LMFDB - Embedded newform 1449.2.h.e.1126.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1449,2,Mod(1126,1449)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1449, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1449.1126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1449 = 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1449.h (of order $2$, degree $1$, 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:	$11.5703232529$
Analytic rank:	$0$
Dimension:	$12$
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} + 17x^{10} + 92x^{8} + 180x^{6} + 92x^{4} + 17x^{2} + 1 $ x^12 + 17x^10 + 92x^8 + 180x^6 + 92x^4 + 17*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 483)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1126.3
Root			$1.77931i$ of defining polynomial
Character	$\chi$	$=$	1449.1126
Dual form			1449.2.h.e.1126.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51820 q^{2} +4.34132 q^{4} +1.21729 q^{5} +(2.34908 - 1.21729i) q^{7} -5.89592 q^{8} +O(q^{10})$	\(q-2.51820 q^{2} +4.34132 q^{4} +1.21729 q^{5} +(2.34908 - 1.21729i) q^{7} -5.89592 q^{8} -3.06538 q^{10} -1.13179i q^{11} -0.518199i q^{13} +(-5.91546 + 3.06538i) q^{14} +6.16445 q^{16} +3.06538 q^{17} +1.13179 q^{19} +5.28466 q^{20} +2.85008i q^{22} +(0.341325 - 4.78367i) q^{23} -3.51820 q^{25} +1.30493i q^{26} +(10.1981 - 5.28466i) q^{28} +2.17687 q^{29} -6.85952i q^{31} -3.73147 q^{32} -7.71925 q^{34} +(2.85952 - 1.48180i) q^{35} -10.1981i q^{37} -2.85008 q^{38} -7.17706 q^{40} -5.00000i q^{41} +6.71726i q^{43} -4.91348i q^{44} +(-0.859523 + 12.0462i) q^{46} +4.21327i q^{47} +(4.03640 - 5.71905i) q^{49} +8.85952 q^{50} -2.24967i q^{52} +5.41447i q^{53} -1.37772i q^{55} +(-13.8500 + 7.17706i) q^{56} -5.48180 q^{58} -0.200848i q^{59} -6.21627 q^{61} +17.2736i q^{62} -2.93232 q^{64} -0.630799i q^{65} +3.65188i q^{67} +13.3078 q^{68} +(-7.20085 + 3.73147i) q^{70} -2.16445 q^{71} +10.2248i q^{73} +25.6809i q^{74} +4.91348 q^{76} +(-1.37772 - 2.65868i) q^{77} -8.59454i q^{79} +7.50394 q^{80} +12.5910i q^{82} -11.6307 q^{83} +3.73147 q^{85} -16.9154i q^{86} +6.67296i q^{88} +5.11366 q^{89} +(-0.630799 - 1.21729i) q^{91} +(1.48180 - 20.7675i) q^{92} -10.6099i q^{94} +1.37772 q^{95} +18.1619 q^{97} +(-10.1645 + 14.4017i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 36 q^{4} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 + 36 * q^4 + 24 * q^8	$ 12 q - 4 q^{2} + 36 q^{4} + 24 q^{8} + 68 q^{16} - 12 q^{23} - 16 q^{25} + 16 q^{29} + 44 q^{32} - 8 q^{35} + 32 q^{46} - 4 q^{49} + 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} - 20 q^{71} + 52 q^{77} - 44 q^{85} + 44 q^{92} - 52 q^{95} - 116 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 + 68 * q^16 - 12 * q^23 - 16 * q^25 + 16 * q^29 + 44 * q^32 - 8 * q^35 + 32 * q^46 - 4 * q^49 + 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 - 20 * q^71 + 52 * q^77 - 44 * q^85 + 44 * q^92 - 52 * q^95 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1449\mathbb{Z}\right)^\times$.

$n$	$442$	$829$	$1289$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−2.51820			−1.78064			−0.890318	−	0.455340i	$-0.849518\pi$
$2$	−2.51820			−1.78064			−0.890318	+	0.455340i	$0.849518\pi$
$3$		0			0
$3$		0			0
$4$	4.34132			2.17066
$5$	1.21729			0.544390			0.272195	−	0.962242i	$-0.412250\pi$
$5$	1.21729			0.544390			0.272195	+	0.962242i	$0.412250\pi$
$6$		0			0
$7$	2.34908	−	1.21729i	0.887871	−	0.460093i
$7$	2.34908	−	1.21729i	0.887871	−	0.460093i
$8$	−5.89592			−2.08452
$9$		0			0
$10$	−3.06538			−0.969360
$11$		−	1.13179i		−	0.341248i	−0.985336	−	0.170624i	$-0.945422\pi$
$11$		−	1.13179i		−	0.341248i	0.985336	−	0.170624i	$-0.0545784\pi$
$12$		0			0
$13$		−	0.518199i		−	0.143722i	−0.997415	−	0.0718612i	$-0.977106\pi$
$13$		−	0.518199i		−	0.143722i	0.997415	−	0.0718612i	$-0.0228939\pi$
$14$	−5.91546	+	3.06538i	−1.58097	+	0.819259i
$15$		0			0
$16$	6.16445			1.54111
$17$	3.06538			0.743465			0.371732	−	0.928340i	$-0.378764\pi$
$17$	3.06538			0.743465			0.371732	+	0.928340i	$0.378764\pi$
$18$		0			0
$19$	1.13179			0.259651			0.129825	−	0.991537i	$-0.458558\pi$
$19$	1.13179			0.259651			0.129825	+	0.991537i	$0.458558\pi$
$20$	5.28466			1.18169
$21$		0			0
$22$			2.85008i			0.607639i
$23$	0.341325	−	4.78367i	0.0711711	−	0.997464i
$23$	0.341325	−	4.78367i	0.0711711	−	0.997464i
$24$		0			0
$25$	−3.51820			−0.703640
$26$			1.30493i			0.255917i
$27$		0			0
$28$	10.1981	−	5.28466i	1.92727	−	0.998707i
$29$	2.17687			0.404235			0.202118	−	0.979361i	$-0.435218\pi$
$29$	2.17687			0.404235			0.202118	+	0.979361i	$0.435218\pi$
$30$		0			0
$31$		−	6.85952i		−	1.23201i	−0.787744	−	0.616003i	$-0.788751\pi$
$31$		−	6.85952i		−	1.23201i	0.787744	−	0.616003i	$-0.211249\pi$
$32$	−3.73147			−0.659637
$33$		0			0
$34$	−7.71925			−1.32384
$35$	2.85952	−	1.48180i	0.483348	−	0.250470i
$36$		0			0
$37$		−	10.1981i		−	1.67656i	−0.545237	−	0.838282i	$-0.683560\pi$
$37$		−	10.1981i		−	1.67656i	0.545237	−	0.838282i	$-0.316440\pi$
$38$	−2.85008			−0.462344
$39$		0			0
$40$	−7.17706			−1.13479
$41$		−	5.00000i		−	0.780869i	−0.920631	−	0.390434i	$-0.872325\pi$
$41$		−	5.00000i		−	0.780869i	0.920631	−	0.390434i	$-0.127675\pi$
$42$		0			0
