LMFDB - Embedded newform 3024.2.t.k.289.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.7
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.k.1873.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.468169 q^{5} +(2.39007 - 1.13471i) q^{7} +O(q^{10})$	$q+0.468169 q^{5} +(2.39007 - 1.13471i) q^{7} -1.34859 q^{11} +(-3.16486 - 5.48171i) q^{13} +(2.47120 + 4.28024i) q^{17} +(-2.38910 + 4.13804i) q^{19} +7.62799 q^{23} -4.78082 q^{25} +(1.80565 - 3.12747i) q^{29} +(3.24939 - 5.62810i) q^{31} +(1.11896 - 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(0.0251630 + 0.0435837i) q^{41} +(0.431869 - 0.748019i) q^{43} +(5.49417 + 9.51619i) q^{47} +(4.42486 - 5.42408i) q^{49} +(-5.84976 - 10.1321i) q^{53} -0.631366 q^{55} +(1.93892 - 3.35831i) q^{59} +(-1.87231 - 3.24294i) q^{61} +(-1.48169 - 2.56637i) q^{65} +(-1.32436 + 2.29385i) q^{67} -7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(-3.22321 + 1.53026i) q^{77} +(1.58951 + 2.75311i) q^{79} +(4.90272 - 8.49176i) q^{83} +(1.15694 + 2.00388i) q^{85} +(-5.30709 + 9.19214i) q^{89} +(-13.7844 - 9.51045i) q^{91} +(-1.11850 + 1.93730i) q^{95} +(6.97792 - 12.0861i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{5} + q^{7}+O(q^{10}) $ 22 * q + 2 * q^5 + q^7	$ 22 q + 2 q^{5} + q^{7} - 6 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} + 44 q^{25} + 7 q^{29} - 6 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} + 17 q^{47} + 29 q^{49} - q^{53} - 2 q^{55} - 21 q^{59} + 31 q^{61} + 3 q^{65} + 26 q^{67} - 32 q^{71} + 17 q^{73} + 4 q^{77} + 16 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} - 24 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q + 2 * q^5 + q^7 - 6 * q^11 + 7 * q^13 + q^17 - 13 * q^19 + 44 * q^25 + 7 * q^29 - 6 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 + 17 * q^47 + 29 * q^49 - q^53 - 2 * q^55 - 21 * q^59 + 31 * q^61 + 3 * q^65 + 26 * q^67 - 32 * q^71 + 17 * q^73 + 4 * q^77 + 16 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 - 24 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.468169			0.209372			0.104686	−	0.994505i	$-0.466616\pi$
$5$	0.468169			0.209372			0.104686	+	0.994505i	$0.466616\pi$
$6$		0			0
$7$	2.39007	−	1.13471i	0.903361	−	0.428881i
$7$	2.39007	−	1.13471i	0.903361	−	0.428881i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.34859			−0.406614			−0.203307	−	0.979115i	$-0.565169\pi$
$11$	−1.34859			−0.406614			−0.203307	+	0.979115i	$0.565169\pi$
$12$		0			0
$13$	−3.16486	−	5.48171i	−0.877775	−	1.52035i	−0.853777	−	0.520640i	$-0.825694\pi$
$13$	−3.16486	−	5.48171i	−0.877775	−	1.52035i	−0.0239988	−	0.999712i	$-0.507640\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.47120	+	4.28024i	0.599353	+	1.03811i	0.992917	+	0.118813i	$0.0379089\pi$
$17$	2.47120	+	4.28024i	0.599353	+	1.03811i	−0.393563	+	0.919298i	$0.628758\pi$
$18$		0			0
$19$	−2.38910	+	4.13804i	−0.548097	+	0.949332i	0.450308	+	0.892873i	$0.351314\pi$
$19$	−2.38910	+	4.13804i	−0.548097	+	0.949332i	−0.998405	+	0.0564585i	$0.982019\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.62799			1.59055			0.795273	−	0.606252i	$-0.207328\pi$
$23$	7.62799			1.59055			0.795273	+	0.606252i	$0.207328\pi$
$24$		0			0
$25$	−4.78082			−0.956164
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.80565	−	3.12747i	0.335300	−	0.580757i	−0.648242	−	0.761434i	$-0.724496\pi$
$29$	1.80565	−	3.12747i	0.335300	−	0.580757i	0.983542	+	0.180677i	$0.0578290\pi$
$30$		0			0
$31$	3.24939	−	5.62810i	0.583607	−	1.01084i	−0.411440	−	0.911437i	$-0.634974\pi$
$31$	3.24939	−	5.62810i	0.583607	−	1.01084i	0.995047	−	0.0994007i	$-0.0316926\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.11896	−	0.531237i	0.189138	−	0.0897954i
$36$		0			0
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	−0.00838383	−	0.999965i	$-0.502669\pi$
$37$	5.24214	−	9.07966i	0.861803	−	1.49269i	0.870187	−	0.492722i	$-0.163998\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.0251630	+	0.0435837i	0.00392981	+	0.00680662i	0.867984	−	0.496593i	$-0.165416\pi$
$41$	0.0251630	+	0.0435837i	0.00392981	+	0.00680662i	−0.864054	+	0.503399i	$0.832082\pi$
$42$		0			0
$43$	0.431869	−	0.748019i	0.0658594	−	0.114072i	−0.831215	−	0.555950i	$-0.812354\pi$
$43$	0.431869	−	0.748019i	0.0658594	−	0.114072i	0.897075	+	0.441879i	$0.145688\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.49417	+	9.51619i	0.801408	+	1.38808i	0.918690	+	0.394980i	$0.129249\pi$
$47$	5.49417	+	9.51619i	0.801408	+	1.38808i	−0.117282	+	0.993099i	$0.537418\pi$
$48$		0			0
$49$	4.42486	−	5.42408i	0.632123	−	0.774868i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.84976	−	10.1321i	−0.803526	−	1.39175i	−0.917282	−	0.398239i	$-0.869622\pi$
$53$	−5.84976	−	10.1321i	−0.803526	−	1.39175i	0.113756	−	0.993509i	$-0.463712\pi$
$54$		0			0
$55$	−0.631366			−0.0851334
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.93892	−	3.35831i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$59$	1.93892	−	3.35831i	0.252426	−	0.437215i	0.964193	+	0.265201i	$0.0854382\pi$
$60$		0			0
$61$	−1.87231	−	3.24294i	−0.239725	−	0.415216i	0.720910	−	0.693028i	$-0.243724\pi$
$61$	−1.87231	−	3.24294i	−0.239725	−	0.415216i	−0.960635	+	0.277813i	$0.910391\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.48169	−	2.56637i	−0.183781	−	0.318318i
$66$		0			0
$67$	−1.32436	+	2.29385i	−0.161796	+	0.280239i	−0.935513	−	0.353293i	$-0.885062\pi$
$67$	−1.32436	+	2.29385i	−0.161796	+	0.280239i	0.773717	+	0.633532i	$0.218395\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.04562			−0.836161			−0.418081	−	0.908410i	$-0.637297\pi$
$71$	−7.04562			−0.836161			−0.418081	+	0.908410i	$0.637297\pi$
$72$		0			0
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	0.605586	−	0.795780i	$-0.292939\pi$
$73$	−3.30117	−	5.71779i	−0.386373	−	0.669217i	−0.991959	+	0.126563i	$0.959605\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.22321	+	1.53026i	−0.367319	+	0.174389i
$78$		0			0
