LMFDB - Embedded newform 729.2.c.d.487.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.2
Root			$3.10658i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.d.244.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.388866 + 0.673536i) q^{2} +(0.697566 + 1.20822i) q^{4} +(-1.18817 - 2.05798i) q^{5} +(1.25069 - 2.16626i) q^{7} -2.64050 q^{8} +O(q^{10})$	\(q+(-0.388866 + 0.673536i) q^{2} +(0.697566 + 1.20822i) q^{4} +(-1.18817 - 2.05798i) q^{5} +(1.25069 - 2.16626i) q^{7} -2.64050 q^{8} +1.84816 q^{10} +(-1.57069 + 2.72051i) q^{11} +(-0.668315 - 1.15756i) q^{13} +(0.972701 + 1.68477i) q^{14} +(-0.368329 + 0.637965i) q^{16} +6.27452 q^{17} +8.06469 q^{19} +(1.65766 - 2.87115i) q^{20} +(-1.22157 - 2.11583i) q^{22} +(-2.02730 - 3.51139i) q^{23} +(-0.323514 + 0.560343i) q^{25} +1.03954 q^{26} +3.48975 q^{28} +(4.64361 - 8.04297i) q^{29} +(-1.41591 - 2.45243i) q^{31} +(-2.92697 - 5.06965i) q^{32} +(-2.43995 + 4.22611i) q^{34} -5.94414 q^{35} +5.53191 q^{37} +(-3.13608 + 5.43186i) q^{38} +(3.13738 + 5.43410i) q^{40} +(3.55288 + 6.15377i) q^{41} +(-1.16845 + 2.02382i) q^{43} -4.38263 q^{44} +3.15339 q^{46} +(2.30710 - 3.99602i) q^{47} +(0.371558 + 0.643557i) q^{49} +(-0.251607 - 0.435797i) q^{50} +(0.932388 - 1.61494i) q^{52} +0.135496 q^{53} +7.46499 q^{55} +(-3.30245 + 5.72001i) q^{56} +(3.61149 + 6.25528i) q^{58} +(1.99937 + 3.46301i) q^{59} +(-0.170899 + 0.296006i) q^{61} +2.20240 q^{62} +3.07947 q^{64} +(-1.58815 + 2.75075i) q^{65} +(-5.06146 - 8.76670i) q^{67} +(4.37689 + 7.58100i) q^{68} +(2.31148 - 4.00359i) q^{70} +8.19080 q^{71} -12.3144 q^{73} +(-2.15117 + 3.72594i) q^{74} +(5.62565 + 9.74392i) q^{76} +(3.92888 + 6.80501i) q^{77} +(-2.04035 + 3.53399i) q^{79} +1.75056 q^{80} -5.52638 q^{82} +(-0.456614 + 0.790879i) q^{83} +(-7.45522 - 12.9128i) q^{85} +(-0.908742 - 1.57399i) q^{86} +(4.14740 - 7.18351i) q^{88} -3.72875 q^{89} -3.34341 q^{91} +(2.82835 - 4.89885i) q^{92} +(1.79431 + 3.10783i) q^{94} +(-9.58225 - 16.5969i) q^{95} +(2.99815 - 5.19294i) q^{97} -0.577945 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.388866	+	0.673536i	−0.274970	+	0.476262i	−0.970128	−	0.242595i	$-0.922001\pi$
$2$	−0.388866	+	0.673536i	−0.274970	+	0.476262i	0.695158	+	0.718857i	$0.255335\pi$
$3$		0			0
$3$		0			0
$4$	0.697566	+	1.20822i	0.348783	+	0.604110i
$5$	−1.18817	−	2.05798i	−0.531367	−	0.920355i	−0.999330	−	0.0366070i	$-0.988345\pi$
$5$	−1.18817	−	2.05798i	−0.531367	−	0.920355i	0.467962	−	0.883748i	$-0.344988\pi$
$6$		0			0
$7$	1.25069	−	2.16626i	0.472716	−	0.818768i	−0.526797	−	0.849991i	$-0.676607\pi$
$7$	1.25069	−	2.16626i	0.472716	−	0.818768i	0.999512	+	0.0312237i	$0.00994042\pi$
$8$	−2.64050			−0.933559
$9$		0			0
$10$	1.84816			0.584440
$11$	−1.57069	+	2.72051i	−0.473579	+	0.820264i	−0.999543	−	0.0302437i	$-0.990372\pi$
$11$	−1.57069	+	2.72051i	−0.473579	+	0.820264i	0.525963	+	0.850507i	$0.323705\pi$
$12$		0			0
$13$	−0.668315	−	1.15756i	−0.185357	−	0.321048i	0.758340	−	0.651860i	$-0.226011\pi$
$13$	−0.668315	−	1.15756i	−0.185357	−	0.321048i	−0.943697	+	0.330812i	$0.892678\pi$
$14$	0.972701	+	1.68477i	0.259965	+	0.450273i
$15$		0			0
$16$	−0.368329	+	0.637965i	−0.0920824	+	0.159491i
$17$	6.27452			1.52179			0.760897	−	0.648873i	$-0.224759\pi$
$17$	6.27452			1.52179			0.760897	+	0.648873i	$0.224759\pi$
$18$		0			0
$19$	8.06469			1.85017			0.925083	−	0.379765i	$-0.123995\pi$
$19$	8.06469			1.85017			0.925083	+	0.379765i	$0.123995\pi$
$20$	1.65766	−	2.87115i	0.370664	−	0.642009i
$21$		0			0
$22$	−1.22157	−	2.11583i	−0.260440	−	0.451096i
$23$	−2.02730	−	3.51139i	−0.422721	−	0.732174i	0.573483	−	0.819217i	$-0.305592\pi$
$23$	−2.02730	−	3.51139i	−0.422721	−	0.732174i	−0.996205	+	0.0870427i	$0.972258\pi$
$24$		0			0
$25$	−0.323514	+	0.560343i	−0.0647028	+	0.112069i
$26$	1.03954			0.203871
$27$		0			0
$28$	3.48975			0.659501
$29$	4.64361	−	8.04297i	0.862297	−	1.49354i	−0.00740849	−	0.999973i	$-0.502358\pi$
$29$	4.64361	−	8.04297i	0.862297	−	1.49354i	0.869706	−	0.493570i	$-0.164308\pi$
$30$		0			0
$31$	−1.41591	−	2.45243i	−0.254305	−	0.440469i	0.710402	−	0.703797i	$-0.248513\pi$
$31$	−1.41591	−	2.45243i	−0.254305	−	0.440469i	−0.964707	+	0.263327i	$0.915180\pi$
$32$	−2.92697	−	5.06965i	−0.517419	−	0.896197i
$33$		0			0
$34$	−2.43995	+	4.22611i	−0.418448	+	0.724772i
$35$	−5.94414			−1.00474
$36$		0			0
$37$	5.53191			0.909441			0.454720	−	0.890634i	$-0.349739\pi$
$37$	5.53191			0.909441			0.454720	+	0.890634i	$0.349739\pi$
$38$	−3.13608	+	5.43186i	−0.508740	+	0.881164i
$39$		0			0
$40$	3.13738	+	5.43410i	0.496063	+	0.859206i
$41$	3.55288	+	6.15377i	0.554867	+	0.961057i	0.997914	+	0.0645591i	$0.0205641\pi$
$41$	3.55288	+	6.15377i	0.554867	+	0.961057i	−0.443047	+	0.896498i	$0.646103\pi$
$42$		0			0
$43$	−1.16845	+	2.02382i	−0.178187	+	0.308629i	−0.941260	−	0.337684i	$-0.890357\pi$
$43$	−1.16845	+	2.02382i	−0.178187	+	0.308629i	0.763073	+	0.646313i	$0.223690\pi$
$44$	−4.38263			−0.660706
$45$		0			0
$46$	3.15339			0.464942
$47$	2.30710	−	3.99602i	0.336526	−	0.582879i	−0.647251	−	0.762277i	$-0.724081\pi$
$47$	2.30710	−	3.99602i	0.336526	−	0.582879i	0.983777	+	0.179397i	$0.0574148\pi$
$48$		0			0
$49$	0.371558	+	0.643557i	0.0530797	+	0.0919368i
$50$	−0.251607	−	0.435797i	−0.0355827	−	0.0616310i
$51$		0			0
$52$	0.932388	−	1.61494i	0.129299	−	0.223952i
$53$	0.135496			0.0186118			0.00930588	−	0.999957i	$-0.497038\pi$
$53$	0.135496			0.0186118			0.00930588	+	0.999957i	$0.497038\pi$
$54$		0			0
$55$	7.46499			1.00658
$56$	−3.30245	+	5.72001i	−0.441308	+	0.764368i
$57$		0			0
