		0			0
$343$	−15.4639	+	10.1916i	−0.834972	+	0.550292i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.83104			−0.205661			−0.102830	−	0.994699i	$-0.532790\pi$
$347$	−3.83104			−0.205661			−0.102830	+	0.994699i	$0.532790\pi$
$348$		0			0
$349$	1.69984	+	2.94421i	0.0909903	+	0.157600i	0.907928	−	0.419126i	$-0.137663\pi$
$349$	1.69984	+	2.94421i	0.0909903	+	0.157600i	−0.816938	+	0.576726i	$0.804330\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.27841	−	10.8745i	0.334166	−	0.578793i	−0.649158	−	0.760653i	$-0.724879\pi$
$353$	6.27841	−	10.8745i	0.334166	−	0.578793i	0.983324	+	0.181861i	$0.0582120\pi$
$354$		0			0
$355$	−19.9815	−	34.6089i	−1.06051	−	1.83685i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.02209	−	10.4306i	0.317834	−	0.550504i	−0.662202	−	0.749325i	$-0.730378\pi$
$359$	6.02209	−	10.4306i	0.317834	−	0.550504i	0.980036	+	0.198821i	$0.0637113\pi$
$360$		0			0
$361$	8.37435	+	14.5048i	0.440756	+	0.763411i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.5554	−	20.0146i	0.604838	−	1.04761i
$366$		0			0
$367$	1.01257	−	1.75382i	0.0528557	−	0.0915487i	−0.838387	−	0.545075i	$-0.816501\pi$
$367$	1.01257	−	1.75382i	0.0528557	−	0.0915487i	0.891243	+	0.453527i	$0.149834\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	10.8105	−	31.6270i	0.561251	−	1.64199i
$372$		0			0
$373$	−10.8130	−	18.7286i	−0.559874	−	0.969731i	−0.997506	−	0.0705766i	$-0.977516\pi$
$373$	−10.8130	−	18.7286i	−0.559874	−	0.969731i	0.437632	−	0.899154i	$-0.355817\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.86142			0.353381
$378$		0			0
$379$	−6.76701			−0.347598			−0.173799	−	0.984781i	$-0.555604\pi$
$379$	−6.76701			−0.347598			−0.173799	+	0.984781i	$0.555604\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.82822	−	6.63068i	−0.195613	−	0.338812i	0.751488	−	0.659747i	$-0.229336\pi$
$383$	−3.82822	−	6.63068i	−0.195613	−	0.338812i	−0.947101	+	0.320935i	$0.896003\pi$
$384$		0			0
$385$	−16.5906	−	18.9988i	−0.845537	−	0.968267i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.5781	+	18.3218i	−0.536329	+	0.928950i	0.462768	+	0.886479i	$0.346856\pi$
$389$	−10.5781	+	18.3218i	−0.536329	+	0.928950i	−0.999098	+	0.0424705i	$0.986477\pi$
$390$		0			0
$391$	−3.09898	+	5.36759i	−0.156722	+	0.271451i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.81360	−	6.60534i	−0.191883	−	0.332351i
$396$		0			0
$397$	4.02642	−	6.97396i	0.202080	−	0.350013i	−0.747118	−	0.664691i	$-0.768563\pi$
$397$	4.02642	−	6.97396i	0.202080	−	0.350013i	0.949199	+	0.314678i	$0.101896\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.88886	−	6.73571i	−0.194201	−	0.336365i	0.752438	−	0.658664i	$-0.228878\pi$
$401$	−3.88886	−	6.73571i	−0.194201	−	0.336365i	−0.946638	+	0.322298i	$0.895545\pi$
$402$		0			0
$403$	3.09495	−	5.36061i	0.154170	−	0.267031i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.57599	+	2.72969i	0.0781188	+	0.135306i
$408$		0			0
$409$	19.5265			0.965526			0.482763	−	0.875751i	$-0.339633\pi$
$409$	19.5265			0.965526			0.482763	+	0.875751i	$0.339633\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.55710	−	2.92827i	−0.125827	−	0.144091i
$414$		0			0
$415$	−15.9604	+	27.6442i	−0.783466	+	1.35700i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.5259	−	21.6955i	0.611932	−	1.05990i	−0.378983	−	0.925404i	$-0.623726\pi$
$419$	12.5259	−	21.6955i	0.611932	−	1.05990i	0.990915	−	0.134493i	$-0.0429406\pi$
$420$		0			0
$421$	18.0746	+	31.3061i	0.880902	+	1.52577i	0.850340	+	0.526234i	$0.176396\pi$
$421$	18.0746	+	31.3061i	0.880902	+	1.52577i	0.0305620	+	0.999533i	$0.490270\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.17383			−0.105446
$426$		0			0