$79$	1.58951	+	2.75311i	0.178834	+	0.309749i	0.941481	−	0.337065i	$-0.109434\pi$
$79$	1.58951	+	2.75311i	0.178834	+	0.309749i	−0.762648	+	0.646814i	$0.776101\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.90272	−	8.49176i	0.538143	−	0.932092i	−0.460861	−	0.887472i	$-0.652459\pi$
$83$	4.90272	−	8.49176i	0.538143	−	0.932092i	0.999004	−	0.0446192i	$-0.0142074\pi$
$84$		0			0
$85$	1.15694	+	2.00388i	0.125488	+	0.217351i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.30709	+	9.19214i	−0.562550	+	0.974365i	0.434723	+	0.900564i	$0.356846\pi$
$89$	−5.30709	+	9.19214i	−0.562550	+	0.974365i	−0.997273	+	0.0738011i	$0.976487\pi$
$90$		0			0
$91$	−13.7844	−	9.51045i	−1.44500	−	0.996966i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.11850	+	1.93730i	−0.114756	+	0.198763i
$96$		0			0
$97$	6.97792	−	12.0861i	0.708500	−	1.22716i	−0.256913	−	0.966434i	$-0.582706\pi$
$97$	6.97792	−	12.0861i	0.708500	−	1.22716i	0.965413	−	0.260724i	$-0.0839611\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.24945			−0.422836			−0.211418	−	0.977396i	$-0.567808\pi$
$101$	−4.24945			−0.422836			−0.211418	+	0.977396i	$0.567808\pi$
$102$		0			0
$103$	8.95640			0.882501			0.441250	−	0.897384i	$-0.354535\pi$
$103$	8.95640			0.882501			0.441250	+	0.897384i	$0.354535\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.810731	+	1.40423i	−0.0783763	+	0.135752i	−0.902550	−	0.430586i	$-0.858307\pi$
$107$	−0.810731	+	1.40423i	−0.0783763	+	0.135752i	0.824173	+	0.566338i	$0.191640\pi$
$108$		0			0
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	0.972631	−	0.232354i	$-0.0746428\pi$
$109$	2.97644	+	5.15534i	0.285091	+	0.493792i	−0.687540	+	0.726146i	$0.741309\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.14346	−	7.17669i	−0.389784	−	0.675126i	0.602636	−	0.798016i	$-0.294117\pi$
$113$	−4.14346	−	7.17669i	−0.389784	−	0.675126i	−0.992420	+	0.122890i	$0.960784\pi$
$114$		0			0
$115$	3.57119			0.333015
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.7632	+	7.42597i	0.986658	+	0.680738i
$120$		0			0
$121$	−9.18132			−0.834665
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.57908			−0.409565
$126$		0			0
$127$	−8.12368			−0.720860			−0.360430	−	0.932786i	$-0.617370\pi$
$127$	−8.12368			−0.720860			−0.360430	+	0.932786i	$0.617370\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	19.4965			1.70341			0.851707	−	0.524018i	$-0.175568\pi$
$131$	19.4965			1.70341			0.851707	+	0.524018i	$0.175568\pi$
$132$		0			0
$133$	−1.01463	+	12.6011i	−0.0879795	+	1.09266i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	15.1035			1.29038			0.645189	−	0.764023i	$-0.276779\pi$
$137$	15.1035			1.29038			0.645189	+	0.764023i	$0.276779\pi$
$138$		0			0
$139$	2.18826	+	3.79017i	0.185605	+	0.321478i	0.943780	−	0.330573i	$-0.107242\pi$
$139$	2.18826	+	3.79017i	0.185605	+	0.321478i	−0.758175	+	0.652051i	$0.773909\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.26809	+	7.39255i	0.356916	+	0.618196i
$144$		0			0
$145$	0.845348	−	1.46419i	0.0702023	−	0.121594i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.7564			0.963121			0.481561	−	0.876413i	$-0.340070\pi$
$149$	11.7564			0.963121			0.481561	+	0.876413i	$0.340070\pi$
$150$		0			0
$151$	5.14305			0.418536			0.209268	−	0.977858i	$-0.432892\pi$
$151$	5.14305			0.418536			0.209268	+	0.977858i	$0.432892\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.52126	−	2.63490i	0.122191	−	0.211641i
$156$		0			0
$157$	6.04447	−	10.4693i	0.482401	−	0.835544i	−0.517395	−	0.855747i	$-0.673098\pi$
$157$	6.04447	−	10.4693i	0.482401	−	0.835544i	0.999796	+	0.0202033i	$0.00643136\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	18.2314	−	8.65557i	1.43684	−	0.682154i
$162$		0			0
$163$	2.74663	−	4.75730i	0.215133	−	0.372621i	−0.738181	−	0.674603i	$-0.764315\pi$
$163$	2.74663	−	4.75730i	0.215133	−	0.372621i	0.953314	+	0.301982i	$0.0976482\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.59378	−	6.22461i	−0.278095	−	0.481675i	0.692816	−	0.721114i	$-0.256370\pi$
$167$	−3.59378	−	6.22461i	−0.278095	−	0.481675i	−0.970911	+	0.239440i	$0.923036\pi$
$168$		0			0
$169$	−13.5327	+	23.4394i	−1.04098	+	1.80303i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.97951	−	6.89271i	−0.302557	−	0.524043i	0.674158	−	0.738587i	$-0.264507\pi$
$173$	−3.97951	−	6.89271i	−0.302557	−	0.524043i	−0.976714	+	0.214544i	$0.931173\pi$
$174$		0			0
$175$	−11.4265	+	5.42485i	−0.863761	+	0.410080i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.168821	+	0.292406i	0.0126182	+	0.0218554i	0.872266	−	0.489032i	$-0.162650\pi$
$179$	0.168821	+	0.292406i	0.0126182	+	0.0218554i	−0.859647	+	0.510888i	$0.829317\pi$
$180$		0			0
$181$	7.05801			0.524618			0.262309	−	0.964984i	$-0.415516\pi$
$181$	7.05801			0.524618			0.262309	+	0.964984i	$0.415516\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.45421	−	4.25082i	0.180437	−	0.312526i
$186$		0			0
$187$	−3.33262	−	5.77227i	−0.243705	−	0.422110i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.85934	−	15.3448i	−0.641039	−	1.11031i	−0.985201	−	0.171402i	$-0.945170\pi$
$191$	−8.85934	−	15.3448i	−0.641039	−	1.11031i	0.344162	−	0.938910i	$-0.388163\pi$
$192$		0			0
$193$	8.40121	−	14.5513i	0.604732	−	1.04743i	−0.387362	−	0.921928i	$-0.626614\pi$
$193$	8.40121	−	14.5513i	0.604732	−	1.04743i	0.992094	−	0.125499i	$-0.0400531\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.97545			−0.425733			−0.212867	−	0.977081i	$-0.568280\pi$
$197$	−5.97545			−0.425733			−0.212867	+	0.977081i	$0.568280\pi$
$198$		0			0
$199$	−6.26093	−	10.8443i	−0.443826	−	0.768729i	0.554144	−	0.832421i	$-0.313046\pi$
$199$	−6.26093	−	10.8443i	−0.443826	−	0.768729i	−0.997970	+	0.0636923i	$0.979712\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.766842	−	9.52376i	0.0538217	−	0.668437i
$204$		0			0
$205$	0.0117806	+	0.0204045i	0.000822790	+	0.00142511i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.22190	−	5.58050i	0.222864	−	0.386011i