$58$	3.61149	+	6.25528i	0.474212	+	0.821359i
$59$	1.99937	+	3.46301i	0.260296	+	0.450845i	0.966320	−	0.257342i	$-0.0828466\pi$
$59$	1.99937	+	3.46301i	0.260296	+	0.450845i	−0.706025	+	0.708187i	$0.749513\pi$
$60$		0			0
$61$	−0.170899	+	0.296006i	−0.0218814	+	0.0378997i	−0.876759	−	0.480930i	$-0.840299\pi$
$61$	−0.170899	+	0.296006i	−0.0218814	+	0.0378997i	0.854877	+	0.518830i	$0.173632\pi$
$62$	2.20240			0.279705
$63$		0			0
$64$	3.07947			0.384934
$65$	−1.58815	+	2.75075i	−0.196986	+	0.341189i
$66$		0			0
$67$	−5.06146	−	8.76670i	−0.618356	−	1.07102i	−0.989786	−	0.142563i	$-0.954466\pi$
$67$	−5.06146	−	8.76670i	−0.618356	−	1.07102i	0.371430	−	0.928461i	$-0.378868\pi$
$68$	4.37689	+	7.58100i	0.530776	+	0.919331i
$69$		0			0
$70$	2.31148	−	4.00359i	0.276274	−	0.478521i
$71$	8.19080			0.972069			0.486035	−	0.873940i	$-0.338443\pi$
$71$	8.19080			0.972069			0.486035	+	0.873940i	$0.338443\pi$
$72$		0			0
$73$	−12.3144			−1.44130			−0.720648	−	0.693301i	$-0.756156\pi$
$73$	−12.3144			−1.44130			−0.720648	+	0.693301i	$0.756156\pi$
$74$	−2.15117	+	3.72594i	−0.250069	+	0.433132i
$75$		0			0
$76$	5.62565	+	9.74392i	0.645307	+	1.11770i
$77$	3.92888	+	6.80501i	0.447737	+	0.775503i
$78$		0			0
$79$	−2.04035	+	3.53399i	−0.229557	+	0.397605i	−0.957677	−	0.287845i	$-0.907061\pi$
$79$	−2.04035	+	3.53399i	−0.229557	+	0.397605i	0.728120	+	0.685450i	$0.240394\pi$
$80$	1.75056			0.195718
$81$		0			0
$82$	−5.52638			−0.610287
$83$	−0.456614	+	0.790879i	−0.0501199	+	0.0868102i	−0.889997	−	0.455966i	$-0.849294\pi$
$83$	−0.456614	+	0.790879i	−0.0501199	+	0.0868102i	0.839877	+	0.542777i	$0.182627\pi$
$84$		0			0
$85$	−7.45522	−	12.9128i	−0.808632	−	1.40059i
$86$	−0.908742	−	1.57399i	−0.0979922	−	0.169727i
$87$		0			0
$88$	4.14740	−	7.18351i	0.442114	−	0.765765i
$89$	−3.72875			−0.395246			−0.197623	−	0.980278i	$-0.563322\pi$
$89$	−3.72875			−0.395246			−0.197623	+	0.980278i	$0.563322\pi$
$90$		0			0
$91$	−3.34341			−0.350485
$92$	2.82835	−	4.89885i	0.294876	−	0.510740i
$93$		0			0
$94$	1.79431	+	3.10783i	0.185069	+	0.320549i
$95$	−9.58225	−	16.5969i	−0.983118	−	1.70281i
$96$		0			0
$97$	2.99815	−	5.19294i	0.304416	−	0.527264i	−0.672715	−	0.739901i	$-0.734872\pi$
$97$	2.99815	−	5.19294i	0.304416	−	0.527264i	0.977131	+	0.212638i	$0.0682054\pi$
$98$	−0.577945			−0.0583813
$99$		0			0
$100$	−0.902690			−0.0902690
$101$	−5.11086	+	8.85226i	−0.508549	+	0.880833i	0.491402	+	0.870933i	$0.336485\pi$
$101$	−5.11086	+	8.85226i	−0.508549	+	0.880833i	−0.999951	+	0.00990009i	$0.996849\pi$
$102$		0			0
$103$	−4.26703	−	7.39071i	−0.420443	−	0.728229i	0.575540	−	0.817774i	$-0.304792\pi$
$103$	−4.26703	−	7.39071i	−0.420443	−	0.728229i	−0.995983	+	0.0895452i	$0.971459\pi$
$104$	1.76469	+	3.05653i	0.173042	+	0.299717i
$105$		0			0
$106$	−0.0526897	+	0.0912612i	−0.00511768	+	0.00886408i
$107$	−7.74500			−0.748738			−0.374369	−	0.927280i	$-0.622141\pi$
$107$	−7.74500			−0.748738			−0.374369	+	0.927280i	$0.622141\pi$
$108$		0			0
$109$	1.25438			0.120148			0.0600738	−	0.998194i	$-0.480866\pi$
$109$	1.25438			0.120148			0.0600738	+	0.998194i	$0.480866\pi$
$110$	−2.90288	+	5.02794i	−0.276779	+	0.479395i
$111$		0			0
$112$	0.921331	+	1.59579i	0.0870576	+	0.150788i
$113$	8.88038	+	15.3813i	0.835396	+	1.44695i	0.893707	+	0.448650i	$0.148095\pi$
$113$	8.88038	+	15.3813i	0.835396	+	1.44695i	−0.0583110	+	0.998298i	$0.518572\pi$
$114$		0			0
$115$	−4.81757	+	8.34427i	−0.449241	+	0.778107i
$116$	12.9569			1.20302
$117$		0			0
$118$	−3.10995			−0.286294
$119$	7.84747	−	13.5922i	0.719376	−	1.24600i
$120$		0			0
$121$	0.565896	+	0.980160i	0.0514451	+	0.0891055i
$122$	−0.132914	−	0.230213i	−0.0120334	−	0.0208425i
$123$		0			0
$124$	1.97538	−	3.42146i	0.177395	−	0.307256i
$125$	−10.3442			−0.925211
$126$		0			0
$127$	−3.96558			−0.351888			−0.175944	−	0.984400i	$-0.556298\pi$
$127$	−3.96558			−0.351888			−0.175944	+	0.984400i	$0.556298\pi$
$128$	4.65643	−	8.06517i	0.411574	−	0.712867i
$129$		0			0
$130$	−1.23515	−	2.13935i	−0.108330	−	0.187633i
$131$	0.0512492	+	0.0887662i	0.00447766	+	0.00775554i	0.868256	−	0.496117i	$-0.165241\pi$
$131$	0.0512492	+	0.0887662i	0.00447766	+	0.00775554i	−0.863778	+	0.503873i	$0.831908\pi$
$132$		0			0
$133$	10.0864	−	17.4702i	0.874603	−	1.51486i
$134$	7.87292			0.680117
$135$		0			0
$136$	−16.5679			−1.42068
$137$	3.80977	−	6.59872i	0.325491	−	0.563767i	−0.656121	−	0.754656i	$-0.727804\pi$
$137$	3.80977	−	6.59872i	0.325491	−	0.563767i	0.981612	+	0.190889i	$0.0611371\pi$
$138$		0			0
$139$	5.22037	+	9.04194i	0.442786	+	0.766927i	0.997895	−	0.0648502i	$-0.0206570\pi$
$139$	5.22037	+	9.04194i	0.442786	+	0.766927i	−0.555109	+	0.831777i	$0.687324\pi$
$140$	−4.14643	−	7.18183i	−0.350437	−	0.606975i
$141$		0			0
$142$	−3.18513	+	5.51680i	−0.267290	+	0.462960i
$143$	4.19885			0.351125
$144$		0			0
$145$	−22.0697			−1.83279
$146$	4.78867	−	8.29422i	0.396313	−	0.686434i
$147$		0			0
$148$	3.85887	+	6.68377i	0.317198	+	0.549402i
$149$	−4.51629	−	7.82244i	−0.369989	−	0.640839i	0.619575	−	0.784938i	$-0.287305\pi$
$149$	−4.51629	−	7.82244i	−0.369989	−	0.640839i	−0.989563	+	0.144098i	$0.953972\pi$
$150$		0			0
$151$	−11.9452	+	20.6897i	−0.972086	+	1.68370i	−0.282853	+	0.959163i	$0.591281\pi$
$151$	−11.9452	+	20.6897i	−0.972086	+	1.68370i	−0.689234	+	0.724539i	$0.742053\pi$
$152$	−21.2948			−1.72724
$153$		0			0
$154$	−6.11123			−0.492457
$155$	−3.36470	+	5.82782i	−0.270259	+	0.468102i
$156$		0			0
$157$	−1.35599	−	2.34865i	−0.108220	−	0.187443i	0.806829	−	0.590785i	$-0.201182\pi$
$157$	−1.35599	−	2.34865i	−0.108220	−	0.187443i	−0.915049	+	0.403342i	$0.867848\pi$