$427$	19.8959	+	22.7838i	0.962829	+	1.10258i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.95636	+	3.38852i	0.0942346	+	0.163219i	0.909289	−	0.416165i	$-0.136626\pi$
$431$	1.95636	+	3.38852i	0.0942346	+	0.163219i	−0.815054	+	0.579385i	$0.803293\pi$
$432$		0			0
$433$	−14.2929			−0.686872			−0.343436	−	0.939176i	$-0.611591\pi$
$433$	−14.2929			−0.686872			−0.343436	+	0.939176i	$0.611591\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.4772			0.549031
$438$		0			0
$439$	−4.78469			−0.228361			−0.114180	−	0.993460i	$-0.536424\pi$
$439$	−4.78469			−0.228361			−0.114180	+	0.993460i	$0.536424\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.26427			0.392647			0.196324	−	0.980539i	$-0.437100\pi$
$443$	8.26427			0.392647			0.196324	+	0.980539i	$0.437100\pi$
$444$		0			0
$445$	28.3497			1.34390
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.6036			0.972346			0.486173	−	0.873863i	$-0.338392\pi$
$449$	20.6036			0.972346			0.486173	+	0.873863i	$0.338392\pi$
$450$		0			0
$451$	−5.76370	−	9.98301i	−0.271402	−	0.470082i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.14028	−	4.74124i	−0.194099	−	0.222273i
$456$		0			0
$457$	−17.9644			−0.840339			−0.420170	−	0.907446i	$-0.638029\pi$
$457$	−17.9644			−0.840339			−0.420170	+	0.907446i	$0.638029\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.03501	−	6.98885i	−0.187929	−	0.325503i	0.756630	−	0.653843i	$-0.226844\pi$
$461$	−4.03501	−	6.98885i	−0.187929	−	0.325503i	−0.944560	+	0.328340i	$0.893511\pi$
$462$		0			0
$463$	−2.50704	+	4.34232i	−0.116512	+	0.201805i	−0.918383	−	0.395692i	$-0.870505\pi$
$463$	−2.50704	+	4.34232i	−0.116512	+	0.201805i	0.801871	+	0.597497i	$0.203838\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.1673	−	22.8063i	0.609308	−	1.05535i	−0.382047	−	0.924143i	$-0.624781\pi$
$467$	13.1673	−	22.8063i	0.609308	−	1.05535i	0.991355	−	0.131209i	$-0.0418859\pi$
$468$		0			0
$469$	28.1944	+	32.2868i	1.30189	+	1.49086i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.28665			−0.381020
$474$		0			0
$475$	2.01272	+	3.48614i	0.0923500	+	0.159955i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.6222	+	21.8623i	−0.576724	+	0.998916i	0.419128	+	0.907927i	$0.362336\pi$
$479$	−12.6222	+	21.8623i	−0.576724	+	0.998916i	−0.995852	+	0.0909886i	$0.970997\pi$
$480$		0			0
$481$	0.393295	+	0.681208i	0.0179327	+	0.0310604i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−10.6119	+	18.3803i	−0.481861	+	0.834608i
$486$		0			0
$487$	1.36124	+	2.35774i	0.0616837	+	0.106839i	0.895218	−	0.445628i	$-0.147020\pi$
$487$	1.36124	+	2.35774i	0.0616837	+	0.106839i	−0.833534	+	0.552468i	$0.813686\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	15.8020	−	27.3698i	0.713134	−	1.23518i	−0.250541	−	0.968106i	$-0.580609\pi$
$491$	15.8020	−	27.3698i	0.713134	−	1.23518i	0.963675	−	0.267078i	$-0.0860581\pi$
$492$		0			0
$493$	3.23860	−	5.60942i	0.145859	−	0.252635i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.0905	−	28.7324i	−1.12546	−	1.28883i
$498$		0			0
$499$	−2.97445	−	5.15190i	−0.133155	−	0.230631i	0.791736	−	0.610863i	$-0.209177\pi$
$499$	−2.97445	−	5.15190i	−0.133155	−	0.230631i	−0.924891	+	0.380232i	$0.875844\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.6905			1.23466			0.617329	−	0.786705i	$-0.288215\pi$
$503$	27.6905			1.23466			0.617329	+	0.786705i	$0.288215\pi$
$504$		0			0
$505$	−10.2169			−0.454647
$506$		0			0
$507$		0			0
$508$		0			0
$509$	18.6443	+	32.2928i	0.826392	+	1.43135i	0.900850	+	0.434129i	$0.142944\pi$
$509$	18.6443	+	32.2928i	0.826392	+	1.43135i	−0.0744581	+	0.997224i	$0.523723\pi$
$510$		0			0
$511$	7.13501	−	20.8741i	0.315634	−	0.923418i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−22.3414	+	38.6964i	−0.984480	+	1.70517i
$516$		0			0