$210$		0			0
$211$	−1.17688	−	2.03842i	−0.0810198	−	0.140330i	0.822668	−	0.568521i	$-0.192484\pi$
$211$	−1.17688	−	2.03842i	−0.0810198	−	0.140330i	−0.903688	+	0.428191i	$0.859151\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.202188	−	0.350199i	0.0137891	−	0.0238834i
$216$		0			0
$217$	1.37999	−	17.1387i	0.0936795	−	1.16345i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.6420	−	27.0928i	1.05220	−	1.82246i
$222$		0			0
$223$	−5.30709	+	9.19215i	−0.355389	+	0.615552i	−0.987184	−	0.159583i	$-0.948985\pi$
$223$	−5.30709	+	9.19215i	−0.355389	+	0.615552i	0.631795	+	0.775135i	$0.282318\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.27550			0.0846578			0.0423289	−	0.999104i	$-0.486522\pi$
$227$	1.27550			0.0846578			0.0423289	+	0.999104i	$0.486522\pi$
$228$		0			0
$229$	−13.4663			−0.889876			−0.444938	−	0.895561i	$-0.646774\pi$
$229$	−13.4663			−0.889876			−0.444938	+	0.895561i	$0.646774\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.98509	+	17.2947i	−0.654145	+	1.13301i	0.327963	+	0.944691i	$0.393638\pi$
$233$	−9.98509	+	17.2947i	−0.654145	+	1.13301i	−0.982107	+	0.188321i	$0.939695\pi$
$234$		0			0
$235$	2.57220	+	4.45519i	0.167792	+	0.290624i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.1092	−	24.4379i	−0.912650	−	1.58076i	−0.810305	−	0.586008i	$-0.800699\pi$
$239$	−14.1092	−	24.4379i	−0.912650	−	1.58076i	−0.102345	−	0.994749i	$-0.532635\pi$
$240$		0			0
$241$	−17.3524			−1.11777			−0.558884	−	0.829246i	$-0.688770\pi$
$241$	−17.3524			−1.11777			−0.558884	+	0.829246i	$0.688770\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.07158	−	2.53939i	0.132349	−	0.162235i
$246$		0			0
$247$	30.2447			1.92442
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.29051			0.397054			0.198527	−	0.980095i	$-0.436384\pi$
$251$	6.29051			0.397054			0.198527	+	0.980095i	$0.436384\pi$
$252$		0			0
$253$	−10.2870			−0.646738
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.13637			0.382777			0.191388	−	0.981514i	$-0.438701\pi$
$257$	6.13637			0.382777			0.191388	+	0.981514i	$0.438701\pi$
$258$		0			0
$259$	2.22629	−	27.6493i	0.138335	−	1.71805i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.87914			0.362523			0.181262	−	0.983435i	$-0.441982\pi$
$263$	5.87914			0.362523			0.181262	+	0.983435i	$0.441982\pi$
$264$		0			0
$265$	−2.73868	−	4.74352i	−0.168235	−	0.291392i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.4633	+	26.7832i	0.942812	+	1.63300i	0.760074	+	0.649837i	$0.225163\pi$
$269$	15.4633	+	26.7832i	0.942812	+	1.63300i	0.182738	+	0.983162i	$0.441504\pi$
$270$		0			0
$271$	−5.44528	+	9.43150i	−0.330777	+	0.572923i	−0.982664	−	0.185393i	$-0.940644\pi$
$271$	−5.44528	+	9.43150i	−0.330777	+	0.572923i	0.651887	+	0.758316i	$0.273978\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.44734			0.388789
$276$		0			0
$277$	19.5900			1.17705			0.588524	−	0.808480i	$-0.299709\pi$
$277$	19.5900			1.17705			0.588524	+	0.808480i	$0.299709\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.142477	−	0.246777i	0.00849944	−	0.0147215i	−0.861744	−	0.507343i	$-0.830628\pi$
$281$	0.142477	−	0.246777i	0.00849944	−	0.0147215i	0.870244	+	0.492621i	$0.163961\pi$
$282$		0			0
$283$	1.42135	−	2.46185i	0.0844903	−	0.146342i	−0.820684	−	0.571383i	$-0.806407\pi$
$283$	1.42135	−	2.46185i	0.0844903	−	0.146342i	0.905174	+	0.425041i	$0.139740\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.109596	+	0.0756152i	0.00646926	+	0.00446342i
$288$		0			0
$289$	−3.71364	+	6.43221i	−0.218449	+	0.378365i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.45979	+	2.52842i	0.0852816	+	0.147712i	0.905511	−	0.424322i	$-0.139488\pi$
$293$	1.45979	+	2.52842i	0.0852816	+	0.147712i	−0.820230	+	0.572034i	$0.806154\pi$
$294$		0			0
$295$	0.907743	−	1.57226i	0.0528509	−	0.0915404i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−24.1415	−	41.8144i	−1.39614	−	2.41819i
$300$		0			0
$301$	0.183411	−	2.27786i	0.0105716	−	0.131294i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.876558	−	1.51824i	−0.0501916	−	0.0869344i
$306$		0			0
$307$	4.12553			0.235457			0.117728	−	0.993046i	$-0.462439\pi$
$307$	4.12553			0.235457			0.117728	+	0.993046i	$0.462439\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.69583	+	13.3296i	−0.436390	+	0.755850i	−0.997408	−	0.0719535i	$-0.977077\pi$
$311$	−7.69583	+	13.3296i	−0.436390	+	0.755850i	0.561018	+	0.827804i	$0.310410\pi$
$312$		0			0
$313$	10.3620	+	17.9475i	0.585694	+	1.01445i	0.994789	+	0.101959i	$0.0325112\pi$
$313$	10.3620	+	17.9475i	0.585694	+	1.01445i	−0.409095	+	0.912492i	$0.634156\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.244146	−	0.422873i	−0.0137126	−	0.0237509i	0.859088	−	0.511828i	$-0.171032\pi$
$317$	−0.244146	−	0.422873i	−0.0137126	−	0.0237509i	−0.872800	+	0.488078i	$0.837698\pi$
$318$		0			0
$319$	−2.43507	+	4.21766i	−0.136338	+	0.236144i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−23.6157			−1.31402
$324$		0			0
$325$	15.1306	+	26.2070i	0.839297	+	1.45370i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	23.9296	+	16.5100i	1.31928	+	0.910228i
$330$		0			0
$331$	−9.47864	−	16.4175i	−0.520993	−	0.902387i	−0.999702	−	0.0244131i	$-0.992228\pi$
$331$	−9.47864	−	16.4175i	−0.520993	−	0.902387i	0.478709	−	0.877974i	$-0.341105\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.620023	+	1.07391i	−0.0338755	+	0.0586740i
$336$		0			0
$337$	11.6202	+	20.1268i	0.632993	+	1.09638i	0.986937	+	0.161109i	$0.0515071\pi$
$337$	11.6202	+	20.1268i	0.632993	+	1.09638i	−0.353944	+	0.935267i	$0.615160\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.38208	+	7.58998i	−0.237303	+	0.411020i
$342$		0			0
$343$	4.42096	−	17.9849i	0.238709	−	0.971091i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.09439	+	15.7519i	−0.488212	+	0.845609i	−0.999908	−	0.0135582i	$-0.995684\pi$
$347$	−9.09439	+	15.7519i	−0.488212	+	0.845609i	0.511696	+	0.859167i	$0.329018\pi$
$348$		0			0