$158$	−1.58684	−	2.74850i	−0.126243	−	0.218659i
$159$		0			0
$160$	−6.95549	+	12.0473i	−0.549880	+	0.952420i
$161$	−10.1421			−0.799308
$162$		0			0
$163$	−22.0489			−1.72701			−0.863504	−	0.504343i	$-0.831735\pi$
$163$	−22.0489			−1.72701			−0.863504	+	0.504343i	$0.831735\pi$
$164$	−4.95674	+	8.58532i	−0.387056	+	0.670401i
$165$		0			0
$166$	−0.355124	−	0.615092i	−0.0275629	−	0.0477404i
$167$	4.47540	+	7.75162i	0.346317	+	0.599839i	0.985592	−	0.169139i	$-0.0540988\pi$
$167$	4.47540	+	7.75162i	0.346317	+	0.599839i	−0.639275	+	0.768978i	$0.720765\pi$
$168$		0			0
$169$	5.60671	−	9.71111i	0.431285	−	0.747008i
$170$	11.5963			0.889398
$171$		0			0
$172$	−3.26029			−0.248595
$173$	1.31712	−	2.28133i	0.100139	−	0.173446i	−0.811603	−	0.584210i	$-0.801405\pi$
$173$	1.31712	−	2.28133i	0.100139	−	0.173446i	0.911742	+	0.410764i	$0.134738\pi$
$174$		0			0
$175$	0.809231	+	1.40163i	0.0611721	+	0.105953i
$176$	−1.15706	−	2.00409i	−0.0872166	−	0.151064i
$177$		0			0
$178$	1.44998	−	2.51144i	0.108681	−	0.188241i
$179$	−3.68453			−0.275395			−0.137697	−	0.990474i	$-0.543970\pi$
$179$	−3.68453			−0.275395			−0.137697	+	0.990474i	$0.543970\pi$
$180$		0			0
$181$	−0.268509			−0.0199581			−0.00997906	−	0.999950i	$-0.503176\pi$
$181$	−0.268509			−0.0199581			−0.00997906	+	0.999950i	$0.503176\pi$
$182$	1.30014	−	2.25191i	0.0963729	−	0.166923i
$183$		0			0
$184$	5.35309	+	9.27183i	0.394635	+	0.683528i
$185$	−6.57287	−	11.3845i	−0.483247	−	0.837009i
$186$		0			0
$187$	−9.85529	+	17.0699i	−0.720690	+	1.24827i
$188$	6.43743			0.469498
$189$		0			0
$190$	14.9049			1.08131
$191$	−1.19899	+	2.07672i	−0.0867561	+	0.150266i	−0.906138	−	0.422982i	$-0.860983\pi$
$191$	−1.19899	+	2.07672i	−0.0867561	+	0.150266i	0.819382	+	0.573248i	$0.194317\pi$
$192$		0			0
$193$	−0.248101	−	0.429724i	−0.0178587	−	0.0309322i	0.856958	−	0.515386i	$-0.172352\pi$
$193$	−0.248101	−	0.429724i	−0.0178587	−	0.0309322i	−0.874817	+	0.484454i	$0.839018\pi$
$194$	2.33176	+	4.03872i	0.167410	+	0.289963i
$195$		0			0
$196$	−0.518373	+	0.897848i	−0.0370266	+	0.0641320i
$197$	22.1468			1.57789			0.788946	−	0.614462i	$-0.210627\pi$
$197$	22.1468			1.57789			0.788946	+	0.614462i	$0.210627\pi$
$198$		0			0
$199$	2.13247			0.151167			0.0755834	−	0.997139i	$-0.475918\pi$
$199$	2.13247			0.151167			0.0755834	+	0.997139i	$0.475918\pi$
$200$	0.854240	−	1.47959i	0.0604039	−	0.104623i
$201$		0			0
$202$	−3.97488	−	6.88469i	−0.279671	−	0.484405i
$203$	−11.6154	−	20.1185i	−0.815243	−	1.41204i
$204$		0			0
$205$	8.44288	−	14.6235i	0.589676	−	1.02135i
$206$	6.63721			0.462437
$207$		0			0
$208$	0.984641			0.0682725
$209$	−12.6671	+	21.9400i	−0.876201	+	1.51762i
$210$		0			0
$211$	−10.0043	−	17.3279i	−0.688724	−	1.19290i	−0.972251	−	0.233941i	$-0.924838\pi$
$211$	−10.0043	−	17.3279i	−0.688724	−	1.19290i	0.283527	−	0.958964i	$-0.408495\pi$
$212$	0.0945172	+	0.163709i	0.00649147	+	0.0112436i
$213$		0			0
$214$	3.01177	−	5.21654i	0.205880	−	0.356595i
$215$	5.55329			0.378731
$216$		0			0
$217$	−7.08345			−0.480856
$218$	−0.487785	+	0.844868i	−0.0330370	+	0.0572217i
$219$		0			0
$220$	5.20732	+	9.01935i	0.351078	+	0.608084i
$221$	−4.19335	−	7.26310i	−0.282076	−	0.488569i
$222$		0			0
$223$	6.63923	−	11.4995i	0.444596	−	0.770063i	−0.553428	−	0.832897i	$-0.686681\pi$
$223$	6.63923	−	11.4995i	0.444596	−	0.770063i	0.998024	+	0.0628343i	$0.0200140\pi$
$224$	−14.6429			−0.978369
$225$		0			0
$226$	−13.8131			−0.918835
$227$	−6.23547	+	10.8001i	−0.413862	+	0.716831i	−0.995308	−	0.0967544i	$-0.969154\pi$
$227$	−6.23547	+	10.8001i	−0.413862	+	0.716831i	0.581446	+	0.813585i	$0.302487\pi$
$228$		0			0
$229$	−12.8308	−	22.2236i	−0.847882	−	1.46857i	−0.883095	−	0.469194i	$-0.844544\pi$
$229$	−12.8308	−	22.2236i	−0.847882	−	1.46857i	0.0352131	−	0.999380i	$-0.488789\pi$
$230$	−3.74678	−	6.48961i	−0.247055	−	0.427912i
$231$		0			0
$232$	−12.2615	+	21.2375i	−0.805006	+	1.39431i
$233$	5.39642			0.353532			0.176766	−	0.984253i	$-0.443436\pi$
$233$	5.39642			0.353532			0.176766	+	0.984253i	$0.443436\pi$
$234$		0			0
$235$	−10.9650			−0.715275
$236$	−2.78938	+	4.83136i	−0.181573	+	0.314494i
$237$		0			0
$238$	6.10323	+	10.5711i	0.395613	+	0.685223i
$239$	4.18552	+	7.24954i	0.270739	+	0.468934i	0.969051	−	0.246860i	$-0.0793987\pi$
$239$	4.18552	+	7.24954i	0.270739	+	0.468934i	−0.698312	+	0.715793i	$0.746065\pi$
$240$		0			0
$241$	0.221095	−	0.382947i	0.0142420	−	0.0246678i	−0.858817	−	0.512283i	$-0.828800\pi$
$241$	0.221095	−	0.382947i	0.0142420	−	0.0246678i	0.873059	+	0.487615i	$0.162133\pi$
$242$	−0.880231			−0.0565834
$243$		0			0
$244$	−0.476854			−0.0305274
$245$	0.882951	−	1.52932i	0.0564097	−	0.0977044i
$246$		0			0
$247$	−5.38975	−	9.33532i	−0.342942	−	0.593992i
$248$	3.73872	+	6.47565i	0.237409	+	0.411204i
$249$		0			0
$250$	4.02250	−	6.96717i	0.254405	−	0.440643i
$251$	−17.0285			−1.07483			−0.537416	−	0.843317i	$-0.680599\pi$
$251$	−17.0285			−1.07483			−0.537416	+	0.843317i	$0.680599\pi$
$252$		0			0
$253$	12.7370			0.800768
$254$	1.54208	−	2.67096i	0.0967587	−	0.167591i
$255$		0			0
$256$	6.70093	+	11.6064i	0.418808	+	0.725397i
$257$	10.4384	+	18.0798i	0.651127	+	1.12779i	0.982850	+	0.184408i	$0.0590368\pi$
$257$	10.4384	+	18.0798i	0.651127	+	1.12779i	−0.331723	+	0.943377i	$0.607630\pi$
$258$		0			0
$259$	6.91870	−	11.9835i	0.429907	−	0.744621i
$260$	−4.43136			−0.274821
$261$		0			0
$262$	−0.0797163			−0.00492489
$263$	9.69578	−	16.7936i	0.597867	−	1.03554i	−0.395268	−	0.918566i	$-0.629348\pi$
$263$	9.69578	−	16.7936i	0.597867	−	1.03554i	0.993135	−	0.116971i	$-0.0373184\pi$