$517$	−1.05769	+	1.83198i	−0.0465174	+	0.0805704i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18.1271	−	31.3971i	−0.794163	−	1.37553i	−0.923370	−	0.383912i	$-0.874577\pi$
$521$	−18.1271	−	31.3971i	−0.794163	−	1.37553i	0.129207	−	0.991618i	$-0.458757\pi$
$522$		0			0
$523$	10.2931	−	17.8282i	0.450086	−	0.779572i	−0.548305	−	0.836278i	$-0.684727\pi$
$523$	10.2931	−	17.8282i	0.450086	−	0.779572i	0.998391	+	0.0567068i	$0.0180600\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.92164	−	5.06043i	−0.127269	−	0.220436i
$528$		0			0
$529$	−17.7559	+	30.7541i	−0.771996	+	1.33714i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.43836	−	2.49131i	−0.0623023	−	0.107911i
$534$		0			0
$535$	−17.5603			−0.759196
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.0388	−	14.7371i	−0.820057	−	0.634772i
$540$		0			0
$541$	−0.649192	+	1.12443i	−0.0279109	+	0.0483432i	−0.879643	−	0.475634i	$-0.842219\pi$
$541$	−0.649192	+	1.12443i	−0.0279109	+	0.0483432i	0.851733	+	0.523977i	$0.175552\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−13.5673	+	23.4993i	−0.581159	+	1.00660i
$546$		0			0
$547$	−13.8412	−	23.9736i	−0.591805	−	1.02504i	−0.993989	−	0.109478i	$-0.965082\pi$
$547$	−13.8412	−	23.9736i	−0.591805	−	1.02504i	0.402184	−	0.915559i	$-0.368251\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−11.9943			−0.510976
$552$		0			0
$553$	−4.78870	−	5.48378i	−0.203636	−	0.233194i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.72089	+	13.3730i	0.327145	+	0.566631i	0.981944	−	0.189172i	$-0.0605802\pi$
$557$	7.72089	+	13.3730i	0.327145	+	0.566631i	−0.654799	+	0.755803i	$0.727247\pi$
$558$		0			0
$559$	−2.06797			−0.0874660
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.91343			−0.0806414			−0.0403207	−	0.999187i	$-0.512838\pi$
$563$	−1.91343			−0.0806414			−0.0403207	+	0.999187i	$0.512838\pi$
$564$		0			0
$565$	−22.5604			−0.949122
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.7628			0.618887			0.309444	−	0.950918i	$-0.399857\pi$
$569$	14.7628			0.618887			0.309444	+	0.950918i	$0.399857\pi$
$570$		0			0
$571$	2.56417			0.107307			0.0536535	−	0.998560i	$-0.482913\pi$
$571$	2.56417			0.107307			0.0536535	+	0.998560i	$0.482913\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.5220			−0.855827
$576$		0			0
$577$	7.01283	+	12.1466i	0.291948	+	0.505669i	0.974270	−	0.225383i	$-0.0723632\pi$
$577$	7.01283	+	12.1466i	0.291948	+	0.505669i	−0.682322	+	0.731052i	$0.739030\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9.85491	+	28.8315i	−0.408851	+	1.19613i
$582$		0			0
$583$	43.4501			1.79952
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−15.7666	−	27.3085i	−0.650756	−	1.12714i	−0.982940	−	0.183928i	$-0.941119\pi$
$587$	−15.7666	−	27.3085i	−0.650756	−	1.12714i	0.332183	−	0.943215i	$-0.392215\pi$
$588$		0			0
$589$	−5.41022	+	9.37078i	−0.222924	+	0.386116i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.72311	−	9.91272i	0.235020	−	0.407067i	−0.724258	−	0.689529i	$-0.757818\pi$
$593$	5.72311	−	9.91272i	0.235020	−	0.407067i	0.959279	+	0.282462i	$0.0911511\pi$
$594$		0			0
$595$	−5.83033	+	1.14693i	−0.239020	+	0.0470196i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5.61368			−0.229369			−0.114684	−	0.993402i	$-0.536586\pi$
$599$	−5.61368			−0.229369			−0.114684	+	0.993402i	$0.536586\pi$
$600$		0			0
$601$	19.2223	+	33.2940i	0.784094	+	1.35809i	0.929539	+	0.368725i	$0.120205\pi$
$601$	19.2223	+	33.2940i	0.784094	+	1.35809i	−0.145444	+	0.989366i	$0.546461\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.14991	−	1.99171i	0.0467507	−	0.0809745i
$606$		0			0
$607$	8.17187	+	14.1541i	0.331686	+	0.574497i	0.982843	−	0.184446i	$-0.0590492\pi$
$607$	8.17187	+	14.1541i	0.331686	+	0.574497i	−0.651157	+	0.758943i	$0.725716\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.263953	+	0.457180i	−0.0106784	+	0.0184955i