$349$	−9.40155	+	16.2840i	−0.503253	+	0.871661i	0.496740	+	0.867900i	$0.334530\pi$
$349$	−9.40155	+	16.2840i	−0.503253	+	0.871661i	−0.999993	+	0.00376081i	$0.998803\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.9199			0.634435			0.317217	−	0.948353i	$-0.397252\pi$
$353$	11.9199			0.634435			0.317217	+	0.948353i	$0.397252\pi$
$354$		0			0
$355$	−3.29854			−0.175068
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−17.3849	+	30.1115i	−0.917540	+	1.58923i	−0.114400	+	0.993435i	$0.536495\pi$
$359$	−17.3849	+	30.1115i	−0.917540	+	1.58923i	−0.803140	+	0.595791i	$0.796839\pi$
$360$		0			0
$361$	−1.91559	−	3.31790i	−0.100821	−	0.174626i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.54551	−	2.67689i	−0.0808954	−	0.140115i
$366$		0			0
$367$	28.8861			1.50784			0.753922	−	0.656964i	$-0.228160\pi$
$367$	28.8861			1.50784			0.753922	+	0.656964i	$0.228160\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−25.4783	−	17.5786i	−1.32277	−	0.912634i
$372$		0			0
$373$	14.3094			0.740915			0.370457	−	0.928849i	$-0.379201\pi$
$373$	14.3094			0.740915			0.370457	+	0.928849i	$0.379201\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−22.8585			−1.17727
$378$		0			0
$379$	−1.15511			−0.0593340			−0.0296670	−	0.999560i	$-0.509445\pi$
$379$	−1.15511			−0.0593340			−0.0296670	+	0.999560i	$0.509445\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	33.8262			1.72844			0.864219	−	0.503115i	$-0.167813\pi$
$383$	33.8262			1.72844			0.864219	+	0.503115i	$0.167813\pi$
$384$		0			0
$385$	−1.50901	+	0.716418i	−0.0769062	+	0.0365121i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−19.3216			−0.979644			−0.489822	−	0.871822i	$-0.662938\pi$
$389$	−19.3216			−0.979644			−0.489822	+	0.871822i	$0.662938\pi$
$390$		0			0
$391$	18.8503	+	32.6496i	0.953299	+	1.65116i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.744159	+	1.28892i	0.0374427	+	0.0648526i
$396$		0			0
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	−0.978419	−	0.206632i	$-0.933750\pi$
$397$	−6.18190	+	10.7074i	−0.310261	+	0.537387i	0.668158	+	0.744019i	$0.267083\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	30.5136			1.52378			0.761889	−	0.647708i	$-0.224272\pi$
$401$	30.5136			1.52378			0.761889	+	0.647708i	$0.224272\pi$
$402$		0			0
$403$	−41.1355			−2.04910
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.06948	+	12.2447i	−0.350421	+	0.606947i
$408$		0			0
$409$	2.62723	−	4.55050i	0.129908	−	0.225008i	−0.793733	−	0.608267i	$-0.791865\pi$
$409$	2.62723	−	4.55050i	0.129908	−	0.225008i	0.923641	+	0.383259i	$0.125198\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.823443	−	10.2267i	0.0405190	−	0.503224i
$414$		0			0
$415$	2.29530	−	3.97558i	0.112672	−	0.195154i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.2824	+	26.4699i	0.746594	+	1.29314i	0.949446	+	0.313930i	$0.101646\pi$
$419$	15.2824	+	26.4699i	0.746594	+	1.29314i	−0.202852	+	0.979209i	$0.565021\pi$
$420$		0			0
$421$	3.11608	−	5.39721i	0.151869	−	0.263044i	−0.780046	−	0.625722i	$-0.784804\pi$
$421$	3.11608	−	5.39721i	0.151869	−	0.263044i	0.931914	+	0.362678i	$0.118138\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.8143	−	20.4630i	−0.573080	−	0.992604i
$426$		0			0
$427$	−8.15475	−	5.62631i	−0.394636	−	0.272276i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.8142	+	25.6590i	0.713576	+	1.23595i	0.963506	+	0.267686i	$0.0862590\pi$
$431$	14.8142	+	25.6590i	0.713576	+	1.23595i	−0.249930	+	0.968264i	$0.580408\pi$
$432$		0			0
$433$	7.36815			0.354091			0.177045	−	0.984203i	$-0.443346\pi$
$433$	7.36815			0.354091			0.177045	+	0.984203i	$0.443346\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−18.2240	+	31.5649i	−0.871773	+	1.50996i
$438$		0			0
$439$	5.22135	+	9.04364i	0.249201	+	0.431629i	0.963304	−	0.268411i	$-0.0864986\pi$
$439$	5.22135	+	9.04364i	0.249201	+	0.431629i	−0.714103	+	0.700041i	$0.753165\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.83332	−	4.90745i	−0.134615	−	0.233160i	0.790835	−	0.612029i	$-0.209646\pi$
$443$	−2.83332	−	4.90745i	−0.134615	−	0.233160i	−0.925450	+	0.378869i	$0.876313\pi$
$444$		0			0
$445$	−2.48461	+	4.30348i	−0.117782	+	0.204004i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.4794			−0.541748			−0.270874	−	0.962615i	$-0.587313\pi$
$449$	−11.4794			−0.541748			−0.270874	+	0.962615i	$0.587313\pi$
$450$		0			0
$451$	−0.0339345	−	0.0587763i	−0.00159791	−	0.00276767i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.45343	−	4.45250i	−0.302541	−	0.208736i
$456$		0			0
$457$	−9.79361	−	16.9630i	−0.458126	−	0.793497i	0.540736	−	0.841192i	$-0.318146\pi$
$457$	−9.79361	−	16.9630i	−0.458126	−	0.793497i	−0.998862	+	0.0476953i	$0.984812\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−17.3028	+	29.9693i	−0.805871	+	1.39581i	0.109830	+	0.993950i	$0.464969\pi$
$461$	−17.3028	+	29.9693i	−0.805871	+	1.39581i	−0.915701	+	0.401859i	$0.868364\pi$
$462$		0			0
$463$	−6.91882	−	11.9837i	−0.321545	−	0.556932i	0.659262	−	0.751913i	$-0.270869\pi$
$463$	−6.91882	−	11.9837i	−0.321545	−	0.556932i	−0.980807	+	0.194981i	$0.937535\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.71088	−	6.42743i	0.171719	−	0.297426i	−0.767302	−	0.641286i	$-0.778401\pi$
$467$	3.71088	−	6.42743i	0.171719	−	0.297426i	0.939021	+	0.343860i	$0.111735\pi$
$468$		0			0
$469$	−0.562442	+	6.98523i	−0.0259712	+	0.322548i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.582412	+	1.00877i	−0.0267793	+	0.0463832i
$474$		0			0
$475$	11.4218	−	19.7832i	0.524070	−	0.907716i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.79154			−0.356005			−0.178002	−	0.984030i	$-0.556963\pi$
$479$	−7.79154			−0.356005			−0.178002	+	0.984030i	$0.556963\pi$
$480$		0			0
$481$	−66.3627			−3.02588
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.26684	−	5.65834i	0.148340	−	0.256932i
$486$		0			0
$487$	1.04434	+	1.80886i	0.0473238	+	0.0819672i	0.888717	−	0.458456i	$-0.151597\pi$