$43$			6.71726i			1.02437i	0.858874	+	0.512186i	$0.171164\pi$
$43$			6.71726i			1.02437i	−0.858874	+	0.512186i	$0.828836\pi$
$44$		−	4.91348i		−	0.740734i
$45$		0			0
$46$	−0.859523	+	12.0462i	−0.126730	+	1.77612i
$47$			4.21327i			0.614569i	0.951618	+	0.307284i	$0.0994203\pi$
$47$			4.21327i			0.614569i	−0.951618	+	0.307284i	$0.900580\pi$
$48$		0			0
$49$	4.03640	−	5.71905i	0.576628	−	0.817007i
$50$	8.85952			1.25293
$51$		0			0
$52$		−	2.24967i		−	0.311973i
$53$			5.41447i			0.743735i	0.928286	+	0.371867i	$0.121282\pi$
$53$			5.41447i			0.743735i	−0.928286	+	0.371867i	$0.878718\pi$
$54$		0			0
$55$		−	1.37772i		−	0.185772i
$56$	−13.8500	+	7.17706i	−1.85079	+	0.959075i
$57$		0			0
$58$	−5.48180			−0.719796
$59$		−	0.200848i		−	0.0261482i	−0.999915	−	0.0130741i	$-0.995838\pi$
$59$		−	0.200848i		−	0.0261482i	0.999915	−	0.0130741i	$-0.00416173\pi$
$60$		0			0
$61$	−6.21627			−0.795912			−0.397956	−	0.917405i	$-0.630280\pi$
$61$	−6.21627			−0.795912			−0.397956	+	0.917405i	$0.630280\pi$
$62$			17.2736i			2.19375i
$63$		0			0
$64$	−2.93232			−0.366540
$65$		−	0.630799i		−	0.0782410i
$66$		0			0
$67$			3.65188i			0.446148i	0.974802	+	0.223074i	$0.0716091\pi$
$67$			3.65188i			0.446148i	−0.974802	+	0.223074i	$0.928391\pi$
$68$	13.3078			1.61381
$69$		0			0
$70$	−7.20085	+	3.73147i	−0.860666	+	0.445996i
$71$	−2.16445			−0.256873			−0.128437	−	0.991718i	$-0.540996\pi$
$71$	−2.16445			−0.256873			−0.128437	+	0.991718i	$0.540996\pi$
$72$		0			0
$73$			10.2248i			1.19672i	0.801226	+	0.598362i	$0.204182\pi$
$73$			10.2248i			1.19672i	−0.801226	+	0.598362i	$0.795818\pi$
$74$			25.6809i			2.98535i
$75$		0			0
$76$	4.91348			0.563614
$77$	−1.37772	−	2.65868i	−0.157006	−	0.302984i
$78$		0			0
$79$		−	8.59454i		−	0.966961i	−0.875355	−	0.483481i	$-0.839372\pi$
$79$		−	8.59454i		−	0.966961i	0.875355	−	0.483481i	$-0.160628\pi$
$80$	7.50394			0.838966
$81$		0			0
$82$			12.5910i			1.39044i
$83$	−11.6307			−1.27664			−0.638320	−	0.769771i	$-0.720370\pi$
$83$	−11.6307			−1.27664			−0.638320	+	0.769771i	$0.720370\pi$
$84$		0			0
$85$	3.73147			0.404735
$86$		−	16.9154i		−	1.82403i
$87$		0			0
$88$			6.67296i			0.711340i
$89$	5.11366			0.542047			0.271024	−	0.962573i	$-0.412638\pi$
$89$	5.11366			0.542047			0.271024	+	0.962573i	$0.412638\pi$
$90$		0			0
$91$	−0.630799	−	1.21729i	−0.0661257	−	0.127607i
$92$	1.48180	−	20.7675i	0.154488	−	2.16516i
$93$		0			0
$94$		−	10.6099i		−	1.09432i
$95$	1.37772			0.141351
$96$		0			0
$97$	18.1619			1.84406			0.922030	−	0.387119i	$-0.126530\pi$
$97$	18.1619			1.84406			0.922030	+	0.387119i	$0.126530\pi$
$98$	−10.1645	+	14.4017i	−1.02676	+	1.45479i
$99$		0			0
$100$	−15.2736			−1.52736
$101$		−	8.88350i		−	0.883941i	−0.897030	−	0.441971i	$-0.854280\pi$
$101$		−	8.88350i		−	0.883941i	0.897030	−	0.441971i	$-0.145720\pi$
$102$		0			0
$103$	−11.5009			−1.13322			−0.566610	−	0.823986i	$-0.691745\pi$
$103$	−11.5009			−1.13322			−0.566610	+	0.823986i	$0.691745\pi$
$104$			3.05526i			0.299593i
$105$		0			0
$106$		−	13.6347i		−	1.32432i
$107$		−	2.67908i		−	0.258996i	−0.991580	−	0.129498i	$-0.958663\pi$
$107$		−	2.67908i		−	0.258996i	0.991580	−	0.129498i	$-0.0413366\pi$
$108$		0			0
$109$			17.7464i			1.69980i	0.526948	+	0.849898i	$0.323336\pi$
$109$			17.7464i			1.69980i	−0.526948	+	0.849898i	$0.676664\pi$
$110$			3.46938i			0.330792i
$111$		0			0
$112$	14.4808	−	7.50394i	1.36831	−	0.709056i
$113$			2.21928i			0.208772i	0.994537	+	0.104386i	$0.0332878\pi$
$113$			2.21928i			0.208772i	−0.994537	+	0.104386i	$0.966712\pi$
$114$		0			0
$115$	0.415492	−	5.82313i	0.0387448	−	0.543009i
$116$	9.45052			0.877458
$117$		0			0
$118$			0.505775i			0.0465604i
$119$	7.20085	−	3.73147i	0.660101	−	0.342063i
$120$		0			0
$121$	9.71905			0.883550
$122$	15.6538			1.41723
$123$		0			0
$124$		−	29.7794i		−	2.67427i
$125$	−10.3691			−0.927444
$126$		0			0
$127$	−2.73147			−0.242379			−0.121189	−	0.992629i	$-0.538671\pi$
$127$	−2.73147			−0.242379			−0.121189	+	0.992629i	$0.538671\pi$
$128$	14.8471			1.31231
$129$		0			0
$130$			1.58848i			0.139319i
$131$		−	18.7190i		−	1.63549i	−0.575580	−	0.817745i	$-0.695224\pi$
$131$		−	18.7190i		−	1.63549i	0.575580	−	0.817745i	$-0.304776\pi$
$132$		0			0
$133$	2.65868	−	1.37772i	0.230536	−	0.119464i
$134$		−	9.19615i		−	0.794427i
$135$		0			0
$136$	−18.0733			−1.54977
$137$			12.3027i			1.05109i	0.850765	+	0.525547i	$0.176139\pi$
$137$			12.3027i			1.05109i	−0.850765	+	0.525547i	$0.823861\pi$
$138$		0			0
$139$		−	13.7794i		−	1.16876i	−0.811482	−	0.584378i	$-0.801339\pi$
$139$		−	13.7794i		−	1.16876i	0.811482	−	0.584378i	$-0.198661\pi$
$140$	12.4141	−	6.43298i	1.04918	−	0.543686i
$141$		0			0
$142$	5.45052			0.457397
$143$	−0.586493			−0.0490450
$144$		0			0
$145$	2.64989			0.220062
$146$		−	25.7481i		−	2.13093i
$147$		0			0
$148$		−	44.2734i		−	3.63925i
$149$		−	8.46473i		−	0.693458i	−0.937965	−	0.346729i	$-0.887292\pi$
$149$		−	8.46473i		−	0.693458i	0.937965	−	0.346729i	$-0.112708\pi$
$150$		0			0
$151$	17.5786			1.43052			0.715262	−	0.698857i	$-0.246307\pi$
$151$	17.5786			1.43052			0.715262	+	0.698857i	$0.246307\pi$
$152$	−6.67296			−0.541248
$153$		0			0
$154$	3.46938	+	6.69507i	0.279570	+	0.539504i
$155$		−	8.35005i		−	0.670692i