$264$		0			0
$265$	−0.160992	−	0.278847i	−0.00988969	−	0.0171294i
$266$	7.84453	+	13.5871i	0.480979	+	0.833080i
$267$		0			0
$268$	7.06141	−	12.2307i	0.431344	−	0.747110i
$269$	−18.6791			−1.13889			−0.569443	−	0.822031i	$-0.692841\pi$
$269$	−18.6791			−1.13889			−0.569443	+	0.822031i	$0.692841\pi$
$270$		0			0
$271$	12.9378			0.785917			0.392958	−	0.919556i	$-0.371452\pi$
$271$	12.9378			0.785917			0.392958	+	0.919556i	$0.371452\pi$
$272$	−2.31109	+	4.00293i	−0.140130	+	0.242713i
$273$		0			0
$274$	2.96298	+	5.13204i	0.179000	+	0.310038i
$275$	−1.01628	−	1.76024i	−0.0612838	−	0.106147i
$276$		0			0
$277$	−5.22066	+	9.04246i	−0.313679	+	0.543309i	−0.979156	−	0.203110i	$-0.934895\pi$
$277$	−5.22066	+	9.04246i	−0.313679	+	0.543309i	0.665477	+	0.746419i	$0.268228\pi$
$278$	−8.12009			−0.487011
$279$		0			0
$280$	15.6955			0.937987
$281$	7.17290	−	12.4238i	0.427899	−	0.741143i	−0.568787	−	0.822485i	$-0.692587\pi$
$281$	7.17290	−	12.4238i	0.427899	−	0.741143i	0.996686	+	0.0813417i	$0.0259205\pi$
$282$		0			0
$283$	9.34630	+	16.1883i	0.555580	+	0.962293i	0.997858	+	0.0654150i	$0.0208371\pi$
$283$	9.34630	+	16.1883i	0.555580	+	0.962293i	−0.442278	+	0.896878i	$0.645830\pi$
$284$	5.71363	+	9.89629i	0.339041	+	0.587237i
$285$		0			0
$286$	−1.63279	+	2.82808i	−0.0965489	+	0.167228i
$287$	17.7742			1.04918
$288$		0			0
$289$	22.3696			1.31586
$290$	8.58215	−	14.8647i	0.503961	−	0.872887i
$291$		0			0
$292$	−8.59014	−	14.8786i	−0.502700	−	0.870701i
$293$	−5.39409	−	9.34284i	−0.315126	−	0.545815i	0.664338	−	0.747432i	$-0.268714\pi$
$293$	−5.39409	−	9.34284i	−0.315126	−	0.545815i	−0.979464	+	0.201618i	$0.935380\pi$
$294$		0			0
$295$	4.75120	−	8.22931i	0.276625	−	0.479129i
$296$	−14.6070			−0.849017
$297$		0			0
$298$	7.02493			0.406943
$299$	−2.70975	+	4.69342i	−0.156709	+	0.271428i
$300$		0			0
$301$	2.92274	+	5.06233i	0.168464	+	0.291788i
$302$	−9.29016	−	16.0910i	−0.534589	−	0.925935i
$303$		0			0
$304$	−2.97046	+	5.14499i	−0.170368	+	0.295086i
$305$	0.812231			0.0465082
$306$		0			0
$307$	0.0497494			0.00283935			0.00141967	−	0.999999i	$-0.499548\pi$
$307$	0.0497494			0.00283935			0.00141967	+	0.999999i	$0.499548\pi$
$308$	−5.48130	+	9.49389i	−0.312326	+	0.540965i
$309$		0			0
$310$	−2.61683	−	4.53249i	−0.148626	−	0.257428i
$311$	6.61773	+	11.4622i	0.375257	+	0.649964i	0.990365	−	0.138478i	$-0.0442211\pi$
$311$	6.61773	+	11.4622i	0.375257	+	0.649964i	−0.615108	+	0.788443i	$0.710888\pi$
$312$		0			0
$313$	7.54146	−	13.0622i	0.426268	−	0.738319i	−0.570269	−	0.821458i	$-0.693161\pi$
$313$	7.54146	−	13.0622i	0.426268	−	0.738319i	0.996538	+	0.0831390i	$0.0264946\pi$
$314$	2.10920			0.119029
$315$		0			0
$316$	−5.69311			−0.320263
$317$	4.31541	−	7.47451i	0.242378	−	0.419810i	−0.719013	−	0.694996i	$-0.755406\pi$
$317$	4.31541	−	7.47451i	0.242378	−	0.419810i	0.961391	+	0.275186i	$0.0887394\pi$
$318$		0			0
$319$	14.5873	+	25.2660i	0.816733	+	1.41462i
$320$	−3.65895	−	6.33749i	−0.204542	−	0.354276i
$321$		0			0
$322$	3.94391	−	6.83105i	0.219786	−	0.380680i
$323$	50.6020			2.81557
$324$		0			0
$325$	0.864837			0.0479725
$326$	8.57409	−	14.8508i	0.474875	−	0.822508i
$327$		0			0
$328$	−9.38140	−	16.2491i	−0.518001	−	0.897204i
$329$	−5.77093	−	9.99555i	−0.318162	−	0.551072i
$330$		0			0
$331$	−15.5127	+	26.8689i	−0.852657	+	1.47685i	0.0261444	+	0.999658i	$0.491677\pi$
$331$	−15.5127	+	26.8689i	−0.852657	+	1.47685i	−0.878802	+	0.477187i	$0.841656\pi$
$332$	−1.27407			−0.0699239
$333$		0			0
$334$	−6.96133			−0.380907
$335$	−12.0278	+	20.8327i	−0.657148	+	1.13821i
$336$		0			0
$337$	11.9337	+	20.6697i	0.650068	+	1.12595i	0.983106	+	0.183037i	$0.0585929\pi$
$337$	11.9337	+	20.6697i	0.650068	+	1.12595i	−0.333038	+	0.942913i	$0.608074\pi$
$338$	4.36052	+	7.55264i	0.237181	+	0.410810i
$339$		0			0
$340$	10.4010	−	18.0151i	0.564074	−	0.977005i
$341$	8.89580			0.481734
$342$		0			0
$343$	19.3684			1.04580
$344$	3.08530	−	5.34390i	0.166348	−	0.288124i
$345$		0			0
$346$	1.02437	+	1.77426i	0.0550705	+	0.0953849i
$347$	10.9556	+	18.9757i	0.588128	+	1.01867i	0.994477	+	0.104950i	$0.0334684\pi$
$347$	10.9556	+	18.9757i	0.588128	+	1.01867i	−0.406349	+	0.913718i	$0.633198\pi$
$348$		0			0
$349$	−7.92343	+	13.7238i	−0.424132	+	0.734618i	−0.996339	−	0.0854915i	$-0.972754\pi$
$349$	−7.92343	+	13.7238i	−0.424132	+	0.734618i	0.572207	+	0.820109i	$0.306087\pi$
$350$	−1.25873			−0.0672819
$351$		0			0
$352$	18.3894			0.980157
$353$	6.45344	−	11.1777i	0.343482	−	0.594929i	−0.641595	−	0.767044i	$-0.721727\pi$
$353$	6.45344	−	11.1777i	0.343482	−	0.594929i	0.985077	+	0.172115i	$0.0550602\pi$
$354$		0			0
$355$	−9.73210	−	16.8565i	−0.516526	−	0.894649i
$356$	−2.60105	−	4.50515i	−0.137855	−	0.238772i
$357$		0			0
$358$	1.43279	−	2.48166i	0.0757253	−	0.131160i
$359$	−25.8285			−1.36318			−0.681588	−	0.731736i	$-0.738710\pi$
$359$	−25.8285			−1.36318			−0.681588	+	0.731736i	$0.738710\pi$
$360$		0			0
$361$	46.0392			2.42312
$362$	0.104414	−	0.180851i	0.00548788	−	0.00950529i
$363$		0			0
$364$	−2.33225	−	4.03958i	−0.122243	−	0.211732i
$365$	14.6317	+	25.3428i	0.765858	+	1.32650i
$366$		0			0
$367$	−7.98729	+	13.8344i	−0.416933	+	0.722149i	−0.995629	−	0.0933940i	$-0.970228\pi$
$367$	−7.98729	+	13.8344i	−0.416933	+	0.722149i	0.578696	+	0.815543i	$0.303562\pi$
$368$	2.98686			0.155701
$369$		0			0
$370$	10.2239			0.531514
$371$	0.169463	−	0.293518i	0.00879807	−	0.0152387i
$372$		0			0
$373$	−0.913283	−	1.58185i	−0.0472880	−	0.0819052i	0.841413	−	0.540393i	$-0.181725\pi$