$612$		0			0
$613$	−6.19332	−	10.7272i	−0.250146	−	0.433266i	0.713420	−	0.700737i	$-0.247145\pi$
$613$	−6.19332	−	10.7272i	−0.250146	−	0.433266i	−0.963566	+	0.267471i	$0.913812\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.9853	+	36.3476i	−0.844836	+	1.46330i	0.0409280	+	0.999162i	$0.486969\pi$
$617$	−20.9853	+	36.3476i	−0.844836	+	1.46330i	−0.885764	+	0.464136i	$0.846365\pi$
$618$		0			0
$619$	17.9473	−	31.0856i	0.721361	−	1.24943i	−0.239093	−	0.970997i	$-0.576850\pi$
$619$	17.9473	−	31.0856i	0.721361	−	1.24943i	0.960454	−	0.278438i	$-0.0898166\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	26.5516	−	5.22319i	1.06377	−	0.209263i
$624$		0			0
$625$	15.6083	+	27.0343i	0.624331	+	1.08137i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.742544			0.0296072
$630$		0			0
$631$	−19.5519			−0.778349			−0.389175	−	0.921164i	$-0.627240\pi$
$631$	−19.5519			−0.778349			−0.389175	+	0.921164i	$0.627240\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−17.4149	−	30.1636i	−0.691091	−	1.19700i
$636$		0			0
$637$	−4.75122	−	3.67772i	−0.188250	−	0.145717i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.30132	+	12.6463i	−0.288385	+	0.499497i	−0.973424	−	0.229009i	$-0.926452\pi$
$641$	−7.30132	+	12.6463i	−0.288385	+	0.499497i	0.685040	+	0.728506i	$0.259785\pi$
$642$		0			0
$643$	−5.96942	+	10.3393i	−0.235411	+	0.407744i	−0.959392	−	0.282076i	$-0.908977\pi$
$643$	−5.96942	+	10.3393i	−0.235411	+	0.407744i	0.723981	+	0.689820i	$0.242310\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.92060	+	3.32658i	0.0755067	+	0.130781i	0.901306	−	0.433182i	$-0.142609\pi$
$647$	1.92060	+	3.32658i	0.0755067	+	0.130781i	−0.825800	+	0.563963i	$0.809276\pi$
$648$		0			0
$649$	2.52692	−	4.37675i	0.0991903	−	0.171803i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.9959	+	34.6339i	0.782501	+	1.35533i	0.930481	+	0.366340i	$0.119389\pi$
$653$	19.9959	+	34.6339i	0.782501	+	1.35533i	−0.147980	+	0.988990i	$0.547277\pi$
$654$		0			0
$655$	−2.19735	+	3.80592i	−0.0858575	+	0.148710i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.60101	−	2.77303i	−0.0623665	−	0.108022i	0.833156	−	0.553038i	$-0.186531\pi$
$659$	−1.60101	−	2.77303i	−0.0623665	−	0.108022i	−0.895523	+	0.445016i	$0.853198\pi$
$660$		0			0
$661$	−43.3030			−1.68429			−0.842146	−	0.539250i	$-0.818708\pi$
$661$	−43.3030			−1.68429			−0.842146	+	0.539250i	$0.818708\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.23755	+	8.28808i	0.280660	+	0.321398i
$666$		0			0
$667$	30.5740	−	52.9557i	1.18383	−	2.05045i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−19.6610	+	34.0539i	−0.759006	+	1.31464i
$672$		0			0
$673$	12.2936	+	21.2931i	0.473883	+	0.820790i	0.999553	−	0.0298991i	$-0.00951859\pi$
$673$	12.2936	+	21.2931i	0.473883	+	0.820790i	−0.525670	+	0.850689i	$0.676185\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	38.4188			1.47655			0.738276	−	0.674498i	$-0.235640\pi$
$677$	38.4188			1.47655			0.738276	+	0.674498i	$0.235640\pi$
$678$		0			0
$679$	−6.55242	+	19.1697i	−0.251459	+	0.735666i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.122464	+	0.212113i	0.00468594	+	0.00811629i	0.868359	−	0.495936i	$-0.165175\pi$
$683$	0.122464	+	0.212113i	0.00468594	+	0.00811629i	−0.863673	+	0.504053i	$0.831842\pi$
$684$		0			0
$685$	13.6591			0.521886
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.8432			0.413093
$690$		0			0
$691$	−7.30292			−0.277816			−0.138908	−	0.990305i	$-0.544359\pi$
$691$	−7.30292			−0.277816			−0.138908	+	0.990305i	$0.544359\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	22.8950			0.868457
$696$		0			0
$697$	−2.71563			−0.102862