$156$		0			0
$157$	−18.6337			−1.48713			−0.743565	−	0.668664i	$-0.766867\pi$
$157$	−18.6337			−1.48713			−0.743565	+	0.668664i	$0.766867\pi$
$158$			21.6428i			1.72181i
$159$		0			0
$160$	−4.54229			−0.359100
$161$	−5.02133	−	11.6527i	−0.395736	−	0.918364i
$162$		0			0
$163$	7.23725			0.566865			0.283432	−	0.958992i	$-0.408527\pi$
$163$	7.23725			0.566865			0.283432	+	0.958992i	$0.408527\pi$
$164$		−	21.7066i		−	1.69500i
$165$		0			0
$166$	29.2885			2.27323
$167$		−	17.8282i		−	1.37959i	−0.724004	−	0.689795i	$-0.757701\pi$
$167$		−	17.8282i		−	1.37959i	0.724004	−	0.689795i	$-0.242299\pi$
$168$		0			0
$169$	12.7315			0.979344
$170$	−9.39658			−0.720685
$171$		0			0
$172$			29.1618i			2.22357i
$173$		−	20.2248i		−	1.53766i	−0.639450	−	0.768832i	$-0.720838\pi$
$173$		−	20.2248i		−	1.53766i	0.639450	−	0.768832i	$-0.279162\pi$
$174$		0			0
$175$	−8.26455	+	4.28268i	−0.624741	+	0.323740i
$176$		−	6.97688i		−	0.525902i
$177$		0			0
$178$	−12.8772			−0.965188
$179$	10.4141			0.778388			0.389194	−	0.921156i	$-0.372754\pi$
$179$	10.4141			0.778388			0.389194	+	0.921156i	$0.372754\pi$
$180$		0			0
$181$	14.0653			1.04547			0.522734	−	0.852496i	$-0.324912\pi$
$181$	14.0653			1.04547			0.522734	+	0.852496i	$0.324912\pi$
$182$	1.58848	+	3.06538i	0.117746	+	0.227221i
$183$		0			0
$184$	−2.01242	+	28.2041i	−0.148358	+	2.07924i
$185$		−	12.4141i		−	0.912704i
$186$		0			0
$187$		−	3.46938i		−	0.253706i
$188$			18.2912i			1.33402i
$189$		0			0
$190$	−3.46938			−0.251695
$191$			12.3319i			0.892306i	0.894957	+	0.446153i	$0.147206\pi$
$191$			12.3319i			0.892306i	−0.894957	+	0.446153i	$0.852794\pi$
$192$		0			0
$193$	−3.17687			−0.228676			−0.114338	−	0.993442i	$-0.536475\pi$
$193$	−3.17687			−0.228676			−0.114338	+	0.993442i	$0.536475\pi$
$194$	−45.7352			−3.28360
$195$		0			0
$196$	17.5233	−	24.8282i	1.25167	−	1.77345i
$197$	−16.5661			−1.18029			−0.590145	−	0.807298i	$-0.700929\pi$
$197$	−16.5661			−1.18029			−0.590145	+	0.807298i	$0.700929\pi$
$198$		0			0
$199$	−9.28165			−0.657959			−0.328980	−	0.944337i	$-0.606705\pi$
$199$	−9.28165			−0.657959			−0.328980	+	0.944337i	$0.606705\pi$
$200$	20.7430			1.46675
$201$		0			0
$202$			22.3704i			1.57398i
$203$	5.11366	−	2.64989i	0.358909	−	0.185986i
$204$		0			0
$205$		−	6.08646i		−	0.425097i
$206$	28.9616			2.01785
$207$		0			0
$208$		−	3.19441i		−	0.221493i
$209$		−	1.28095i		−	0.0886054i
$210$		0			0
$211$	7.96360			0.548237			0.274119	−	0.961696i	$-0.411614\pi$
$211$	7.96360			0.548237			0.274119	+	0.961696i	$0.411614\pi$
$212$			23.5060i			1.61440i
$213$		0			0
$214$			6.74645i			0.461178i
$215$			8.17687i			0.557658i
$216$		0			0
$217$	−8.35005	−	16.1136i	−0.566838	−	1.09386i
$218$		−	44.6889i		−	3.02672i
$219$		0			0
$220$		−	5.98114i		−	0.403248i
$221$		−	1.58848i		−	0.106853i
$222$		0			0
$223$		−	21.0968i		−	1.41274i	−0.707841	−	0.706372i	$-0.750331\pi$
$223$		−	21.0968i		−	1.41274i	0.707841	−	0.706372i	$-0.249669\pi$
$224$	−8.76554	+	4.54229i	−0.585672	+	0.303495i
$225$		0			0
$226$		−	5.58858i		−	0.371747i
$227$	24.8791			1.65129			0.825643	−	0.564193i	$-0.190812\pi$
$227$	24.8791			1.65129			0.825643	+	0.564193i	$0.190812\pi$
$228$		0			0
$229$	19.5090			1.28919			0.644595	−	0.764524i	$-0.277026\pi$
$229$	19.5090			1.28919			0.644595	+	0.764524i	$0.277026\pi$
$230$	−1.04629	+	14.6638i	−0.0689904	+	0.966902i
$231$		0			0
$232$	−12.8347			−0.842638
$233$	8.34132			0.546458			0.273229	−	0.961949i	$-0.411908\pi$
$233$	8.34132			0.546458			0.273229	+	0.961949i	$0.411908\pi$
$234$		0			0
$235$			5.12878i			0.334565i
$236$		−	0.871947i		−	0.0567589i
$237$		0			0
$238$	−18.1332	+	9.39658i	−1.17540	+	0.609090i
$239$	21.3777			1.38281			0.691405	−	0.722467i	$-0.256992\pi$
$239$	21.3777			1.38281			0.691405	+	0.722467i	$0.256992\pi$
$240$		0			0
$241$	−8.86616			−0.571120			−0.285560	−	0.958361i	$-0.592180\pi$
$241$	−8.86616			−0.571120			−0.285560	+	0.958361i	$0.592180\pi$
$242$	−24.4745			−1.57328
$243$		0			0
$244$	−26.9868			−1.72766
$245$	4.91348	−	6.96175i	0.313911	−	0.444770i
$246$		0			0
$247$		−	0.586493i		−	0.0373177i
$248$			40.4432i			2.56815i
$249$		0			0
$250$	26.1116			1.65144
$251$	−13.0925			−0.826393			−0.413196	−	0.910642i	$-0.635588\pi$
$251$	−13.0925			−0.826393			−0.413196	+	0.910642i	$0.635588\pi$
$252$		0			0
$253$	−5.41412	−	0.386309i	−0.340383	−	0.0242870i
$254$	6.87838			0.431588
$255$		0			0
$256$	−31.5233			−1.97021
$257$			13.9075i			0.867524i	0.901027	+	0.433762i	$0.142814\pi$
$257$			13.9075i			0.867524i	−0.901027	+	0.433762i	$0.857186\pi$
$258$		0			0
$259$	−12.4141	−	23.9563i	−0.771376	−	1.48857i
$260$		−	2.73851i		−	0.169835i
$261$		0			0
$262$			47.1383i			2.91221i
$263$			23.7917i			1.46706i	0.679659	+	0.733528i	$0.262128\pi$
$263$			23.7917i			1.46706i	−0.679659	+	0.733528i	$0.737872\pi$
$264$		0			0
$265$			6.59099i			0.404882i
$266$	−6.69507	+	3.46938i	−0.410501	+	0.212721i
$267$		0			0
$268$			15.8540i			0.968436i
$269$			5.76275i			0.351361i	0.984447	+	0.175681i	$0.0562126\pi$
$269$			5.76275i			0.351361i	−0.984447	+	0.175681i	$0.943787\pi$
$270$		0			0
$271$		−	11.5422i		−	0.701137i	−0.936537	−	0.350569i	$-0.885988\pi$
$271$		−	11.5422i		−	0.701137i	0.936537	−	0.350569i	$-0.114012\pi$