$373$	−0.913283	−	1.58185i	−0.0472880	−	0.0819052i	−0.888701	+	0.458488i	$0.848391\pi$
$374$	−7.66478	−	13.2758i	−0.396336	−	0.686475i
$375$		0			0
$376$	−6.09192	+	10.5515i	−0.314167	+	0.544152i
$377$	−12.4136			−0.639332
$378$		0			0
$379$	1.14694			0.0589141			0.0294571	−	0.999566i	$-0.490622\pi$
$379$	1.14694			0.0589141			0.0294571	+	0.999566i	$0.490622\pi$
$380$	13.3685	−	23.1549i	0.685790	−	1.18782i
$381$		0			0
$382$	−0.932496	−	1.61513i	−0.0477106	−	0.0826372i
$383$	10.9138	+	18.9032i	0.557668	+	0.965909i	0.997691	+	0.0679223i	$0.0216370\pi$
$383$	10.9138	+	18.9032i	0.557668	+	0.965909i	−0.440023	+	0.897987i	$0.645030\pi$
$384$		0			0
$385$	9.33637	−	16.1711i	0.475826	−	0.824154i
$386$	0.385913			0.0196425
$387$		0			0
$388$	8.36563			0.424700
$389$	−13.0981	+	22.6866i	−0.664099	+	1.15025i	0.315429	+	0.948949i	$0.397852\pi$
$389$	−13.0981	+	22.6866i	−0.664099	+	1.15025i	−0.979529	+	0.201305i	$0.935482\pi$
$390$		0			0
$391$	−12.7203	−	22.0322i	−0.643294	−	1.11422i
$392$	−0.981101	−	1.69932i	−0.0495531	−	0.0858284i
$393$		0			0
$394$	−8.61213	+	14.9166i	−0.433873	+	0.751490i
$395$	9.69715			0.487917
$396$		0			0
$397$	4.19831			0.210707			0.105353	−	0.994435i	$-0.466403\pi$
$397$	4.19831			0.210707			0.105353	+	0.994435i	$0.466403\pi$
$398$	−0.829246	+	1.43630i	−0.0415663	+	0.0719950i
$399$		0			0
$400$	−0.238320	−	0.412782i	−0.0119160	−	0.0206391i
$401$	−3.91490	−	6.78081i	−0.195501	−	0.338618i	0.751564	−	0.659661i	$-0.229300\pi$
$401$	−3.91490	−	6.78081i	−0.195501	−	0.338618i	−0.947065	+	0.321043i	$0.895967\pi$
$402$		0			0
$403$	−1.89255	+	3.27799i	−0.0942745	+	0.163288i
$404$	−14.2606			−0.709493
$405$		0			0
$406$	18.0674			0.896669
$407$	−8.68889	+	15.0496i	−0.430692	+	0.745981i
$408$		0			0
$409$	8.71450	+	15.0940i	0.430904	+	0.746348i	0.996951	−	0.0780249i	$-0.0248614\pi$
$409$	8.71450	+	15.0940i	0.430904	+	0.746348i	−0.566047	+	0.824373i	$0.691528\pi$
$410$	6.56630	+	11.3732i	0.324286	+	0.561681i
$411$		0			0
$412$	5.95307	−	10.3110i	0.293287	−	0.507988i
$413$	10.0024			0.492183
$414$		0			0
$415$	2.17015			0.106528
$416$	−3.91227	+	6.77625i	−0.191815	+	0.332233i
$417$		0			0
$418$	−9.85160	−	17.0635i	−0.481858	−	0.834602i
$419$	5.74159	+	9.94472i	0.280495	+	0.485831i	0.971507	−	0.237012i	$-0.0761681\pi$
$419$	5.74159	+	9.94472i	0.280495	+	0.485831i	−0.691012	+	0.722843i	$0.742835\pi$
$420$		0			0
$421$	−3.64561	+	6.31439i	−0.177676	+	0.307744i	−0.941084	−	0.338172i	$-0.890191\pi$
$421$	−3.64561	+	6.31439i	−0.177676	+	0.307744i	0.763408	+	0.645917i	$0.223525\pi$
$422$	15.5613			0.757513
$423$		0			0
$424$	−0.357777			−0.0173752
$425$	−2.02989	+	3.51588i	−0.0984644	+	0.170545i
$426$		0			0
$427$	0.427483	+	0.740422i	0.0206873	+	0.0358315i
$428$	−5.40265	−	9.35767i	−0.261147	−	0.452320i
$429$		0			0
$430$	−2.15949	+	3.74034i	−0.104140	+	0.180375i
$431$	−0.389084			−0.0187415			−0.00937075	−	0.999956i	$-0.502983\pi$
$431$	−0.389084			−0.0187415			−0.00937075	+	0.999956i	$0.502983\pi$
$432$		0			0
$433$	24.1011			1.15822			0.579112	−	0.815248i	$-0.303400\pi$
$433$	24.1011			1.15822			0.579112	+	0.815248i	$0.303400\pi$
$434$	2.75451	−	4.77096i	0.132221	−	0.229013i
$435$		0			0
$436$	0.875011	+	1.51556i	0.0419054	+	0.0725823i
$437$	−16.3495	−	28.3182i	−0.782104	−	1.35464i
$438$		0			0
$439$	−18.3328	+	31.7533i	−0.874977	+	1.51550i	−0.0181892	+	0.999835i	$0.505790\pi$
$439$	−18.3328	+	31.7533i	−0.874977	+	1.51550i	−0.856788	+	0.515670i	$0.827543\pi$
$440$	−19.7113			−0.939701
$441$		0			0
$442$	6.52261			0.310249
$443$	−18.8933	+	32.7242i	−0.897649	+	1.55477i	−0.0671579	+	0.997742i	$0.521393\pi$
$443$	−18.8933	+	32.7242i	−0.897649	+	1.55477i	−0.830491	+	0.557032i	$0.811940\pi$
$444$		0			0
$445$	4.43040	+	7.67367i	0.210021	+	0.363767i
$446$	5.16355	+	8.94352i	0.244501	+	0.423488i
$447$		0			0
$448$	3.85146	−	6.67093i	0.181965	−	0.315172i
$449$	−11.7858			−0.556205			−0.278103	−	0.960551i	$-0.589706\pi$
$449$	−11.7858			−0.556205			−0.278103	+	0.960551i	$0.589706\pi$
$450$		0			0
$451$	−22.3218			−1.05109
$452$	−12.3893	+	21.4589i	−0.582744	+	1.00934i
$453$		0			0
$454$	−4.84952	−	8.39962i	−0.227599	−	0.394214i
$455$	3.97256	+	6.88067i	0.186236	+	0.322571i
$456$		0			0
$457$	9.92795	−	17.1957i	0.464410	−	0.804382i	−0.534765	−	0.845001i	$-0.679600\pi$
$457$	9.92795	−	17.1957i	0.464410	−	0.804382i	0.999175	+	0.0406193i	$0.0129331\pi$
$458$	19.9578			0.932568
$459$		0			0
$460$	−13.4423			−0.626750
$461$	−3.82091	+	6.61802i	−0.177958	+	0.308232i	−0.941181	−	0.337903i	$-0.890282\pi$
$461$	−3.82091	+	6.61802i	−0.177958	+	0.308232i	0.763223	+	0.646135i	$0.223616\pi$
$462$		0			0
$463$	7.97721	+	13.8169i	0.370732	+	0.642127i	0.989678	−	0.143306i	$-0.0457734\pi$
$463$	7.97721	+	13.8169i	0.370732	+	0.642127i	−0.618946	+	0.785434i	$0.712440\pi$
$464$	3.42076	+	5.92493i	0.158805	+	0.275058i
$465$		0			0
$466$	−2.09849	+	3.63469i	−0.0972105	+	0.168374i
$467$	−26.1406			−1.20964			−0.604822	−	0.796360i	$-0.706756\pi$
$467$	−26.1406			−1.20964			−0.604822	+	0.796360i	$0.706756\pi$
$468$		0			0
$469$	−25.3212			−1.16923
$470$	4.26390	−	7.38529i	0.196679	−	0.340658i
$471$		0			0
$472$	−5.27934	−	9.14409i	−0.243001	−	0.420891i
$473$	−3.67054	−	6.35756i	−0.168771	−	0.292321i
$474$		0			0
$475$	−2.60904	+	4.51899i	−0.119711	+	0.207345i
$476$	21.8965			1.00362
$477$		0			0
$478$	−6.51043			−0.297780
$479$	19.6751	−	34.0783i	0.898980	−	1.55708i	0.0701801	−	0.997534i	$-0.477643\pi$
$479$	19.6751	−	34.0783i	0.898980	−	1.55708i	0.828800	−	0.559545i	$-0.189024\pi$
$480$		0			0
$481$	−3.69706	−	6.40350i	−0.168571	−	0.291974i