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−32.3889			−1.22331			−0.611656	−	0.791124i	$-0.709496\pi$
$701$	−32.3889			−1.22331			−0.611656	+	0.791124i	$0.709496\pi$
$702$		0			0
$703$	−0.687513	−	1.19081i	−0.0259301	−	0.0449122i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.56893	+	1.88238i	−0.359877	+	0.0707943i
$708$		0			0
$709$	2.92274			0.109766			0.0548828	−	0.998493i	$-0.482521\pi$
$709$	2.92274			0.109766			0.0548828	+	0.998493i	$0.482521\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−27.5817	−	47.7729i	−1.03294	−	1.78911i
$714$		0			0
$715$	4.09141	−	7.08652i	0.153010	−	0.265021i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.78527	+	15.2165i	−0.327635	+	0.567481i	−0.982042	−	0.188662i	$-0.939585\pi$
$719$	−8.78527	+	15.2165i	−0.327635	+	0.567481i	0.654407	+	0.756143i	$0.272918\pi$
$720$		0			0
$721$	−13.7949	+	40.3584i	−0.513750	+	1.50302i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	21.4466			0.796506
$726$		0			0
$727$	20.0486	+	34.7252i	0.743561	+	1.28789i	0.950864	+	0.309609i	$0.100198\pi$
$727$	20.0486	+	34.7252i	0.743561	+	1.28789i	−0.207303	+	0.978277i	$0.566469\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.976087	+	1.69063i	−0.0361019	+	0.0625303i
$732$		0			0
$733$	3.56234	+	6.17016i	0.131578	+	0.227900i	0.924285	−	0.381703i	$-0.124662\pi$
$733$	3.56234	+	6.17016i	0.131578	+	0.227900i	−0.792707	+	0.609603i	$0.791329\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−27.8615	+	48.2576i	−1.02629	+	1.77759i
$738$		0			0
$739$	−2.13570	−	3.69914i	−0.0785631	−	0.136075i	0.824067	−	0.566492i	$-0.191700\pi$
$739$	−2.13570	−	3.69914i	−0.0785631	−	0.136075i	−0.902630	+	0.430417i	$0.858367\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.108257	+	0.187507i	−0.00397157	+	0.00687896i	−0.868004	−	0.496557i	$-0.834598\pi$
$743$	−0.108257	+	0.187507i	−0.00397157	+	0.00687896i	0.864033	+	0.503436i	$0.167931\pi$
$744$		0			0
$745$	19.2833	−	33.3997i	0.706487	−	1.22367i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.4465	+	3.23533i	−0.600942	+	0.118216i
$750$		0			0
$751$	−11.7920	−	20.4244i	−0.430297	−	0.745296i	0.566602	−	0.823992i	$-0.308258\pi$
$751$	−11.7920	−	20.4244i	−0.430297	−	0.745296i	−0.996899	+	0.0786955i	$0.974925\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−63.7312			−2.31942
$756$		0			0
$757$	−22.0176			−0.800242			−0.400121	−	0.916462i	$-0.631032\pi$
$757$	−22.0176			−0.800242			−0.400121	+	0.916462i	$0.631032\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.05699	−	15.6872i	−0.328316	−	0.568659i	0.653862	−	0.756614i	$-0.273148\pi$
$761$	−9.05699	−	15.6872i	−0.328316	−	0.568659i	−0.982178	+	0.187954i	$0.939814\pi$
$762$		0			0
$763$	−8.37727	+	24.5085i	−0.303277	+	0.887267i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.630606	−	1.09224i	0.0227699	−	0.0394385i
$768$		0			0
$769$	3.16710	−	5.48558i	0.114209	−	0.197815i	−0.803255	−	0.595636i	$-0.796900\pi$
$769$	3.16710	−	5.48558i	0.114209	−	0.197815i	0.917463	+	0.397821i	$0.130233\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.10740	−	5.38218i	−0.111765	−	0.193584i	0.804717	−	0.593659i	$-0.202317\pi$
$773$	−3.10740	−	5.38218i	−0.111765	−	0.193584i	−0.916482	+	0.400076i	$0.868984\pi$
$774$		0			0
$775$	9.67381	−	16.7555i	0.347494	−	0.601876i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.51437	+	4.35502i	0.0900867	+	0.156035i
$780$		0			0
$781$	24.7944	−	42.9451i	0.887212	−	1.53670i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	25.7506	+	44.6014i	0.919079	+	1.59189i
$786$		0			0
$787$	−19.3183			−0.688624			−0.344312	−	0.938855i	$-0.611888\pi$
$787$	−19.3183			−0.688624			−0.344312	+	0.938855i	$0.611888\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−21.1295	+	4.15656i	−0.751279	+	0.147790i