$272$	18.8964			1.14576
$273$		0			0
$274$		−	30.9807i		−	1.87161i
$275$			3.98187i			0.240116i
$276$		0			0
$277$	24.5713			1.47634			0.738172	−	0.674613i	$-0.235689\pi$
$277$	24.5713			1.47634			0.738172	+	0.674613i	$0.235689\pi$
$278$			34.6993i			2.08113i
$279$		0			0
$280$	−16.8595	+	8.73658i	−1.00755	+	0.522111i
$281$		−	16.7001i		−	0.996244i	−0.867107	−	0.498122i	$-0.834023\pi$
$281$		−	16.7001i		−	0.996244i	0.867107	−	0.498122i	$-0.165977\pi$
$282$		0			0
$283$	12.2172			0.726239			0.363120	−	0.931743i	$-0.381712\pi$
$283$	12.2172			0.726239			0.363120	+	0.931743i	$0.381712\pi$
$284$	−9.39658			−0.557585
$285$		0			0
$286$	1.47691			0.0873313
$287$	−6.08646	−	11.7454i	−0.359273	−	0.693310i
$288$		0			0
$289$	−7.60342			−0.447260
$290$	−6.67296			−0.391849
$291$		0			0
$292$			44.3893i			2.59769i
$293$	−22.0582			−1.28866			−0.644328	−	0.764749i	$-0.722863\pi$
$293$	−22.0582			−1.28866			−0.644328	+	0.764749i	$0.722863\pi$
$294$		0			0
$295$		−	0.244491i		−	0.0142348i
$296$			60.1274i			3.49484i
$297$		0			0
$298$			21.3159i			1.23480i
$299$	−2.47889	−	0.176874i	−0.143358	−	0.0102289i
$300$		0			0
$301$	8.17687	+	15.7794i	0.471307	+	0.909511i
$302$	−44.2663			−2.54724
$303$		0			0
$304$	6.97688			0.400151
$305$	−7.56702			−0.433286
$306$		0			0
$307$			20.0167i			1.14241i	0.820807	+	0.571206i	$0.193524\pi$
$307$			20.0167i			1.14241i	−0.820807	+	0.571206i	$0.806476\pi$
$308$	−5.98114	−	11.5422i	−0.340807	−	0.657676i
$309$		0			0
$310$			21.0271i			1.19426i
$311$			15.7430i			0.892705i	0.894857	+	0.446352i	$0.147277\pi$
$311$			15.7430i			0.892705i	−0.894857	+	0.446352i	$0.852723\pi$
$312$		0			0
$313$	−8.46473			−0.478455			−0.239227	−	0.970964i	$-0.576894\pi$
$313$	−8.46473			−0.478455			−0.239227	+	0.970964i	$0.576894\pi$
$314$	46.9233			2.64804
$315$		0			0
$316$		−	37.3117i		−	2.09895i
$317$	−28.1083			−1.57872			−0.789360	−	0.613930i	$-0.789588\pi$
$317$	−28.1083			−1.57872			−0.789360	+	0.613930i	$0.789588\pi$
$318$		0			0
$319$		−	2.46377i		−	0.137945i
$320$	−3.56949			−0.199541
$321$		0			0
$322$	12.6447	+	29.3439i	0.704661	+	1.63527i
$323$	3.46938			0.193041
$324$		0			0
$325$			1.82313i			0.101129i
$326$	−18.2248			−1.00938
$327$		0			0
$328$			29.4796i			1.62774i
$329$	5.12878	+	9.89733i	0.282759	+	0.545658i
$330$		0			0
$331$	−9.22482			−0.507042			−0.253521	−	0.967330i	$-0.581589\pi$
$331$	−9.22482			−0.507042			−0.253521	+	0.967330i	$0.581589\pi$
$332$	−50.4928			−2.77115
$333$		0			0
$334$			44.8950i			2.45655i
$335$			4.44540i			0.242878i
$336$		0			0
$337$			14.0794i			0.766953i	0.923551	+	0.383476i	$0.125273\pi$
$337$			14.0794i			0.766953i	−0.923551	+	0.383476i	$0.874727\pi$
$338$	−32.0604			−1.74385
$339$		0			0
$340$	16.1995			0.878543
$341$	−7.76355			−0.420420
$342$		0			0
$343$	2.52009	−	18.3480i	0.136072	−	0.990699i
$344$		−	39.6044i		−	2.13533i
$345$		0			0
$346$			50.9301i			2.73802i
$347$	4.50578			0.241883			0.120941	−	0.992660i	$-0.461409\pi$
$347$	4.50578			0.241883			0.120941	+	0.992660i	$0.461409\pi$
$348$		0			0
$349$		−	11.8522i		−	0.634434i	−0.948353	−	0.317217i	$-0.897252\pi$
$349$		−	11.8522i		−	0.634434i	0.948353	−	0.317217i	$-0.102748\pi$
$350$	20.8118	−	10.7846i	1.11244	−	0.576463i
$351$		0			0
$352$			4.22325i			0.225100i
$353$			24.0167i			1.27828i	0.769091	+	0.639139i	$0.220709\pi$
$353$			24.0167i			1.27828i	−0.769091	+	0.639139i	$0.779291\pi$
$354$		0			0
$355$	−2.63477			−0.139839
$356$	22.2001			1.17660
$357$		0			0
$358$	−26.2248			−1.38602
$359$			1.21729i			0.0642462i	0.999484	+	0.0321231i	$0.0102269\pi$
$359$			1.21729i			0.0642462i	−0.999484	+	0.0321231i	$0.989773\pi$
$360$		0			0
$361$	−17.7190			−0.932581
$362$	−35.4193			−1.86160
$363$		0			0
$364$	−2.73851	−	5.28466i	−0.143537	−	0.276992i
$365$			12.4466i			0.651485i
$366$		0			0
$367$	10.7434			0.560803			0.280401	−	0.959883i	$-0.409532\pi$
$367$	10.7434			0.560803			0.280401	+	0.959883i	$0.409532\pi$
$368$	2.10408	−	29.4887i	0.109683	−	1.53720i
$369$		0			0
$370$			31.2612i			1.62519i
$371$	6.59099	+	12.7190i	0.342187	+	0.660340i
$372$		0			0
$373$			28.3308i			1.46691i	0.679735	+	0.733457i	$0.262095\pi$
$373$			28.3308i			1.46691i	−0.679735	+	0.733457i	$0.737905\pi$
$374$			8.73658i			0.451758i
$375$		0			0
$376$		−	24.8411i		−	1.28108i
$377$		−	1.12805i		−	0.0580977i
$378$		0			0
$379$			4.86917i			0.250112i	0.992150	+	0.125056i	$0.0399111\pi$
$379$			4.86917i			0.250112i	−0.992150	+	0.125056i	$0.960089\pi$
$380$	5.98114			0.306826
$381$		0			0
$382$		−	31.0542i		−	1.58887i
$383$	34.6326			1.76964			0.884822	−	0.465930i	$-0.154280\pi$
$383$	34.6326			1.76964			0.884822	+	0.465930i	$0.154280\pi$
$384$		0			0
$385$	−1.67709	−	3.23639i	−0.0854725	−	0.164941i
$386$	8.00000			0.407189
$387$		0			0
$388$	78.8466			4.00283
$389$			11.6307i			0.589702i	0.955543	+	0.294851i	$0.0952700\pi$
$389$			11.6307i			0.589702i	−0.955543	+	0.294851i	$0.904730\pi$
$390$		0			0
$391$	1.04629	−	14.6638i	0.0529132	−	0.741580i
$392$	−23.7983	+	33.7190i	−1.20199	+	1.70307i
$393$		0			0
$394$	41.7168			2.10166
$395$		−	10.4621i		−	0.526404i
$396$		0			0
$397$			27.5109i			1.38073i	0.723460	+	0.690366i	$0.242550\pi$