$482$	0.171953	+	0.297831i	0.00783222	+	0.0135658i
$483$		0			0
$484$	−0.789499	+	1.36745i	−0.0358863	+	0.0621570i
$485$	−14.2493			−0.647027
$486$		0			0
$487$	11.7133			0.530779			0.265389	−	0.964141i	$-0.414500\pi$
$487$	11.7133			0.530779			0.265389	+	0.964141i	$0.414500\pi$
$488$	0.451260	−	0.781605i	0.0204276	−	0.0353816i
$489$		0			0
$490$	0.686700	+	1.18940i	0.0310219	+	0.0537316i
$491$	−19.2749	−	33.3851i	−0.869865	−	1.50665i	−0.862134	−	0.506680i	$-0.830873\pi$
$491$	−19.2749	−	33.3851i	−0.869865	−	1.50665i	−0.00773080	−	0.999970i	$-0.502461\pi$
$492$		0			0
$493$	29.1364	−	50.4658i	1.31224	−	2.27286i
$494$	8.38357			0.377195
$495$		0			0
$496$	2.08609			0.0936680
$497$	10.2441	−	17.7434i	0.459512	−	0.795899i
$498$		0			0
$499$	14.7808	+	25.6011i	0.661679	+	1.14606i	0.980174	+	0.198138i	$0.0634893\pi$
$499$	14.7808	+	25.6011i	0.661679	+	1.14606i	−0.318495	+	0.947925i	$0.603177\pi$
$500$	−7.21575	−	12.4980i	−0.322698	−	0.558929i
$501$		0			0
$502$	6.62182	−	11.4693i	0.295546	−	0.511901i
$503$	−35.5775			−1.58632			−0.793161	−	0.609011i	$-0.791566\pi$
$503$	−35.5775			−1.58632			−0.793161	+	0.609011i	$0.791566\pi$
$504$		0			0
$505$	24.2903			1.08091
$506$	−4.95299	+	8.57883i	−0.220187	+	0.381375i
$507$		0			0
$508$	−2.76625	−	4.79129i	−0.122733	−	0.212579i
$509$	−14.1912	−	24.5798i	−0.629013	−	1.08948i	−0.987750	−	0.156043i	$-0.950126\pi$
$509$	−14.1912	−	24.5798i	−0.629013	−	1.08948i	0.358738	−	0.933438i	$-0.383207\pi$
$510$		0			0
$511$	−15.4015	+	26.6762i	−0.681323	+	1.18009i
$512$	8.20265			0.362510
$513$		0			0
$514$	−16.2365			−0.716161
$515$	−10.1399	+	17.5629i	−0.446819	+	0.773914i
$516$		0			0
$517$	7.24747	+	12.5530i	0.318743	+	0.552079i
$518$	5.38089	+	9.31998i	0.236423	+	0.409497i
$519$		0			0
$520$	4.19351	−	7.26338i	0.183898	−	0.318520i
$521$	25.4351			1.11433			0.557167	−	0.830401i	$-0.311888\pi$
$521$	25.4351			1.11433			0.557167	+	0.830401i	$0.311888\pi$
$522$		0			0
$523$	8.40790			0.367652			0.183826	−	0.982959i	$-0.441152\pi$
$523$	8.40790			0.367652			0.183826	+	0.982959i	$0.441152\pi$
$524$	−0.0714994	+	0.123841i	−0.00312347	+	0.00541000i
$525$		0			0
$526$	7.54072	+	13.0609i	0.328791	+	0.569483i
$527$	−8.88415	−	15.3878i	−0.387000	−	0.670303i
$528$		0			0
$529$	3.28012	−	5.68133i	0.142614	−	0.247014i
$530$	0.250418			0.0108775
$531$		0			0
$532$	28.1438			1.22019
$533$	4.74889	−	8.22531i	0.205697	−	0.356278i
$534$		0			0
$535$	9.20241	+	15.9390i	0.397855	+	0.689105i
$536$	13.3648	+	23.1485i	0.577272	+	0.999864i
$537$		0			0
$538$	7.26368	−	12.5811i	0.313160	−	0.542408i
$539$	−2.33440			−0.100550
$540$		0			0
$541$	−12.8635			−0.553043			−0.276522	−	0.961008i	$-0.589182\pi$
$541$	−12.8635			−0.553043			−0.276522	+	0.961008i	$0.589182\pi$
$542$	−5.03108	+	8.71409i	−0.216103	+	0.374302i
$543$		0			0
$544$	−18.3653	−	31.8096i	−0.787406	−	1.36383i
$545$	−1.49042	−	2.58148i	−0.0638425	−	0.110578i
$546$		0			0
$547$	−6.54598	+	11.3380i	−0.279886	+	0.484777i	−0.971356	−	0.237628i	$-0.923630\pi$
$547$	−6.54598	+	11.3380i	−0.279886	+	0.484777i	0.691470	+	0.722405i	$0.256963\pi$
$548$	10.6303			0.454103
$549$		0			0
$550$	1.58078			0.0674049
$551$	37.4493	−	64.8641i	1.59539	−	2.76330i
$552$		0			0
$553$	5.10368	+	8.83983i	0.217031	+	0.375908i
$554$	−4.06028	−	7.03261i	−0.172505	−	0.298787i
$555$		0			0
$556$	−7.28310	+	12.6147i	−0.308872	+	0.534982i
$557$	−4.58220			−0.194154			−0.0970769	−	0.995277i	$-0.530949\pi$
$557$	−4.58220			−0.194154			−0.0970769	+	0.995277i	$0.530949\pi$
$558$		0			0
$559$	3.12357			0.132113
$560$	2.18940	−	3.79216i	0.0925191	−	0.160248i
$561$		0			0
$562$	5.57859	+	9.66241i	0.235319	+	0.407584i
$563$	6.14196	+	10.6382i	0.258853	+	0.448346i	0.965935	−	0.258785i	$-0.0833222\pi$
$563$	6.14196	+	10.6382i	0.258853	+	0.448346i	−0.707082	+	0.707131i	$0.749989\pi$
$564$		0			0
$565$	21.1029	−	36.5513i	0.887805	−	1.53772i
$566$	−14.5378			−0.611071
$567$		0			0
$568$	−21.6278			−0.907484
$569$	7.24683	−	12.5519i	0.303803	−	0.526202i	−0.673191	−	0.739468i	$-0.735077\pi$
$569$	7.24683	−	12.5519i	0.303803	−	0.526202i	0.976994	+	0.213266i	$0.0684102\pi$
$570$		0			0
$571$	11.0227	+	19.0918i	0.461285	+	0.798969i	0.999025	−	0.0441418i	$-0.0140553\pi$
$571$	11.0227	+	19.0918i	0.461285	+	0.798969i	−0.537741	+	0.843110i	$0.680722\pi$
$572$	2.92898	+	5.07313i	0.122467	+	0.212118i
$573$		0			0
$574$	−6.91178	+	11.9716i	−0.288492	+	0.499683i
$575$	2.62344			0.109405
$576$		0			0
$577$	−31.4835			−1.31068			−0.655338	−	0.755336i	$-0.727474\pi$
$577$	−31.4835			−1.31068			−0.655338	+	0.755336i	$0.727474\pi$
$578$	−8.69877	+	15.0667i	−0.361821	+	0.626693i
$579$		0			0
$580$	−15.3951	−	26.6650i	−0.639245	−	1.10721i
$581$	1.14216	+	1.97829i	0.0473849	+	0.0820731i
$582$		0			0
$583$	−0.212821	+	0.368617i	−0.00881415	+	0.0152666i
$584$	32.5163			1.34554
$585$		0			0
$586$	8.39032			0.346601
$587$	−7.18472	+	12.4443i	−0.296545	+	0.513631i	−0.975343	−	0.220694i	$-0.929168\pi$
$587$	−7.18472	+	12.4443i	−0.296545	+	0.513631i	0.678798	+	0.734325i	$0.262501\pi$
$588$		0			0
$589$	−11.4189	−	19.7781i	−0.470507	−	0.814941i
$590$	3.69516	+	6.40020i	0.152127	+	0.263492i
$591$		0			0
$592$	−2.03757	+	3.52917i	−0.0837435	+	0.145048i
$593$	41.0988			1.68772			0.843862	−	0.536560i	$-0.180276\pi$
$593$	41.0988			1.68772			0.843862	+	0.536560i	$0.180276\pi$
$594$		0			0
$595$	−37.2966			−1.52901
$596$	6.30082	−	10.9133i	0.258092	−	0.447028i
$597$		0			0
$598$	−2.10746	−	3.65023i	−0.0861804	−	0.149269i
$599$	4.28108	+	7.41505i	0.174920	+	0.302971i	0.940134	−	0.340806i	$-0.110700\pi$