$487$	1.04434	+	1.80886i	0.0473238	+	0.0819672i	−0.841393	+	0.540423i	$0.818264\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−16.8767	−	29.2312i	−0.761633	−	1.31919i	−0.942008	−	0.335590i	$-0.891064\pi$
$491$	−16.8767	−	29.2312i	−0.761633	−	1.31919i	0.180375	−	0.983598i	$-0.442269\pi$
$492$		0			0
$493$	17.8484			0.803853
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.8395	+	7.99475i	−0.755356	+	0.358613i
$498$		0			0
$499$	−41.8196			−1.87210			−0.936052	−	0.351862i	$-0.885549\pi$
$499$	−41.8196			−1.87210			−0.936052	+	0.351862i	$0.885549\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.54978			0.292040			0.146020	−	0.989282i	$-0.453354\pi$
$503$	6.54978			0.292040			0.146020	+	0.989282i	$0.453354\pi$
$504$		0			0
$505$	−1.98946			−0.0885299
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.6131			0.559064			0.279532	−	0.960136i	$-0.409821\pi$
$509$	12.6131			0.559064			0.279532	+	0.960136i	$0.409821\pi$
$510$		0			0
$511$	−14.3781	−	9.92004i	−0.636048	−	0.438837i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.19311			0.184771
$516$		0			0
$517$	−7.40936	−	12.8334i	−0.325863	−	0.564412i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.2688	−	17.7861i	−0.449883	−	0.779221i	0.548495	−	0.836154i	$-0.315201\pi$
$521$	−10.2688	−	17.7861i	−0.449883	−	0.779221i	−0.998378	+	0.0569331i	$0.981868\pi$
$522$		0			0
$523$	−14.4579	+	25.0419i	−0.632202	+	1.09501i	0.354899	+	0.934905i	$0.384515\pi$
$523$	−14.4579	+	25.0419i	−0.632202	+	1.09501i	−0.987101	+	0.160101i	$0.948818\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	32.1195			1.39915
$528$		0			0
$529$	35.1862			1.52983
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.159275	−	0.275873i	0.00689897	−	0.0119494i
$534$		0			0
$535$	−0.379559	+	0.657416i	−0.0164098	+	0.0284226i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.96730	+	7.31483i	−0.257030	+	0.315072i
$540$		0			0
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	−0.786524	−	0.617560i	$-0.788121\pi$
$541$	3.29262	−	5.70299i	0.141561	−	0.245191i	0.928085	+	0.372369i	$0.121455\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.39348	+	2.41357i	0.0596900	+	0.103386i
$546$		0			0
$547$	−4.46777	+	7.73840i	−0.191028	+	0.330870i	−0.945591	−	0.325357i	$-0.894515\pi$
$547$	−4.46777	+	7.73840i	−0.191028	+	0.330870i	0.754563	+	0.656227i	$0.227849\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.62774	+	14.9437i	0.367554	+	0.636622i
$552$		0			0
$553$	6.92302	+	4.77649i	0.294397	+	0.203117i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.93523	+	5.08396i	0.124370	+	0.215414i	0.921486	−	0.388411i	$-0.126976\pi$
$557$	2.93523	+	5.08396i	0.124370	+	0.215414i	−0.797117	+	0.603825i	$0.793642\pi$
$558$		0			0
$559$	−5.46723			−0.231239
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−13.7986	+	23.8998i	−0.581541	+	1.00726i	0.413756	+	0.910388i	$0.364217\pi$
$563$	−13.7986	+	23.8998i	−0.581541	+	1.00726i	−0.995297	+	0.0968707i	$0.969117\pi$
$564$		0			0
$565$	−1.93984	−	3.35991i	−0.0816098	−	0.141352i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.9601	−	24.1796i	−0.585238	−	1.01366i	−0.994846	−	0.101400i	$-0.967668\pi$
$569$	−13.9601	−	24.1796i	−0.585238	−	1.01366i	0.409608	−	0.912262i	$-0.365665\pi$
$570$		0			0
$571$	−15.8987	+	27.5373i	−0.665339	+	1.15240i	0.313854	+	0.949471i	$0.398380\pi$
$571$	−15.8987	+	27.5373i	−0.665339	+	1.15240i	−0.979193	+	0.202930i	$0.934954\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−36.4680			−1.52082
$576$		0			0
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	0.996327	+	0.0856281i	$0.0272897\pi$
$577$	13.7476	+	23.8115i	0.572320	+	0.991287i	−0.424007	+	0.905659i	$0.639377\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.08214	−	25.8591i	0.0863817	−	1.07281i
$582$		0			0
$583$	7.88889	+	13.6640i	0.326725	+	0.565904i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.12422	+	12.3395i	−0.294048	+	0.509306i	−0.974763	−	0.223242i	$-0.928336\pi$
$587$	−7.12422	+	12.3395i	−0.294048	+	0.509306i	0.680715	+	0.732548i	$0.261669\pi$
$588$		0			0
$589$	15.5262	+	26.8922i	0.639747	+	1.10807i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.4636	+	26.7838i	−0.635015	+	1.09988i	0.351498	+	0.936189i	$0.385673\pi$
$593$	−15.4636	+	26.7838i	−0.635015	+	1.09988i	−0.986512	+	0.163689i	$0.947661\pi$
$594$		0			0
$595$	5.03898	+	3.47661i	0.206578	+	0.142527i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.2657	+	31.6372i	−0.746318	+	1.29266i	0.203258	+	0.979125i	$0.434847\pi$
$599$	−18.2657	+	31.6372i	−0.746318	+	1.29266i	−0.949576	+	0.313536i	$0.898486\pi$
$600$		0			0
$601$	7.11575	−	12.3248i	0.290257	−	0.502741i	−0.683613	−	0.729845i	$-0.739592\pi$
$601$	7.11575	−	12.3248i	0.290257	−	0.502741i	0.973871	+	0.227104i	$0.0729257\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.29841			−0.174755
$606$		0			0
$607$	29.3457			1.19111			0.595553	−	0.803316i	$-0.296933\pi$
$607$	29.3457			1.19111			0.595553	+	0.803316i	$0.296933\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	34.7766	−	60.2349i	1.40691	−	2.43684i
$612$		0			0
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	0.779213	−	0.626760i	$-0.215619\pi$
$613$	−3.79264	−	6.56905i	−0.153183	−	0.265321i	−0.932396	+	0.361438i	$0.882286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.4367	+	18.0769i	0.420165	+	0.727748i	0.995955	−	0.0898500i	$-0.0286388\pi$
$617$	10.4367	+	18.0769i	0.420165	+	0.727748i	−0.575790	+	0.817598i	$0.695305\pi$
$618$		0			0
$619$	25.2600			1.01528			0.507642	−	0.861568i	$-0.330517\pi$
$619$	25.2600			1.01528			0.507642	+	0.861568i	$0.330517\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.25387	+	27.9919i	−0.0902995	+	1.12147i
$624$		0			0
$625$	21.7603			0.870412
$626$		0			0
$627$		0			0
$628$		0			0
$629$	51.8175			2.06610
$630$		0			0
$631$	34.0114			1.35397			0.676986	−	0.735996i	$-0.263286\pi$
$631$	34.0114			1.35397			0.676986	+	0.735996i	$0.263286\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.80326			−0.150928