$397$			27.5109i			1.38073i	−0.723460	+	0.690366i	$0.757450\pi$
$398$	23.3731			1.17159
$399$		0			0
$400$	−21.6878			−1.08439
$401$		−	15.1679i		−	0.757450i	−0.925509	−	0.378725i	$-0.876363\pi$
$401$		−	15.1679i		−	0.757450i	0.925509	−	0.378725i	$-0.123637\pi$
$402$		0			0
$403$	−3.55460			−0.177067
$404$		−	38.5661i		−	1.91874i
$405$		0			0
$406$	−12.8772	+	6.67296i	−0.639085	+	0.331173i
$407$	−11.5422			−0.572124
$408$		0			0
$409$		−	23.2861i		−	1.15142i	−0.817653	−	0.575711i	$-0.804725\pi$
$409$		−	23.2861i		−	1.15142i	0.817653	−	0.575711i	$-0.195275\pi$
$410$			15.3269i			0.756943i
$411$		0			0
$412$	−49.9293			−2.45984
$413$	−0.244491	−	0.471809i	−0.0120306	−	0.0232162i
$414$		0			0
$415$	−14.1580			−0.694990
$416$			1.93364i			0.0948046i
$417$		0			0
$418$			3.22569i			0.157774i
$419$	5.31385			0.259598			0.129799	−	0.991540i	$-0.458567\pi$
$419$	5.31385			0.259598			0.129799	+	0.991540i	$0.458567\pi$
$420$		0			0
$421$		−	16.1136i		−	0.785329i	−0.919682	−	0.392664i	$-0.871553\pi$
$421$		−	16.1136i		−	0.785329i	0.919682	−	0.392664i	$-0.128447\pi$
$422$	−20.0539			−0.976210
$423$		0			0
$424$		−	31.9233i		−	1.55033i
$425$	−10.7846			−0.523132
$426$		0			0
$427$	−14.6025	+	7.56702i	−0.706667	+	0.366194i
$428$		−	11.6307i		−	0.562193i
$429$		0			0
$430$		−	20.5910i		−	0.992986i
$431$		−	11.4274i		−	0.550441i	−0.961381	−	0.275220i	$-0.911249\pi$
$431$		−	11.4274i		−	0.550441i	0.961381	−	0.275220i	$-0.0887508\pi$
$432$		0			0
$433$	13.5351			0.650458			0.325229	−	0.945635i	$-0.394559\pi$
$433$	13.5351			0.650458			0.325229	+	0.945635i	$0.394559\pi$
$434$	21.0271	+	40.5772i	1.00933	+	1.94777i
$435$		0			0
$436$			77.0428i			3.68968i
$437$	0.386309	−	5.41412i	0.0184796	−	0.258992i
$438$		0			0
$439$		−	36.0415i		−	1.72017i	−0.510153	−	0.860084i	$-0.670411\pi$
$439$		−	36.0415i		−	1.72017i	0.510153	−	0.860084i	$-0.329589\pi$
$440$			8.12294i			0.387246i
$441$		0			0
$442$			4.00010i			0.190266i
$443$	32.8034			1.55854			0.779268	−	0.626691i	$-0.215591\pi$
$443$	32.8034			1.55854			0.779268	+	0.626691i	$0.215591\pi$
$444$		0			0
$445$	6.22482			0.295085
$446$			53.1259i			2.51558i
$447$		0			0
$448$	−6.88826	+	3.56949i	−0.325440	+	0.168643i
$449$	20.7430			0.978924			0.489462	−	0.872025i	$-0.337193\pi$
$449$	20.7430			0.978924			0.489462	+	0.872025i	$0.337193\pi$
$450$		0			0
$451$	−5.65896			−0.266470
$452$			9.63461i			0.453174i
$453$		0			0
$454$	−62.6506			−2.94034
$455$	−0.767868	−	1.48180i	−0.0359982	−	0.0694679i
$456$		0			0
$457$		−	3.13887i		−	0.146830i	−0.997301	−	0.0734152i	$-0.976610\pi$
$457$		−	3.13887i		−	0.146830i	0.997301	−	0.0734152i	$-0.0233898\pi$
$458$	−49.1275			−2.29558
$459$		0			0
$460$	1.80379	−	25.2801i	0.0841019	−	1.17869i
$461$			39.0094i			1.81685i	0.418051	+	0.908423i	$0.362713\pi$
$461$			39.0094i			1.81685i	−0.418051	+	0.908423i	$0.637287\pi$
$462$		0			0
$463$	−20.2299			−0.940165			−0.470082	−	0.882623i	$-0.655776\pi$
$463$	−20.2299			−0.940165			−0.470082	+	0.882623i	$0.655776\pi$
$464$	13.4192			0.622972
$465$		0			0
$466$	−21.0051			−0.973043
$467$	−12.4617			−0.576660			−0.288330	−	0.957531i	$-0.593100\pi$
$467$	−12.4617			−0.576660			−0.288330	+	0.957531i	$0.593100\pi$
$468$		0			0
$469$	4.44540	+	8.57857i	0.205270	+	0.396122i
$470$		−	12.9153i		−	0.595738i
$471$		0			0
$472$			1.18418i			0.0545065i
$473$	7.60254			0.349565
$474$		0			0
$475$	−3.98187			−0.182701
$476$	31.2612	−	16.1995i	1.43286	−	0.742504i
$477$		0			0
$478$	−53.8334			−2.46228
$479$	−25.2363			−1.15307			−0.576537	−	0.817071i	$-0.695596\pi$
$479$	−25.2363			−1.15307			−0.576537	+	0.817071i	$0.695596\pi$
$480$		0			0
$481$	−5.28466			−0.240960
$482$	22.3268			1.01696
$483$		0			0
$484$	42.1935			1.91789
$485$	22.1083			1.00389
$486$		0			0
$487$	−19.0531			−0.863377			−0.431688	−	0.902023i	$-0.642082\pi$
$487$	−19.0531			−0.863377			−0.431688	+	0.902023i	$0.642082\pi$
$488$	36.6506			1.65910
$489$		0			0
$490$	−12.3731	+	17.5311i	−0.558960	+	0.791973i
$491$	12.8471			0.579782			0.289891	−	0.957060i	$-0.406381\pi$
$491$	12.8471			0.579782			0.289891	+	0.957060i	$0.406381\pi$
$492$		0			0
$493$	6.67296			0.300535
$494$			1.47691i			0.0664492i
$495$		0			0
$496$		−	42.2852i		−	1.89866i
$497$	−5.08448	+	2.63477i	−0.228070	+	0.118186i
$498$		0			0
$499$	−8.62228			−0.385986			−0.192993	−	0.981200i	$-0.561819\pi$
$499$	−8.62228			−0.385986			−0.192993	+	0.981200i	$0.561819\pi$
$500$	−45.0158			−2.01317
$501$		0			0
$502$	32.9696			1.47150
$503$	3.30988			0.147580			0.0737900	−	0.997274i	$-0.476491\pi$
$503$	3.30988			0.147580			0.0737900	+	0.997274i	$0.476491\pi$
$504$		0			0
$505$		−	10.8138i		−	0.481208i
$506$	13.6338	+	0.972802i	0.606098	+	0.0432463i
$507$		0			0
$508$	−11.8582			−0.526122
$509$			8.92077i			0.395406i	0.980262	+	0.197703i	$0.0633482\pi$
$509$			8.92077i			0.395406i	−0.980262	+	0.197703i	$0.936652\pi$
$510$		0			0
$511$	12.4466	+	24.0190i	0.550605	+	1.06254i
$512$	49.6878			2.19591
$513$		0			0
$514$		−	35.0218i		−	1.54474i
$515$	−14.0000			−0.616914
$516$		0			0
$517$	4.76855			0.209720
$518$	31.2612	+	60.3267i	1.37354	+	2.65060i
$519$		0			0
$520$			3.71914i			0.163095i
$521$	42.6255			1.86746			0.933729	−	0.357980i	$-0.116535\pi$