$599$	4.28108	+	7.41505i	0.174920	+	0.302971i	−0.765213	+	0.643777i	$0.777367\pi$
$600$		0			0
$601$	0.817605	−	1.41613i	0.0333508	−	0.0577653i	−0.848868	−	0.528605i	$-0.822715\pi$
$601$	0.817605	−	1.41613i	0.0333508	−	0.0577653i	0.882219	+	0.470839i	$0.156049\pi$
$602$	−4.54621			−0.185290
$603$		0			0
$604$	−33.3303			−1.35619
$605$	1.34476	−	2.32920i	0.0546725	−	0.0946955i
$606$		0			0
$607$	−3.28472	−	5.68929i	−0.133322	−	0.230921i	0.791633	−	0.610997i	$-0.209231\pi$
$607$	−3.28472	−	5.68929i	−0.133322	−	0.230921i	−0.924955	+	0.380076i	$0.875898\pi$
$608$	−23.6051	−	40.8852i	−0.957312	−	1.65811i
$609$		0			0
$610$	−0.315849	+	0.547067i	−0.0127884	+	0.0221501i
$611$	−6.16749			−0.249510
$612$		0			0
$613$	−26.2726			−1.06114			−0.530569	−	0.847642i	$-0.678022\pi$
$613$	−26.2726			−1.06114			−0.530569	+	0.847642i	$0.678022\pi$
$614$	−0.0193459	+	0.0335080i	−0.000780736	+	0.00135227i
$615$		0			0
$616$	−10.3742	−	17.9687i	−0.417989	−	0.723978i
$617$	−3.13651	−	5.43260i	−0.126271	−	0.218708i	0.795958	−	0.605352i	$-0.206968\pi$
$617$	−3.13651	−	5.43260i	−0.126271	−	0.218708i	−0.922229	+	0.386644i	$0.873634\pi$
$618$		0			0
$619$	−2.47044	+	4.27892i	−0.0992952	+	0.171984i	−0.911393	−	0.411537i	$-0.864992\pi$
$619$	−2.47044	+	4.27892i	−0.0992952	+	0.171984i	0.812098	+	0.583521i	$0.198325\pi$
$620$	−9.38839			−0.377047
$621$		0			0
$622$	−10.2936			−0.412738
$623$	−4.66350	+	8.07742i	−0.186839	+	0.323615i
$624$		0			0
$625$	13.9082	+	24.0898i	0.556330	+	0.963592i
$626$	5.86524	+	10.1589i	0.234422	+	0.406031i
$627$		0			0
$628$	1.89179	−	3.27668i	0.0754907	−	0.130754i
$629$	34.7101			1.38398
$630$		0			0
$631$	−6.92420			−0.275648			−0.137824	−	0.990457i	$-0.544011\pi$
$631$	−6.92420			−0.275648			−0.137824	+	0.990457i	$0.544011\pi$
$632$	5.38755	−	9.33151i	0.214305	−	0.371187i
$633$		0			0
$634$	3.35624	+	5.81317i	0.133293	+	0.230870i
$635$	4.71180	+	8.16107i	0.186982	+	0.323862i
$636$		0			0
$637$	0.496636	−	0.860198i	0.0196774	−	0.0340823i
$638$	−22.6900			−0.898308
$639$		0			0
$640$	−22.1306			−0.874788
$641$	−16.9594	+	29.3746i	−0.669858	+	1.16023i	0.308086	+	0.951359i	$0.400312\pi$
$641$	−16.9594	+	29.3746i	−0.669858	+	1.16023i	−0.977944	+	0.208869i	$0.933022\pi$
$642$		0			0
$643$	−3.86161	−	6.68850i	−0.152287	−	0.263769i	0.779781	−	0.626053i	$-0.215330\pi$
$643$	−3.86161	−	6.68850i	−0.152287	−	0.263769i	−0.932068	+	0.362284i	$0.881997\pi$
$644$	−7.07477	−	12.2539i	−0.278785	−	0.482870i
$645$		0			0
$646$	−19.6774	+	34.0823i	−0.774198	+	1.34095i
$647$	−35.1862			−1.38331			−0.691655	−	0.722228i	$-0.743118\pi$
$647$	−35.1862			−1.38331			−0.691655	+	0.722228i	$0.743118\pi$
$648$		0			0
$649$	−12.5615			−0.493083
$650$	−0.336306	+	0.582499i	−0.0131910	+	0.0228475i
$651$		0			0
$652$	−15.3806	−	26.6400i	−0.602351	−	1.04330i
$653$	9.75599	+	16.8979i	0.381781	+	0.661264i	0.991317	−	0.131494i	$-0.0419774\pi$
$653$	9.75599	+	16.8979i	0.381781	+	0.661264i	−0.609536	+	0.792759i	$0.708644\pi$
$654$		0			0
$655$	0.121786	−	0.210939i	0.00475857	−	0.00824208i
$656$	−5.23452			−0.204374
$657$		0			0
$658$	8.97648			0.349940
$659$	11.5432	−	19.9934i	0.449660	−	0.778834i	−0.548704	−	0.836017i	$-0.684878\pi$
$659$	11.5432	−	19.9934i	0.449660	−	0.778834i	0.998364	+	0.0571827i	$0.0182118\pi$
$660$		0			0
$661$	3.43818	+	5.95510i	0.133730	+	0.231627i	0.925111	−	0.379696i	$-0.123971\pi$
$661$	3.43818	+	5.95510i	0.133730	+	0.231627i	−0.791382	+	0.611322i	$0.790638\pi$
$662$	−12.0648	−	20.8968i	−0.468910	−	0.812176i
$663$		0			0
$664$	1.20569	−	2.08832i	0.0467899	−	0.0810425i
$665$	−47.9376			−1.85894
$666$		0			0
$667$	−37.6560			−1.45805
$668$	−6.24378	+	10.8145i	−0.241579	+	0.418427i
$669$		0			0
$670$	−9.35440	−	16.2023i	−0.361392	−	0.625949i
$671$	−0.536857	−	0.929864i	−0.0207251	−	0.0358970i
$672$		0			0
$673$	15.3362	−	26.5630i	0.591166	−	1.02393i	−0.402910	−	0.915239i	$-0.632001\pi$
$673$	15.3362	−	26.5630i	0.591166	−	1.02393i	0.994076	−	0.108689i	$-0.0346653\pi$
$674$	−18.5624			−0.714997
$675$		0			0
$676$	15.6442			0.601700
$677$	−6.79198	+	11.7641i	−0.261037	+	0.452130i	−0.966518	−	0.256600i	$-0.917398\pi$
$677$	−6.79198	+	11.7641i	−0.261037	+	0.452130i	0.705481	+	0.708729i	$0.250731\pi$
$678$		0			0
$679$	−7.49950	−	12.9895i	−0.287804	−	0.498492i
$680$	19.6855	+	34.0963i	0.754906	+	1.30754i
$681$		0			0
$682$	−3.45928	+	5.99164i	−0.132462	+	0.229432i
$683$	6.06700			0.232147			0.116074	−	0.993241i	$-0.462969\pi$
$683$	6.06700			0.232147			0.116074	+	0.993241i	$0.462969\pi$
$684$		0			0
$685$	−18.1067			−0.691821
$686$	−7.53173	+	13.0453i	−0.287563	+	0.498074i
$687$		0			0
$688$	−0.860750	−	1.49086i	−0.0328158	−	0.0568386i
$689$	−0.0905538	−	0.156844i	−0.00344983	−	0.00597527i
$690$		0			0
$691$	−10.3325	+	17.8965i	−0.393068	+	0.680814i	−0.992853	−	0.119347i	$-0.961920\pi$
$691$	−10.3325	+	17.8965i	−0.393068	+	0.680814i	0.599784	+	0.800162i	$0.295253\pi$
$692$	3.67513			0.139707
$693$		0			0
$694$	−17.0411			−0.646871
$695$	12.4054	−	21.4868i	0.470564	−	0.815040i
$696$		0			0
$697$	22.2926	+	38.6119i	0.844393	+	1.46253i
$698$	−6.16231	−	10.6734i	−0.233247	−	0.403995i
$699$		0			0
$700$	−1.12898	+	1.95546i	−0.0426716	+	0.0739093i
$701$	−11.0222			−0.416303			−0.208151	−	0.978097i	$-0.566745\pi$
$701$	−11.0222			−0.416303			−0.208151	+	0.978097i	$0.566745\pi$
$702$		0			0
$703$	44.6131			1.68262
$704$	−4.83689	+	8.37773i	−0.182297	+	0.315748i
$705$		0			0
$706$	5.01905	+	8.69325i	0.188895	+	0.327175i
$707$	12.7842	+	22.1428i	0.480798	+	0.832767i
$708$		0			0