$792$		0			0
$793$	−4.90651	+	8.49832i	−0.174235	+	0.301784i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.09519	−	8.82513i	0.180481	−	0.312602i	−0.761563	−	0.648090i	$-0.775568\pi$
$797$	5.09519	−	8.82513i	0.180481	−	0.312602i	0.942044	+	0.335488i	$0.108901\pi$
$798$		0			0
$799$	0.249172	+	0.431579i	0.00881509	+	0.0152682i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	28.6775			1.01201
$804$		0			0
$805$	−55.0412	+	10.8276i	−1.93995	+	0.381623i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	23.7068	+	41.0613i	0.833485	+	1.44364i	0.895258	+	0.445548i	$0.146991\pi$
$809$	23.7068	+	41.0613i	0.833485	+	1.44364i	−0.0617729	+	0.998090i	$0.519675\pi$
$810$		0			0
$811$	47.4177			1.66506			0.832531	−	0.553979i	$-0.186891\pi$
$811$	47.4177			1.66506			0.832531	+	0.553979i	$0.186891\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−13.5925			−0.476126
$816$		0			0
$817$	3.61499			0.126473
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−53.6353			−1.87189			−0.935943	−	0.352152i	$-0.885450\pi$
$821$	−53.6353			−1.87189			−0.935943	+	0.352152i	$0.885450\pi$
$822$		0			0
$823$	−0.950384			−0.0331283			−0.0165641	−	0.999863i	$-0.505273\pi$
$823$	−0.950384			−0.0331283			−0.0165641	+	0.999863i	$0.505273\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−20.7813			−0.722636			−0.361318	−	0.932443i	$-0.617673\pi$
$827$	−20.7813			−0.722636			−0.361318	+	0.932443i	$0.617673\pi$
$828$		0			0
$829$	12.1615	+	21.0644i	0.422387	+	0.731596i	0.996172	−	0.0874096i	$-0.0278589\pi$
$829$	12.1615	+	21.0644i	0.422387	+	0.731596i	−0.573785	+	0.819006i	$0.694526\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.24923	+	2.14838i	−0.181875	+	0.0744368i
$834$		0			0
$835$	30.3508			1.05033
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.7367	+	27.2567i	0.543290	+	0.941006i	0.998712	+	0.0507305i	$0.0161550\pi$
$839$	15.7367	+	27.2567i	0.543290	+	0.941006i	−0.455422	+	0.890276i	$0.650512\pi$
$840$		0			0
$841$	−17.4514	+	30.2268i	−0.601774	+	1.04230i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−16.9957	+	29.4373i	−0.584668	+	1.01268i
$846$		0			0
$847$	0.710026	−	2.07725i	0.0243968	−	0.0713751i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.00998			0.240299
$852$		0			0
$853$	−26.6959	−	46.2386i	−0.914049	−	1.58318i	−0.808287	−	0.588788i	$-0.799605\pi$
$853$	−26.6959	−	46.2386i	−0.914049	−	1.58318i	−0.105762	−	0.994391i	$-0.533728\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.8149	−	18.7319i	0.369428	−	0.639869i	−0.620048	−	0.784564i	$-0.712887\pi$
$857$	10.8149	−	18.7319i	0.369428	−	0.639869i	0.989476	+	0.144695i	$0.0462202\pi$
$858$		0			0
$859$	17.2144	+	29.8162i	0.587348	+	1.01732i	0.994578	+	0.103991i	$0.0331614\pi$
$859$	17.2144	+	29.8162i	0.587348	+	1.01732i	−0.407230	+	0.913326i	$0.633505\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.4262	−	23.2548i	0.457033	−	0.791604i	−0.541770	−	0.840527i	$-0.682246\pi$
$863$	13.4262	−	23.2548i	0.457033	−	0.791604i	0.998803	+	0.0489229i	$0.0155789\pi$
$864$		0			0
$865$	18.5786	+	32.1790i	0.631690	+	1.09412i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.73217	−	8.19636i	0.160528	−	0.278043i
$870$		0			0
$871$	−6.95299	+	12.0429i	−0.235593	+	0.408059i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.1771	+	12.7994i	0.377854	+	0.432700i
$876$		0			0
$877$	−16.2034	−	28.0651i	−0.547150	−	0.947692i	−0.998468	−	0.0553291i	$-0.982379\pi$
$877$	−16.2034	−	28.0651i	−0.547150	−	0.947692i	0.451318	−	0.892363i	$-0.350954\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	39.0404			1.31530			0.657652	−	0.753322i	$-0.271550\pi$
$881$	39.0404			1.31530			0.657652	+	0.753322i	$0.271550\pi$
$882$		0			0
$883$	−13.8079			−0.464672			−0.232336	−	0.972636i	$-0.574637\pi$