$521$	42.6255			1.86746			0.933729	+	0.357980i	$0.116535\pi$
$522$		0			0
$523$	−20.5553			−0.898819			−0.449410	−	0.893326i	$-0.648366\pi$
$523$	−20.5553			−0.898819			−0.449410	+	0.893326i	$0.648366\pi$
$524$		−	81.2655i		−	3.55010i
$525$		0			0
$526$		−	59.9121i		−	2.61229i
$527$		−	21.0271i		−	0.915954i
$528$		0			0
$529$	−22.7670	−	3.26557i	−0.989869	−	0.141981i
$530$		−	16.5974i		−	0.720946i
$531$		0			0
$532$	11.5422	−	5.98114i	0.500417	−	0.259315i
$533$	−2.59099			−0.112228
$534$		0			0
$535$		−	3.26122i		−	0.140995i
$536$		−	21.5312i		−	0.930005i
$537$		0			0
$538$		−	14.5118i		−	0.625646i
$539$	−6.47277	−	4.56836i	−0.278802	−	0.196773i
$540$		0			0
$541$	5.98027			0.257112			0.128556	−	0.991702i	$-0.458966\pi$
$541$	5.98027			0.257112			0.128556	+	0.991702i	$0.458966\pi$
$542$			29.0655i			1.24847i
$543$		0			0
$544$	−11.4384			−0.490417
$545$			21.6025i			0.925351i
$546$		0			0
$547$	4.06037			0.173609			0.0868045	−	0.996225i	$-0.472334\pi$
$547$	4.06037			0.173609			0.0868045	+	0.996225i	$0.472334\pi$
$548$			53.4102i			2.28157i
$549$		0			0
$550$		−	10.0271i		−	0.427559i
$551$	2.46377			0.104960
$552$		0			0
$553$	−10.4621	−	20.1893i	−0.444892	−	0.858536i
$554$	−61.8753			−2.62883
$555$		0			0
$556$		−	59.8209i		−	2.53697i
$557$		−	2.49295i		−	0.105630i	−0.998604	−	0.0528149i	$-0.983181\pi$
$557$		−	2.49295i		−	0.105630i	0.998604	−	0.0528149i	$-0.0168193\pi$
$558$		0			0
$559$	3.48088			0.147225
$560$	17.6274	−	9.13449i	0.744893	−	0.386003i
$561$		0			0
$562$			42.0542i			1.77395i
$563$	0.846107			0.0356592			0.0178296	−	0.999841i	$-0.494324\pi$
$563$	0.846107			0.0356592			0.0178296	+	0.999841i	$0.494324\pi$
$564$		0			0
$565$			2.70151i			0.113653i
$566$	−30.7654			−1.29317
$567$		0			0
$568$	12.7614			0.535458
$569$		−	40.2916i		−	1.68911i	−0.535469	−	0.844555i	$-0.679865\pi$
$569$		−	40.2916i		−	1.68911i	0.535469	−	0.844555i	$-0.320135\pi$
$570$		0			0
$571$		−	38.1275i		−	1.59559i	−0.602930	−	0.797794i	$-0.706000\pi$
$571$		−	38.1275i		−	1.59559i	0.602930	−	0.797794i	$-0.294000\pi$
$572$	−2.54616			−0.106460
$573$		0			0
$574$	15.3269	+	29.5773i	0.639733	+	1.23453i
$575$	−1.20085	+	16.8299i	−0.0500788	+	0.701855i
$576$		0			0
$577$			23.7918i			0.990467i	0.868760	+	0.495234i	$0.164918\pi$
$577$			23.7918i			0.990467i	−0.868760	+	0.495234i	$0.835082\pi$
$578$	19.1469			0.796407
$579$		0			0
$580$	11.5040			0.477679
$581$	−27.3216	+	14.1580i	−1.13349	+	0.587373i
$582$		0			0
$583$	6.12805			0.253798
$584$		−	60.2847i		−	2.49460i
$585$		0			0
$586$	55.5470			2.29463
$587$			16.3049i			0.672976i	0.941688	+	0.336488i	$0.109239\pi$
$587$			16.3049i			0.672976i	−0.941688	+	0.336488i	$0.890761\pi$
$588$		0			0
$589$		−	7.76355i		−	0.319892i
$590$			0.615677i			0.0253470i
$591$		0			0
$592$		−	62.8659i		−	2.58377i
$593$			3.57346i			0.146744i	0.997305	+	0.0733721i	$0.0233761\pi$
$593$			3.57346i			0.146744i	−0.997305	+	0.0733721i	$0.976624\pi$
$594$		0			0
$595$	8.76554	−	4.54229i	0.359352	−	0.186216i
$596$		−	36.7481i		−	1.50526i
$597$		0			0
$598$	6.24234	+	0.445404i	0.255268	+	0.0182139i
$599$	16.3100			0.666410			0.333205	−	0.942854i	$-0.391870\pi$
$599$	16.3100			0.666410			0.333205	+	0.942854i	$0.391870\pi$
$600$		0			0
$601$			21.8771i			0.892384i	0.894937	+	0.446192i	$0.147220\pi$
$601$			21.8771i			0.892384i	−0.894937	+	0.446192i	$0.852780\pi$
$602$	−20.5910	−	39.7357i	−0.839226	−	1.61951i
$603$		0			0
$604$	76.3143			3.10518
$605$	11.8309			0.480995
$606$		0			0
$607$		−	17.8355i		−	0.723923i	−0.932193	−	0.361961i	$-0.882107\pi$
$607$		−	17.8355i		−	0.723923i	0.932193	−	0.361961i	$-0.117893\pi$
$608$	−4.22325			−0.171275
$609$		0			0
$610$	19.0553			0.771525
$611$	2.18331			0.0883273
$612$		0			0
$613$			28.6488i			1.15711i	0.815642	+	0.578557i	$0.196384\pi$
$613$			28.6488i			1.15711i	−0.815642	+	0.578557i	$0.803616\pi$
$614$		−	50.4059i		−	2.03422i
$615$		0			0
$616$	8.12294	+	15.6753i	0.327283	+	0.631577i
$617$			30.6387i			1.23347i	0.787171	+	0.616734i	$0.211545\pi$
$617$			30.6387i			1.23347i	−0.787171	+	0.616734i	$0.788455\pi$
$618$		0			0
$619$	−27.1135			−1.08979			−0.544893	−	0.838506i	$-0.683430\pi$
$619$	−27.1135			−1.08979			−0.544893	+	0.838506i	$0.683430\pi$
$620$		−	36.2503i		−	1.45585i
$621$		0			0
$622$		−	39.6441i		−	1.58958i
$623$	12.0124	−	6.22482i	0.481268	−	0.249392i
$624$		0			0
$625$	4.96872			0.198749
$626$	21.3159			0.851954
$627$		0			0
$628$	−80.8949			−3.22806
$629$		−	31.2612i		−	1.24647i
$630$		0			0
$631$			39.5904i			1.57607i	0.615631	+	0.788034i	$0.288901\pi$
$631$			39.5904i			1.57607i	−0.615631	+	0.788034i	$0.711099\pi$
$632$			50.6727i			2.01565i
$633$		0			0
$634$	70.7823			2.81113
$635$	−3.32500			−0.131949
$636$		0			0
$637$	−2.96360	−	2.09166i	−0.117422	−	0.0828744i
$638$			6.20426i			0.245629i
$639$		0			0
$640$	18.0733			0.714409
$641$			27.2725i			1.07720i	0.842562	+	0.538600i	$0.181047\pi$
$641$			27.2725i			1.07720i	−0.842562	+	0.538600i	$0.818953\pi$
$642$		0			0
$643$	32.3127			1.27429			0.637144	−	0.770745i	$-0.280116\pi$
$643$	32.3127			1.27429			0.637144	+	0.770745i	$0.280116\pi$
$644$	−21.7992	−	50.5883i	−0.859009	−	1.99346i
$645$		0			0
$646$	−8.73658			−0.343736