$636$		0			0
$637$	−43.7373	−	7.08931i	−1.73293	−	0.280889i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.29894			−0.209296			−0.104648	−	0.994509i	$-0.533372\pi$
$641$	−5.29894			−0.209296			−0.104648	+	0.994509i	$0.533372\pi$
$642$		0			0
$643$	−19.4304	−	33.6544i	−0.766260	−	1.32720i	−0.939578	−	0.342335i	$-0.888782\pi$
$643$	−19.4304	−	33.6544i	−0.766260	−	1.32720i	0.173318	−	0.984866i	$-0.444551\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.11420	+	7.12601i	0.161746	+	0.280152i	0.935495	−	0.353340i	$-0.114954\pi$
$647$	4.11420	+	7.12601i	0.161746	+	0.280152i	−0.773749	+	0.633492i	$0.781621\pi$
$648$		0			0
$649$	−2.61480	+	4.52897i	−0.102640	+	0.177778i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−42.0328			−1.64487			−0.822436	−	0.568858i	$-0.807385\pi$
$653$	−42.0328			−1.64487			−0.822436	+	0.568858i	$0.807385\pi$
$654$		0			0
$655$	9.12764			0.356647
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.33484	−	12.7043i	0.285725	−	0.494890i	−0.687060	−	0.726601i	$-0.741099\pi$
$659$	7.33484	−	12.7043i	0.285725	−	0.494890i	0.972785	+	0.231711i	$0.0744323\pi$
$660$		0			0
$661$	−2.93303	+	5.08015i	−0.114081	+	0.197595i	−0.917412	−	0.397938i	$-0.869726\pi$
$661$	−2.93303	+	5.08015i	−0.114081	+	0.197595i	0.803331	+	0.595533i	$0.203059\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.475018	+	5.89947i	−0.0184204	+	0.228771i
$666$		0			0
$667$	13.7734	−	23.8563i	0.533310	−	0.923720i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.52497	+	4.37338i	0.0974754	+	0.168832i
$672$		0			0
$673$	9.42591	−	16.3261i	0.363342	−	0.629327i	−0.625167	−	0.780491i	$-0.714969\pi$
$673$	9.42591	−	16.3261i	0.363342	−	0.629327i	0.988509	+	0.151165i	$0.0483023\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.9572	+	25.9067i	0.574852	+	0.995674i	0.996058	+	0.0887082i	$0.0282739\pi$
$677$	14.9572	+	25.9067i	0.574852	+	0.995674i	−0.421205	+	0.906965i	$0.638393\pi$
$678$		0			0
$679$	2.96346	−	36.8045i	0.113727	−	1.41243i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.8525	+	22.2612i	0.491788	+	0.851802i	0.999955	−	0.00945677i	$-0.00301023\pi$
$683$	12.8525	+	22.2612i	0.491788	+	0.851802i	−0.508167	+	0.861258i	$0.669677\pi$
$684$		0			0
$685$	7.07099			0.270169
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−37.0274	+	64.1333i	−1.41063	+	2.44328i
$690$		0			0
$691$	19.2010	+	33.2571i	0.730440	+	1.26516i	0.956695	+	0.291092i	$0.0940185\pi$
$691$	19.2010	+	33.2571i	0.730440	+	1.26516i	−0.226255	+	0.974068i	$0.572648\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.02447	+	1.77444i	0.0388605	+	0.0673084i
$696$		0			0
$697$	−0.124366	+	0.215408i	−0.00471069	+	0.00815915i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−11.5694			−0.436972			−0.218486	−	0.975840i	$-0.570112\pi$
$701$	−11.5694			−0.436972			−0.218486	+	0.975840i	$0.570112\pi$
$702$		0			0
$703$	25.0480	+	43.3844i	0.944703	+	1.63627i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−10.1565	+	4.82190i	−0.381974	+	0.181346i
$708$		0			0
$709$	−26.0275	−	45.0810i	−0.977483	−	1.69305i	−0.671484	−	0.741019i	$-0.734343\pi$
$709$	−26.0275	−	45.0810i	−0.977483	−	1.69305i	−0.305999	−	0.952032i	$-0.598990\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	24.7863	−	42.9311i	0.928254	−	1.60778i
$714$		0			0
$715$	1.99819	+	3.46096i	0.0747280	+	0.129433i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.416175	−	0.720836i	0.0155207	−	0.0268827i	−0.858161	−	0.513381i	$-0.828393\pi$
$719$	0.416175	−	0.720836i	0.0155207	−	0.0268827i	0.873681	+	0.486498i	$0.161726\pi$
$720$		0			0
$721$	21.4064	−	10.1629i	0.797217	−	0.378488i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.63247	+	14.9519i	−0.320602	+	0.555299i
$726$		0			0
$727$	−10.7029	+	18.5379i	−0.396948	+	0.687534i	−0.993348	−	0.115154i	$-0.963264\pi$
$727$	−10.7029	+	18.5379i	−0.396948	+	0.687534i	0.596400	+	0.802687i	$0.296597\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.26894			0.157892
$732$		0			0
$733$	−7.45240			−0.275261			−0.137630	−	0.990484i	$-0.543949\pi$
$733$	−7.45240			−0.275261			−0.137630	+	0.990484i	$0.543949\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.78601	−	3.09346i	0.0657885	−	0.113949i
$738$		0			0
$739$	17.9473	+	31.0857i	0.660203	+	1.14351i	0.980562	+	0.196210i	$0.0628633\pi$
$739$	17.9473	+	31.0857i	0.660203	+	1.14351i	−0.320358	+	0.947296i	$0.603803\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.8379	+	29.1641i	0.617723	+	1.06993i	0.989900	+	0.141766i	$0.0452781\pi$
$743$	16.8379	+	29.1641i	0.617723	+	1.06993i	−0.372177	+	0.928162i	$0.621389\pi$
$744$		0			0
$745$	5.50398			0.201650
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.344310	+	4.27615i	−0.0125808	+	0.156247i
$750$		0			0
$751$	−15.0338			−0.548590			−0.274295	−	0.961646i	$-0.588445\pi$
$751$	−15.0338			−0.548590			−0.274295	+	0.961646i	$0.588445\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.40782			0.0876295
$756$		0			0
$757$	−34.2548			−1.24501			−0.622507	−	0.782615i	$-0.713886\pi$
$757$	−34.2548			−1.24501			−0.622507	+	0.782615i	$0.713886\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−42.2086			−1.53006			−0.765031	−	0.643993i	$-0.777276\pi$
$761$	−42.2086			−1.53006			−0.765031	+	0.643993i	$0.777276\pi$
$762$		0			0
$763$	12.9637	+	8.94423i	0.469318	+	0.323803i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−24.5457			−0.886294
$768$		0			0
$769$	22.2741	+	38.5799i	0.803226	+	1.39123i	0.917482	+	0.397777i	$0.130218\pi$
$769$	22.2741	+	38.5799i	0.803226	+	1.39123i	−0.114256	+	0.993451i	$0.536448\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.61003	+	16.6451i	0.345649	+	0.598681i	0.985471	−	0.169841i	$-0.0543256\pi$
$773$	9.61003	+	16.6451i	0.345649	+	0.598681i	−0.639823	+	0.768523i	$0.720992\pi$
$774$		0			0
$775$	−15.5347	+	26.9069i	−0.558024	+	0.966526i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.240468			−0.00861566