$709$	5.49372	−	9.51541i	0.206321	−	0.357359i	−0.744232	−	0.667922i	$-0.767184\pi$
$709$	5.49372	−	9.51541i	0.206321	−	0.357359i	0.950553	+	0.310563i	$0.100518\pi$
$710$	15.1379			0.568116
$711$		0			0
$712$	9.84577			0.368986
$713$	−5.74095	+	9.94361i	−0.215000	+	0.372391i
$714$		0			0
$715$	−4.98896	−	8.64114i	−0.186577	−	0.323160i
$716$	−2.57020	−	4.45172i	−0.0960530	−	0.166369i
$717$		0			0
$718$	10.0438	−	17.3964i	0.374832	−	0.649228i
$719$	−32.7057			−1.21972			−0.609859	−	0.792510i	$-0.708774\pi$
$719$	−32.7057			−1.21972			−0.609859	+	0.792510i	$0.708774\pi$
$720$		0			0
$721$	−21.3469			−0.795000
$722$	−17.9031	+	31.0091i	−0.666284	+	1.15404i
$723$		0			0
$724$	−0.187303	−	0.324418i	−0.00696106	−	0.0120569i
$725$	3.00455	+	5.20403i	0.111586	+	0.193273i
$726$		0			0
$727$	−19.2303	+	33.3079i	−0.713213	+	1.23532i	0.250432	+	0.968134i	$0.419427\pi$
$727$	−19.2303	+	33.3079i	−0.713213	+	1.23532i	−0.963645	+	0.267186i	$0.913906\pi$
$728$	8.82830			0.327199
$729$		0			0
$730$	−22.7591			−0.842352
$731$	−7.33146	+	12.6985i	−0.271164	+	0.469670i
$732$		0			0
$733$	−7.05387	−	12.2177i	−0.260541	−	0.451270i	0.705845	−	0.708366i	$-0.250568\pi$
$733$	−7.05387	−	12.2177i	−0.260541	−	0.451270i	−0.966386	+	0.257096i	$0.917234\pi$
$734$	−6.21197	−	10.7595i	−0.229288	−	0.397139i
$735$		0			0
$736$	−11.8677	+	20.5554i	−0.437448	+	0.757683i
$737$	31.7998			1.17136
$738$		0			0
$739$	−11.8457			−0.435752			−0.217876	−	0.975977i	$-0.569913\pi$
$739$	−11.8457			−0.435752			−0.217876	+	0.975977i	$0.569913\pi$
$740$	9.17003	−	15.8830i	0.337097	−	0.583869i
$741$		0			0
$742$	0.131797	+	0.228279i	0.00483841	+	0.00838037i
$743$	−10.8838	−	18.8513i	−0.399287	−	0.691586i	0.594351	−	0.804206i	$-0.297409\pi$
$743$	−10.8838	−	18.8513i	−0.399287	−	0.691586i	−0.993638	+	0.112620i	$0.964076\pi$
$744$		0			0
$745$	−10.7323	+	18.5888i	−0.393200	+	0.681043i
$746$	1.42058			0.0520111
$747$		0			0
$748$	−27.4989			−1.00546
$749$	−9.68659	+	16.7777i	−0.353940	+	0.613042i
$750$		0			0
$751$	21.2745	+	36.8485i	0.776318	+	1.34462i	0.934051	+	0.357140i	$0.116248\pi$
$751$	21.2745	+	36.8485i	0.776318	+	1.34462i	−0.157733	+	0.987482i	$0.550418\pi$
$752$	1.69955	+	2.94370i	0.0619761	+	0.107346i
$753$		0			0
$754$	4.82722	−	8.36100i	0.175797	−	0.304490i
$755$	56.7719			2.06614
$756$		0			0
$757$	−20.6382			−0.750110			−0.375055	−	0.927003i	$-0.622376\pi$
$757$	−20.6382			−0.750110			−0.375055	+	0.927003i	$0.622376\pi$
$758$	−0.446004	+	0.772502i	−0.0161996	+	0.0280585i
$759$		0			0
$760$	25.3020	+	43.8243i	0.917799	+	1.58967i
$761$	−24.7225	−	42.8207i	−0.896190	−	1.55225i	−0.832324	−	0.554289i	$-0.812990\pi$
$761$	−24.7225	−	42.8207i	−0.896190	−	1.55225i	−0.0638661	−	0.997958i	$-0.520343\pi$
$762$		0			0
$763$	1.56883	−	2.71730i	0.0567956	−	0.0983729i
$764$	−3.34551			−0.121036
$765$		0			0
$766$	−16.9760			−0.613367
$767$	2.67242	−	4.62876i	0.0964954	−	0.167135i
$768$		0			0
$769$	−11.0668	−	19.1683i	−0.399079	−	0.691225i	0.594534	−	0.804071i	$-0.297337\pi$
$769$	−11.0668	−	19.1683i	−0.399079	−	0.691225i	−0.993613	+	0.112846i	$0.964003\pi$
$770$	7.26120	+	12.5768i	0.261675	+	0.453235i
$771$		0			0
$772$	0.346134	−	0.599522i	0.0124576	−	0.0215773i
$773$	−21.9671			−0.790102			−0.395051	−	0.918659i	$-0.629273\pi$
$773$	−21.9671			−0.790102			−0.395051	+	0.918659i	$0.629273\pi$
$774$		0			0
$775$	1.83227			0.0658170
$776$	−7.91662	+	13.7120i	−0.284190	+	0.492232i
$777$		0			0
$778$	−10.1868	−	17.6441i	−0.365215	−	0.632571i
$779$	28.6529	+	49.6282i	1.02660	+	1.77812i
$780$		0			0
$781$	−12.8652	+	22.2831i	−0.460352	+	0.797353i
$782$	19.7860			0.707547
$783$		0

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.388866 + 0.673536i) q^{2} +(0.697566 + 1.20822i) q^{4} +(-1.18817 - 2.05798i) q^{5} +(1.25069 - 2.16626i) q^{7} -2.64050 q^{8} +O(q^{10})\)	\(q+(-0.388866 + 0.673536i) q^{2} +(0.697566 + 1.20822i) q^{4} +(-1.18817 - 2.05798i) q^{5} +(1.25069 - 2.16626i) q^{7} -2.64050 q^{8} +1.84816 q^{10} +(-1.57069 + 2.72051i) q^{11} +(-0.668315 - 1.15756i) q^{13} +(0.972701 + 1.68477i) q^{14} +(-0.368329 + 0.637965i) q^{16} +6.27452 q^{17} +8.06469 q^{19} +(1.65766 - 2.87115i) q^{20} +(-1.22157 - 2.11583i) q^{22} +(-2.02730 - 3.51139i) q^{23} +(-0.323514 + 0.560343i) q^{25} +1.03954 q^{26} +3.48975 q^{28} +(4.64361 - 8.04297i) q^{29} +(-1.41591 - 2.45243i) q^{31} +(-2.92697 - 5.06965i) q^{32} +(-2.43995 + 4.22611i) q^{34} -5.94414 q^{35} +5.53191 q^{37} +(-3.13608 + 5.43186i) q^{38} +(3.13738 + 5.43410i) q^{40} +(3.55288 + 6.15377i) q^{41} +(-1.16845 + 2.02382i) q^{43} -4.38263 q^{44} +3.15339 q^{46} +(2.30710 - 3.99602i) q^{47} +(0.371558 + 0.643557i) q^{49} +(-0.251607 - 0.435797i) q^{50} +(0.932388 - 1.61494i) q^{52} +0.135496 q^{53} +7.46499 q^{55} +(-3.30245 + 5.72001i) q^{56} +(3.61149 + 6.25528i) q^{58} +(1.99937 + 3.46301i) q^{59} +(-0.170899 + 0.296006i) q^{61} +2.20240 q^{62} +3.07947 q^{64} +(-1.58815 + 2.75075i) q^{65} +(-5.06146 - 8.76670i) q^{67} +(4.37689 + 7.58100i) q^{68} +(2.31148 - 4.00359i) q^{70} +8.19080 q^{71} -12.3144 q^{73} +(-2.15117 + 3.72594i) q^{74} +(5.62565 + 9.74392i) q^{76} +(3.92888 + 6.80501i) q^{77} +(-2.04035 + 3.53399i) q^{79} +1.75056 q^{80} -5.52638 q^{82} +(-0.456614 + 0.790879i) q^{83} +(-7.45522 - 12.9128i) q^{85} +(-0.908742 - 1.57399i) q^{86} +(4.14740 - 7.18351i) q^{88} -3.72875 q^{89} -3.34341 q^{91} +(2.82835 - 4.89885i) q^{92} +(1.79431 + 3.10783i) q^{94} +(-9.58225 - 16.5969i) q^{95} +(2.99815 - 5.19294i) q^{97} -0.577945 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more