$883$	−13.8079			−0.464672			−0.232336	+	0.972636i	$0.574637\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.9778	+	20.7461i	0.402174	+	0.696586i	0.993988	−	0.109489i	$-0.0349214\pi$
$887$	11.9778	+	20.7461i	0.402174	+	0.696586i	−0.591814	+	0.806074i	$0.701588\pi$
$888$		0			0
$889$	−21.8678	−	25.0419i	−0.733422	−	0.839879i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.461412	−	0.799189i	0.0154406	−	0.0267438i
$894$		0			0
$895$	−18.4293	+	31.9206i	−0.616025	+	1.06699i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	28.8244	+	49.9253i	0.961346	+	1.66510i
$900$		0			0
$901$	5.11801	−	8.86465i	0.170505	−	0.295324i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−15.1326	−	26.2104i	−0.503025	−	0.871264i
$906$		0			0
$907$	−2.35064	+	4.07143i	−0.0780517	+	0.135190i	−0.902409	−	0.430880i	$-0.858203\pi$
$907$	−2.35064	+	4.07143i	−0.0780517	+	0.135190i	0.824358	+	0.566069i	$0.191537\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.0884	−	36.5262i	−0.698689	−	1.21017i	−0.968921	−	0.247370i	$-0.920434\pi$
$911$	−21.0884	−	36.5262i	−0.698689	−	1.21017i	0.270232	−	0.962795i	$-0.412900\pi$
$912$		0			0
$913$	−39.6095			−1.31088
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.35677	+	3.96937i	−0.0448046	+	0.131080i
$918$		0			0
$919$	−20.1071	+	34.8265i	−0.663271	+	1.14882i	0.316480	+	0.948599i	$0.397499\pi$
$919$	−20.1071	+	34.8265i	−0.663271	+	1.14882i	−0.979751	+	0.200220i	$0.935834\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.18756	−	10.7172i	0.203666	−	0.352760i
$924$		0			0
$925$	1.22932	+	2.12924i	0.0404196	+	0.0700089i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	30.1424			0.988938			0.494469	−	0.869195i	$-0.335362\pi$
$929$	30.1424			0.988938			0.494469	+	0.869195i	$0.335362\pi$
$930$		0			0
$931$	8.30552	+	6.42896i	0.272203	+	0.210701i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.86230	−	6.68970i	−0.126311	−	0.218776i
$936$		0			0
$937$	35.1550			1.14846			0.574231	−	0.818693i	$-0.305301\pi$
$937$	35.1550			1.14846			0.574231	+	0.818693i	$0.305301\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.04326			0.0992075			0.0496038	−	0.998769i	$-0.484204\pi$
$941$	3.04326			0.0992075			0.0496038	+	0.998769i	$0.484204\pi$
$942$		0			0
$943$	−25.6369			−0.834852
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.6781			−0.411983			−0.205991	−	0.978554i	$-0.566042\pi$
$947$	−12.6781			−0.411983			−0.205991	+	0.978554i	$0.566042\pi$
$948$		0			0
$949$	7.15662			0.232314
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−23.0052			−0.745212			−0.372606	−	0.927990i	$-0.621536\pi$
$953$	−23.0052			−0.745212			−0.372606	+	0.927990i	$0.621536\pi$
$954$		0			0
$955$	25.7930	+	44.6749i	0.834643	+	1.44564i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	12.7928	−	2.51657i	0.413100	−	0.0812642i
$960$		0			0
$961$	21.0067			0.677634
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.05985	+	7.03187i	0.130691	+	0.226364i
$966$		0			0
$967$	−0.617767	+	1.07000i	−0.0198660	+	0.0344090i	−0.875788	−	0.482697i	$-0.839657\pi$
$967$	−0.617767	+	1.07000i	−0.0198660	+	0.0344090i	0.855921	+	0.517106i	$0.172991\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.01657	−	12.1530i	0.225172	−	0.390010i	−0.731199	−	0.682164i	$-0.761039\pi$
$971$	7.01657	−	12.1530i	0.225172	−	0.390010i	0.956371	+	0.292155i	$0.0943722\pi$
$972$		0			0
$973$	21.4429	−	4.21821i	0.687428	−	0.135230i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.2603			−0.712169			−0.356084	−	0.934454i	$-0.615888\pi$
$977$	−22.2603			−0.712169			−0.356084	+	0.934454i	$0.615888\pi$
$978$		0			0
$979$	17.5891	+	30.4652i	0.562151	+	0.973673i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.8671	−	29.2146i	0.537976	−	0.931801i	−0.461037	−	0.887381i	$-0.652522\pi$