$780$		0			0
$781$	9.50162			0.339995
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.82984	−	4.90142i	0.101001	−	0.174939i
$786$		0			0
$787$	−20.1751	+	34.9443i	−0.719165	+	1.24563i	0.242166	+	0.970235i	$0.422142\pi$
$787$	−20.1751	+	34.9443i	−0.719165	+	1.24563i	−0.961331	+	0.275396i	$0.911191\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−18.0466	−	12.4512i	−0.641665	−	0.442712i
$792$		0			0
$793$	−11.8512	+	20.5269i	−0.420849	+	0.728932i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.4965	−	38.9651i	−0.796867	−	1.38021i	−0.921647	−	0.388029i	$-0.873156\pi$
$797$	−22.4965	−	38.9651i	−0.796867	−	1.38021i	0.124780	−	0.992184i	$-0.460177\pi$
$798$		0			0
$799$	−27.1544	+	47.0328i	−0.960653	+	1.66390i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.45191	+	7.71093i	0.157104	+	0.272113i
$804$		0			0
$805$	8.53539	−	4.05227i	0.300833	−	0.142824i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.8858	−	29.2470i	−0.593672	−	1.02827i	−0.993733	−	0.111782i	$-0.964344\pi$
$809$	−16.8858	−	29.2470i	−0.593672	−	1.02827i	0.400061	−	0.916489i	$-0.368989\pi$
$810$		0			0
$811$	31.7254			1.11403			0.557014	−	0.830503i	$-0.311947\pi$
$811$	31.7254			1.11403			0.557014	+	0.830503i	$0.311947\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.28589	−	2.22722i	0.0450427	−	0.0780162i
$816$		0			0
$817$	2.06356	+	3.57418i	0.0721947	+	0.125045i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.87521	−	10.1762i	−0.205046	−	0.355151i	0.745101	−	0.666951i	$-0.232401\pi$
$821$	−5.87521	−	10.1762i	−0.205046	−	0.355151i	−0.950147	+	0.311801i	$0.899068\pi$
$822$		0			0
$823$	−4.25371	+	7.36764i	−0.148275	+	0.256820i	−0.930590	−	0.366063i	$-0.880705\pi$
$823$	−4.25371	+	7.36764i	−0.148275	+	0.256820i	0.782315	+	0.622883i	$0.214039\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.9662			−0.485651			−0.242825	−	0.970070i	$-0.578074\pi$
$827$	−13.9662			−0.485651			−0.242825	+	0.970070i	$0.578074\pi$
$828$		0			0
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	−0.984483	−	0.175480i	$-0.943852\pi$
$829$	−18.5484	−	32.1267i	−0.644212	−	1.11581i	0.340271	−	0.940327i	$-0.389481\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	34.1511	+	5.53549i	1.18326	+	0.191793i
$834$		0			0
$835$	−1.68250	−	2.91417i	−0.0582252	−	0.100849i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.32105	+	2.28813i	−0.0456077	+	0.0789949i	−0.887928	−	0.459982i	$-0.847856\pi$
$839$	−1.32105	+	2.28813i	−0.0456077	+	0.0789949i	0.842320	+	0.538977i	$0.181189\pi$
$840$		0			0
$841$	7.97928	+	13.8205i	0.275148	+	0.476570i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.33561	+	10.9736i	−0.217952	+	0.377503i
$846$		0			0
$847$	−21.9440	+	10.4181i	−0.754004	+	0.357972i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	39.9870	−	69.2595i	1.37074	−	2.37419i
$852$		0			0
$853$	17.3405	−	30.0346i	0.593726	−	1.02836i	−0.399999	−	0.916516i	$-0.630990\pi$
$853$	17.3405	−	30.0346i	0.593726	−	1.02836i	0.993725	−	0.111848i	$-0.0356771\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.7223			−0.810338			−0.405169	−	0.914242i	$-0.632787\pi$
$857$	−23.7223			−0.810338			−0.405169	+	0.914242i	$0.632787\pi$
$858$		0			0
$859$	21.8150			0.744317			0.372158	−	0.928169i	$-0.378618\pi$
$859$	21.8150			0.744317			0.372158	+	0.928169i	$0.378618\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.6899	+	25.4436i	−0.500049	+	0.866111i	0.499951	+	0.866054i	$0.333351\pi$
$863$	−14.6899	+	25.4436i	−0.500049	+	0.866111i	−1.00000		5.68129e-5i	$0.999982\pi$
$864$		0			0
$865$	−1.86308	−	3.22696i	−0.0633467	−	0.109720i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.14359	−	3.71280i	−0.0727162	−	0.125948i
$870$		0			0
$871$	16.7656			0.568082
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−10.9443	+	5.19593i	−0.369985	+	0.175655i
$876$		0			0
$877$	−5.62129			−0.189817			−0.0949087	−	0.995486i	$-0.530256\pi$
$877$	−5.62129			−0.189817			−0.0949087	+	0.995486i	$0.530256\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.75442			−0.0927987			−0.0463994	−	0.998923i	$-0.514775\pi$
$881$	−2.75442			−0.0927987			−0.0463994	+	0.998923i	$0.514775\pi$
$882$		0			0
$883$	−33.8917			−1.14055			−0.570274	−	0.821455i	$-0.693163\pi$
$883$	−33.8917			−1.14055			−0.570274	+	0.821455i	$0.693163\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−55.6893			−1.86986			−0.934932	−	0.354827i	$-0.884540\pi$
$887$	−55.6893			−1.86986			−0.934932	+	0.354827i	$0.884540\pi$
$888$		0			0
$889$	−19.4162	+	9.21803i	−0.651197	+	0.309163i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−52.5045			−1.75700
$894$		0			0
$895$	0.0790366	+	0.136895i	0.00264190	+	0.00457591i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−11.7345	−	20.3247i	−0.391367	−	0.677868i
$900$		0			0
$901$	28.9118	−	50.0767i	0.963192	−	1.66830i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.30434			0.109840
$906$		0			0
$907$	−53.4626			−1.77519			−0.887597	−	0.460620i	$-0.847627\pi$
$907$	−53.4626			−1.77519			−0.887597	+	0.460620i	$0.847627\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.77060	−	16.9232i	0.323714	−	0.560690i	−0.657537	−	0.753422i	$-0.728402\pi$
$911$	9.77060	−	16.9232i	0.323714	−	0.560690i	0.981251	+	0.192732i	$0.0617350\pi$
$912$		0			0
$913$	−6.61174	+	11.4519i	−0.218817	+	0.379001i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	46.5979	−	22.1229i	1.53880	−	0.730561i
$918$		0			0
$919$	−0.0878895	+	0.152229i	−0.00289921	+	0.00502157i	−0.867471	−	0.497487i	$-0.834256\pi$
$919$	−0.0878895	+	0.152229i	−0.00289921	+	0.00502157i	0.864572	+	0.502509i	$0.167590\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	22.2984	+	38.6220i	0.733962	+	1.27126i
$924$		0			0
$925$	−25.0617	+	43.4082i	−0.824025	+	1.42725i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.3008	−	21.3056i	−0.403576	−	0.699014i	0.590579	−	0.806980i	$-0.298900\pi$