$647$		−	1.89168i		−	0.0743696i	−0.999308	−	0.0371848i	$-0.988161\pi$
$647$		−	1.89168i		−	0.0743696i	0.999308	−	0.0371848i	$-0.0118390\pi$
$648$		0			0
$649$	−0.227318			−0.00892302
$650$		−	4.59099i		−	0.180074i
$651$		0			0
$652$	31.4192			1.23047
$653$	−39.2903			−1.53755			−0.768774	−	0.639520i	$-0.779133\pi$
$653$	−39.2903			−1.53755			−0.768774	+	0.639520i	$0.779133\pi$
$654$		0			0
$655$		−	22.7866i		−	0.890344i
$656$		−	30.8223i		−	1.20341i
$657$		0			0
$658$	−12.9153	−	24.9234i	−0.503491	−	0.971617i
$659$		−	22.8600i		−	0.890501i	−0.895406	−	0.445251i	$-0.853115\pi$
$659$		−	22.8600i		−	0.890501i	0.895406	−	0.445251i	$-0.146885\pi$
$660$		0			0
$661$	−46.0209			−1.79001			−0.895003	−	0.446060i	$-0.852827\pi$
$661$	−46.0209			−1.79001			−0.895003	+	0.446060i	$0.852827\pi$
$662$	23.2299			0.902857
$663$		0			0
$664$	68.5739			2.66118
$665$	3.23639	−	1.67709i	0.125502	−	0.0650348i
$666$		0			0
$667$	0.743021	−	10.4134i	0.0287699	−	0.403210i
$668$		−	77.3982i		−	2.99463i
$669$		0			0
$670$		−	11.1944i		−	0.432478i
$671$			7.03552i			0.271603i
$672$		0			0
$673$	−11.6347			−0.448485			−0.224242	−	0.974533i	$-0.571991\pi$
$673$	−11.6347			−0.448485			−0.224242	+	0.974533i	$0.571991\pi$
$674$		−	35.4547i		−	1.36566i
$675$		0			0
$676$	55.2714			2.12582
$677$	36.8519			1.41633			0.708166	−	0.706046i	$-0.249523\pi$
$677$	36.8519			1.41633			0.708166	+	0.706046i	$0.249523\pi$
$678$		0			0
$679$	42.6638	−	22.1083i	1.63729	−	0.848439i
$680$	−22.0005			−0.843679
$681$		0			0
$682$	19.5502			0.748615
$683$	20.6034			0.788368			0.394184	−	0.919032i	$-0.371027\pi$
$683$	20.6034			0.788368			0.394184	+	0.919032i	$0.371027\pi$
$684$		0			0
$685$			14.9760i			0.572205i
$686$	−6.34608	+	46.2039i	−0.242294	+	1.76407i
$687$		0			0
$688$			41.4082i			1.57867i
$689$	2.80577			0.106891
$690$		0			0
$691$			27.9314i			1.06256i	0.847196	+	0.531281i	$0.178289\pi$
$691$			27.9314i			1.06256i	−0.847196	+	0.531281i	$0.821711\pi$
$692$		−	87.8025i		−	3.33775i
$693$		0			0
$694$	−11.3464			−0.430705
$695$		−	16.7736i		−	0.636258i
$696$		0			0
$697$		−	15.3269i		−	0.580549i
$698$			29.8462i			1.12970i
$699$		0			0
$700$	−35.8791	+	18.5925i	−1.35610	+	0.702730i
$701$			45.7180i			1.72675i	0.504566	+	0.863373i	$0.331653\pi$
$701$			45.7180i			1.72675i	−0.504566	+	0.863373i	$0.668347\pi$
$702$		0			0
$703$		−	11.5422i		−	0.435321i
$704$			3.31877i			0.125081i
$705$		0			0
$706$		−	60.4787i		−	2.27615i
$707$	−10.8138	−	20.8681i	−0.406695	−	0.784825i
$708$		0			0
$709$		−	15.4536i		−	0.580373i	−0.956970	−	0.290186i	$-0.906283\pi$
$709$		−	15.4536i		−	0.580373i	0.956970	−	0.290186i	$-0.0937173\pi$
$710$	6.63487			0.249002
$711$		0			0
$712$	−30.1497			−1.12991
$713$	−32.8137	−	2.34132i	−1.22888	−	0.0876833i
$714$		0			0
$715$	−0.713934			−0.0266996
$716$	45.2111			1.68962
$717$		0			0
$718$		−	3.06538i		−	0.114399i
$719$		−	23.3820i		−	0.872000i	−0.899947	−	0.436000i	$-0.856395\pi$
$719$		−	23.3820i		−	0.872000i	0.899947	−	0.436000i	$-0.143605\pi$
$720$		0			0
$721$	−27.0167	+	14.0000i	−1.00615	+	0.521387i
$722$	44.6201			1.66059
$723$		0			0
$724$	61.0621			2.26936
$725$	−7.65868			−0.284436
$726$		0			0
$727$	0.447787			0.0166075			0.00830376	−	0.999966i	$-0.497357\pi$
$727$	0.447787			0.0166075			0.00830376	+	0.999966i	$0.497357\pi$
$728$	3.71914	+	7.17706i	0.137841	+	0.266000i
$729$		0			0
$730$		−	31.3430i		−	1.16006i
$731$			20.5910i			0.761585i
$732$		0			0
$733$	−19.9959			−0.738566			−0.369283	−	0.929317i	$-0.620397\pi$
$733$	−19.9959			−0.738566			−0.369283	+	0.929317i	$0.620397\pi$
$734$	−27.0541			−0.998585
$735$		0			0
$736$	−1.27364	+	17.8501i	−0.0469471	+	0.657964i
$737$	4.13317			0.152247
$738$		0			0
$739$	−18.8449			−0.693221			−0.346610	−	0.938009i	$-0.612667\pi$
$739$	−18.8449			−0.693221			−0.346610	+	0.938009i	$0.612667\pi$
$740$		−	53.8937i		−	1.98117i
$741$		0			0
$742$	−16.5974	−	32.0291i	−0.609311	−	1.17582i
$743$		−	4.81285i		−	0.176566i	−0.996095	−	0.0882832i	$-0.971862\pi$
$743$		−	4.81285i		−	0.176566i	0.996095	−	0.0882832i	$-0.0281381\pi$
$744$		0			0
$745$		−	10.3041i		−	0.377511i
$746$		−	71.3427i		−	2.61204i
$747$		0			0
$748$		−	15.0617i		−	0.550710i
$749$	−3.26122	−	6.29338i	−0.119162	−	0.229955i
$750$		0			0
$751$			40.5772i			1.48068i	0.672230	+	0.740342i	$0.265337\pi$
$751$			40.5772i			1.48068i	−0.672230	+	0.740342i	$0.734663\pi$
$752$			25.9725i			0.947120i
$753$		0			0
$754$			2.84066i			0.103451i
$755$	21.3983			0.778763
$756$		0			0
$757$			39.0471i			1.41919i	0.704609	+	0.709596i	$0.251123\pi$
$757$			39.0471i			1.41919i	−0.704609	+	0.709596i	$0.748877\pi$
$758$		−	12.2615i		−	0.445359i
$759$		0			0
$760$	−8.12294			−0.294650
$761$			40.8959i			1.48248i	0.671242	+	0.741238i	$0.265761\pi$
$761$			40.8959i			1.48248i	−0.671242	+	0.741238i	$0.734239\pi$
$762$		0			0
$763$	21.6025	+	41.6878i	0.782065	+	1.50920i
$764$			53.5369i			1.93690i
$765$		0			0
$766$	−87.2118			−3.15109
$767$	−0.104079			−0.00375808
$768$		0			0
$769$	28.8730			1.04119			0.520594	−	0.853804i	$-0.325711\pi$
$769$	28.8730			1.04119			0.520594	+	0.853804i	$0.325711\pi$
$770$	4.22325	+	8.14986i	0.152195	+	0.293701i
$771$		0			0
$772$	−13.7918			−0.496379