$983$	16.8671	−	29.2146i	0.537976	−	0.931801i	0.999013	−	0.0444206i	$-0.0141442\pi$
$984$		0			0
$985$	25.6461	+	44.4203i	0.817152	+	1.41535i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.21474	+	15.9604i	−0.293012	+	0.507511i
$990$		0			0
$991$	6.87364	+	11.9055i	0.218348	+	0.378191i	0.954303	−	0.298840i	$-0.0965997\pi$
$991$	6.87364	+	11.9055i	0.218348	+	0.378191i	−0.735955	+	0.677031i	$0.763266\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.20035	+	3.81112i	−0.0697559	+	0.120821i
$996$		0			0
$997$	−18.6283	+	32.2651i	−0.589963	+	1.02185i	0.404273	+	0.914638i	$0.367524\pi$
$997$	−18.6283	+	32.2651i	−0.589963	+	1.02185i	−0.994237	+	0.107208i	$0.965809\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.q.d.793.9		22
3.2	odd	2		504.2.q.c.121.8	yes	22
4.3	odd	2		3024.2.q.l.2305.9		22
7.4	even	3		1512.2.t.c.361.3		22
9.2	odd	6		504.2.t.c.457.2	yes	22
9.7	even	3		1512.2.t.c.289.3		22
12.11	even	2		1008.2.q.l.625.4		22
21.11	odd	6		504.2.t.c.193.2	yes	22
28.11	odd	6		3024.2.t.k.1873.3		22
36.7	odd	6		3024.2.t.k.289.3		22
36.11	even	6		1008.2.t.l.961.10		22
63.11	odd	6		504.2.q.c.25.8	✓	22
63.25	even	3	inner	1512.2.q.d.1369.9		22
84.11	even	6		1008.2.t.l.193.10		22
252.11	even	6		1008.2.q.l.529.4		22
252.151	odd	6		3024.2.q.l.2881.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.8	✓	22	63.11	odd	6
504.2.q.c.121.8	yes	22	3.2	odd	2
504.2.t.c.193.2	yes	22	21.11	odd	6
504.2.t.c.457.2	yes	22	9.2	odd	6
1008.2.q.l.529.4		22	252.11	even	6
1008.2.q.l.625.4		22	12.11	even	2
1008.2.t.l.193.10		22	84.11	even	6
1008.2.t.l.961.10		22	36.11	even	6
1512.2.q.d.793.9		22	1.1	even	1	trivial
1512.2.q.d.1369.9		22	63.25	even	3	inner
1512.2.t.c.289.3		22	9.7	even	3
1512.2.t.c.361.3		22	7.4	even	3
3024.2.q.l.2305.9		22	4.3	odd	2
3024.2.q.l.2881.9		22	252.151	odd	6
3024.2.t.k.289.3		22	36.7	odd	6
3024.2.t.k.1873.3		22	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38590 + 2.40045i) q^{5} +(1.74026 + 1.99286i) q^{7} +O(q^{10})\)	\(q+(1.38590 + 2.40045i) q^{5} +(1.74026 + 1.99286i) q^{7} +(-1.71972 + 2.97864i) q^{11} +(-0.429164 + 0.743335i) q^{13} +(0.405132 + 0.701710i) q^{17} +(0.750215 - 1.29941i) q^{19} +(3.82465 + 6.62449i) q^{23} +(-1.34143 + 2.32343i) q^{25} +(-3.99696 - 6.92294i) q^{29} -7.21156 q^{31} +(-2.37193 + 6.93931i) q^{35} +(0.458211 - 0.793644i) q^{37} +(-1.67577 + 2.90251i) q^{41} +(1.20465 + 2.08652i) q^{43} +0.615039 q^{47} +(-0.942983 + 6.93619i) q^{49} +(-6.31646 - 10.9404i) q^{53} -9.53342 q^{55} -1.46938 q^{59} +11.4327 q^{61} -2.37911 q^{65} +16.2012 q^{67} -14.4177 q^{71} +(-4.16893 - 7.22079i) q^{73} +(-8.92877 + 1.75645i) q^{77} -2.75171 q^{79} +(5.75814 + 9.97340i) q^{83} +(-1.12294 + 1.94500i) q^{85} +(5.11395 - 8.85763i) q^{89} +(-2.22822 + 0.438331i) q^{91} +4.15889 q^{95} +(3.82852 + 6.63119i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - q^5 + 5 * q^7	\( 22 q - q^{5} + 5 q^{7} - 3 q^{11} + 7 q^{13} + q^{17} + 13 q^{19} - 22 q^{25} + 7 q^{29} - 12 q^{31} - 2 q^{35} + 6 q^{37} - 4 q^{41} + 2 q^{43} + 34 q^{47} - 25 q^{49} - q^{53} + 2 q^{55} - 42 q^{59} - 62 q^{61} - 6 q^{65} + 52 q^{67} + 32 q^{71} + 17 q^{73} + q^{77} + 32 q^{79} + 36 q^{83} + 28 q^{85} + 2 q^{89} + 15 q^{91} - 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 + 5 * q^7 - 3 * q^11 + 7 * q^13 + q^17 + 13 * q^19 - 22 * q^25 + 7 * q^29 - 12 * q^31 - 2 * q^35 + 6 * q^37 - 4 * q^41 + 2 * q^43 + 34 * q^47 - 25 * q^49 - q^53 + 2 * q^55 - 42 * q^59 - 62 * q^61 - 6 * q^65 + 52 * q^67 + 32 * q^71 + 17 * q^73 + q^77 + 32 * q^79 + 36 * q^83 + 28 * q^85 + 2 * q^89 + 15 * q^91 - 48 * q^95 + 19 * q^97

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