$929$	−12.3008	−	21.3056i	−0.403576	−	0.699014i	−0.994155	+	0.107966i	$0.965566\pi$
$930$		0			0
$931$	11.8736	+	31.2689i	0.389142	+	1.02480i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.56023	−	2.70240i	−0.0510250	−	0.0883779i
$936$		0			0
$937$	−28.5655			−0.933195			−0.466598	−	0.884470i	$-0.654520\pi$
$937$	−28.5655			−0.933195			−0.466598	+	0.884470i	$0.654520\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.7802	−	32.5283i	0.612217	−	1.06039i	−0.378648	−	0.925541i	$-0.623611\pi$
$941$	18.7802	−	32.5283i	0.612217	−	1.06039i	0.990866	−	0.134851i	$-0.0430556\pi$
$942$		0			0
$943$	0.191943	+	0.332456i	0.00625053	+	0.0108262i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.83381	−	8.37241i	−0.157078	−	0.272067i	0.776736	−	0.629827i	$-0.216874\pi$
$947$	−4.83381	−	8.37241i	−0.157078	−	0.272067i	−0.933814	+	0.357760i	$0.883541\pi$
$948$		0			0
$949$	−20.8955	+	36.1921i	−0.678297	+	1.17484i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−58.1964			−1.88517			−0.942583	−	0.333971i	$-0.891611\pi$
$953$	−58.1964			−1.88517			−0.942583	+	0.333971i	$0.891611\pi$
$954$		0			0
$955$	−4.14767	−	7.18397i	−0.134215	−	0.232468i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	36.0984	−	17.1381i	1.16568	−	0.553418i
$960$		0			0
$961$	−5.61704	−	9.72900i	−0.181195	−	0.313839i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.93319	−	6.81248i	0.126614	−	0.219301i
$966$		0			0
$967$	−7.97991	−	13.8216i	−0.256617	−	0.444473i	0.708717	−	0.705493i	$-0.249274\pi$
$967$	−7.97991	−	13.8216i	−0.256617	−	0.444473i	−0.965333	+	0.261020i	$0.915941\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.67394	+	2.89935i	−0.0537193	+	0.0930445i	−0.891635	−	0.452756i	$-0.850441\pi$
$971$	−1.67394	+	2.89935i	−0.0537193	+	0.0930445i	0.837915	+	0.545800i	$0.183774\pi$
$972$		0			0
$973$	9.53083	+	6.57573i	0.305544	+	0.210808i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.9402	−	20.6810i	0.382000	−	0.661643i	−0.609348	−	0.792903i	$-0.708569\pi$
$977$	11.9402	−	20.6810i	0.382000	−	0.661643i	0.991348	+	0.131260i	$0.0419022\pi$
$978$		0			0
$979$	7.15706	−	12.3964i	0.228741	−	0.396190i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	37.7573			1.20427			0.602135	−	0.798394i	$-0.294317\pi$
$983$	37.7573			1.20427			0.602135	+	0.798394i	$0.294317\pi$
$984$		0			0
$985$	−2.79752			−0.0891364
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.29429	−	5.70588i	0.104752	−	0.181436i
$990$		0			0
$991$	1.08487	+	1.87904i	0.0344619	+	0.0596898i	0.882742	−	0.469858i	$-0.155695\pi$
$991$	1.08487	+	1.87904i	0.0344619	+	0.0596898i	−0.848280	+	0.529548i	$0.822362\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.93117	−	5.07694i	−0.0929245	−	0.160950i
$996$		0			0
$997$	−8.69454			−0.275359			−0.137679	−	0.990477i	$-0.543964\pi$
$997$	−8.69454			−0.275359			−0.137679	+	0.990477i	$0.543964\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.k.289.7		22
3.2	odd	2		1008.2.t.l.961.5		22
4.3	odd	2		1512.2.t.c.289.7		22
7.4	even	3		3024.2.q.l.2881.5		22
9.4	even	3		3024.2.q.l.2305.5		22
9.5	odd	6		1008.2.q.l.625.11		22
12.11	even	2		504.2.t.c.457.7	yes	22
21.11	odd	6		1008.2.q.l.529.11		22
28.11	odd	6		1512.2.q.d.1369.5		22
36.23	even	6		504.2.q.c.121.1	yes	22
36.31	odd	6		1512.2.q.d.793.5		22
63.4	even	3	inner	3024.2.t.k.1873.7		22
63.32	odd	6		1008.2.t.l.193.5		22
84.11	even	6		504.2.q.c.25.1	✓	22
252.67	odd	6		1512.2.t.c.361.7		22
252.95	even	6		504.2.t.c.193.7	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.1	✓	22	84.11	even	6
504.2.q.c.121.1	yes	22	36.23	even	6
504.2.t.c.193.7	yes	22	252.95	even	6
504.2.t.c.457.7	yes	22	12.11	even	2
1008.2.q.l.529.11		22	21.11	odd	6
1008.2.q.l.625.11		22	9.5	odd	6
1008.2.t.l.193.5		22	63.32	odd	6
1008.2.t.l.961.5		22	3.2	odd	2
1512.2.q.d.793.5		22	36.31	odd	6
1512.2.q.d.1369.5		22	28.11	odd	6
1512.2.t.c.289.7		22	4.3	odd	2
1512.2.t.c.361.7		22	252.67	odd	6
3024.2.q.l.2305.5		22	9.4	even	3
3024.2.q.l.2881.5		22	7.4	even	3
3024.2.t.k.289.7		22	1.1	even	1	trivial
3024.2.t.k.1873.7		22	63.4	even	3	inner

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.468169 q^{5} +(2.39007 - 1.13471i) q^{7} +O(q^{10})\)	\(q+0.468169 q^{5} +(2.39007 - 1.13471i) q^{7} -1.34859 q^{11} +(-3.16486 - 5.48171i) q^{13} +(2.47120 + 4.28024i) q^{17} +(-2.38910 + 4.13804i) q^{19} +7.62799 q^{23} -4.78082 q^{25} +(1.80565 - 3.12747i) q^{29} +(3.24939 - 5.62810i) q^{31} +(1.11896 - 0.531237i) q^{35} +(5.24214 - 9.07966i) q^{37} +(0.0251630 + 0.0435837i) q^{41} +(0.431869 - 0.748019i) q^{43} +(5.49417 + 9.51619i) q^{47} +(4.42486 - 5.42408i) q^{49} +(-5.84976 - 10.1321i) q^{53} -0.631366 q^{55} +(1.93892 - 3.35831i) q^{59} +(-1.87231 - 3.24294i) q^{61} +(-1.48169 - 2.56637i) q^{65} +(-1.32436 + 2.29385i) q^{67} -7.04562 q^{71} +(-3.30117 - 5.71779i) q^{73} +(-3.22321 + 1.53026i) q^{77} +(1.58951 + 2.75311i) q^{79} +(4.90272 - 8.49176i) q^{83} +(1.15694 + 2.00388i) q^{85} +(-5.30709 + 9.19214i) q^{89} +(-13.7844 - 9.51045i) q^{91} +(-1.11850 + 1.93730i) q^{95} +(6.97792 - 12.0861i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{5} + q^{7}+O(q^{10}) \) 22 * q + 2 * q^5 + q^7	\( 22 q + 2 q^{5} + q^{7} - 6 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} + 44 q^{25} + 7 q^{29} - 6 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} + 17 q^{47} + 29 q^{49} - q^{53} - 2 q^{55} - 21 q^{59} + 31 q^{61} + 3 q^{65} + 26 q^{67} - 32 q^{71} + 17 q^{73} + 4 q^{77} + 16 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} - 24 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q + 2 * q^5 + q^7 - 6 * q^11 + 7 * q^13 + q^17 - 13 * q^19 + 44 * q^25 + 7 * q^29 - 6 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 + 17 * q^47 + 29 * q^49 - q^53 - 2 * q^55 - 21 * q^59 + 31 * q^61 + 3 * q^65 + 26 * q^67 - 32 * q^71 + 17 * q^73 + 4 * q^77 + 16 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 - 24 * q^95 + 19 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more