$773$	−23.7213			−0.853195			−0.426598	−	0.904442i	$-0.640288\pi$
$773$	−23.7213			−0.853195			−0.426598	+	0.904442i	$0.640288\pi$
$774$		0			0
$775$			24.1332i			0.866889i
$776$	−107.081			−3.84398
$777$		0			0
$778$		−	29.2885i		−	1.05004i
$779$		−	5.65896i		−	0.202753i
$780$		0			0
$781$			2.44971i			0.0876574i
$782$	−2.63477	+	36.9263i	−0.0942192	+	1.32048i
$783$		0			0
$784$	24.8822	−	35.2548i	0.888649	−	1.25910i
$785$	−22.6826			−0.809578
$786$		0			0
$787$	33.2615			1.18564			0.592822	−	0.805334i	$-0.298014\pi$
$787$	33.2615			1.18564			0.592822	+	0.805334i	$0.298014\pi$
$788$	−71.9190			−2.56201
$789$		0			0
$790$			26.3456i			0.937333i
$791$	2.70151	+	5.21327i	0.0960547	+	0.185363i
$792$		0			0
$793$			3.22126i			0.114390i
$794$		−	69.2779i		−	2.45858i
$795$		0			0
$796$	−40.2947			−1.42821
$797$	−9.62571			−0.340960			−0.170480	−	0.985361i	$-0.554532\pi$
$797$	−9.62571			−0.340960			−0.170480	+	0.985361i	$0.554532\pi$
$798$		0			0
$799$			12.9153i			0.456910i
$800$	13.1281			0.464147
$801$		0			0
$802$			38.1959i			1.34874i
$803$	11.5724			0.408380
$804$		0			0
$805$	−6.11242	−	14.1848i	−0.215435	−	0.499948i
$806$	8.95118			0.315292
$807$		0			0
$808$			52.3764i			1.84260i
$809$	−20.6869			−0.727312			−0.363656	−	0.931533i	$-0.618472\pi$
$809$	−20.6869			−0.727312			−0.363656	+	0.931533i	$0.618472\pi$
$810$		0			0
$811$			2.81158i			0.0987278i	0.998781	+	0.0493639i	$0.0157194\pi$
$811$			2.81158i			0.0987278i	−0.998781	+	0.0493639i	$0.984281\pi$
$812$	22.2001	−	11.5040i	0.779070	−	0.403713i
$813$		0			0
$814$	29.0655			1.01874
$815$	8.80985			0.308595
$816$		0			0
$817$			7.60254i			0.265979i
$818$			58.6389i			2.05026i
$819$		0			0
$820$		−	26.4233i		−	0.922742i
$821$	−39.1092			−1.36492			−0.682460	−	0.730923i	$-0.739090\pi$
$821$	−39.1092			−1.36492			−0.682460	+	0.730923i	$0.739090\pi$
$822$		0			0
$823$	34.8689			1.21545			0.607726	−	0.794147i	$-0.292082\pi$
$823$	34.8689			1.21545			0.607726	+	0.794147i	$0.292082\pi$
$824$	67.8086			2.36222
$825$		0			0
$826$	0.615677	+	1.18811i	0.0214221	+	0.0413396i
$827$			56.4343i			1.96241i	0.192957	+	0.981207i	$0.438192\pi$
$827$			56.4343i			1.96241i	−0.192957	+	0.981207i	$0.561808\pi$
$828$		0			0
$829$			49.9687i			1.73549i	0.497014	+	0.867743i	$0.334430\pi$
$829$			49.9687i			1.73549i	−0.497014	+	0.867743i	$0.665570\pi$
$830$	35.6527			1.23752
$831$		0			0
$832$			1.51952i			0.0526800i
$833$	12.3731	−	17.5311i	0.428703	−	0.607416i
$834$		0			0
$835$		−	21.7022i		−	0.751035i
$836$		−	5.56103i		−	0.192332i
$837$		0			0
$838$	−13.3813			−0.462250
$839$	−10.4958			−0.362356			−0.181178	−	0.983450i	$-0.557991\pi$
$839$	−10.4958			−0.362356			−0.181178	+	0.983450i	$0.557991\pi$
$840$		0			0
$841$	−24.2612			−0.836594
$842$			40.5772i			1.39838i
$843$		0			0
$844$	34.5726			1.19004
$845$	15.4979			0.533145
$846$		0			0
$847$	22.8309	−	11.8309i	0.784478	−	0.406515i
$848$			33.3772i			1.14618i
$849$		0			0
$850$	27.1578			0.931506
$851$	−48.7845	−	3.48088i	−1.67231	−	0.119323i
$852$		0			0
$853$			40.7803i			1.39629i	0.715956	+	0.698145i	$0.245991\pi$
$853$			40.7803i			1.39629i	−0.715956	+	0.698145i	$0.754009\pi$
$854$	36.7721	−	19.0553i	1.25832	−	0.652058i
$855$		0			0
$856$			15.7956i			0.539883i
$857$			22.6150i			0.772513i	0.922392	+	0.386256i	$0.126232\pi$
$857$			22.6150i			0.772513i	−0.922392	+	0.386256i	$0.873768\pi$
$858$		0			0
$859$		−	35.5983i		−	1.21460i	−0.794473	−	0.607299i	$-0.792253\pi$
$859$		−	35.5983i		−	1.21460i	0.794473	−	0.607299i	$-0.207747\pi$
$860$			35.4985i			1.21049i
$861$		0			0
$862$			28.7766i			0.980134i
$863$	−34.8282			−1.18557			−0.592784	−	0.805362i	$-0.701971\pi$
$863$	−34.8282			−1.18557			−0.592784	+	0.805362i	$0.701971\pi$
$864$		0			0
$865$		−	24.6195i		−	0.837089i
$866$	−34.0842			−1.15823
$867$		0			0
$868$	−36.2503	−	69.9544i	−1.23041	−	2.37441i
$869$	−9.72723			−0.329974
$870$		0			0
$871$	1.89240			0.0641215
$872$		−	104.631i		−	3.54326i
$873$		0			0
$874$	−0.972802	+	13.6338i	−0.0329055	+	0.461171i
$875$	−24.3580	+	12.6223i	−0.823450	+	0.426711i
$876$		0			0
$877$	45.2350			1.52748			0.763740	−	0.645525i	$-0.223361\pi$
$877$	45.2350			1.52748			0.763740	+	0.645525i	$0.223361\pi$
$878$			90.7597i			3.06299i
$879$		0			0
$880$		−	8.49290i		−	0.286296i
$881$	−47.2653			−1.59241			−0.796205	−	0.605027i	$-0.793162\pi$
$881$	−47.2653			−1.59241			−0.796205	+	0.605027i	$0.793162\pi$
$882$		0			0
$883$	3.85865			0.129854			0.0649270	−	0.997890i	$-0.479319\pi$
$883$	3.85865			0.129854			0.0649270	+	0.997890i	$0.479319\pi$
$884$		−	6.89610i		−	0.231941i
$885$		0			0
$886$	−82.6055			−2.77518
$887$		−	41.3944i		−	1.38989i	−0.719064	−	0.694944i	$-0.755429\pi$
$887$		−	41.3944i		−	1.38989i	0.719064	−	0.694944i	$-0.244571\pi$
$888$		0			0
$889$	−6.41645	+	3.32500i	−0.215201	+	0.111517i
$890$	−15.6753			−0.525439
$891$		0			0
$892$		−	91.5879i		−	3.06659i
$893$			4.76855i			0.159573i
$894$		0			0
$895$	12.6770			0.423746
$896$	34.8771	−	18.0733i	1.16516	−	0.603785i
$897$		0			0
$898$	−52.2350			−1.74311
$899$		−	14.9323i		−	0.498021i
$900$		0			0
$901$			16.5974i			0.552941i
$902$	14.2504			0.474486
$903$		0			0
$904$		−	13.0847i		−	0.435190i
$905$	17.1216			0.569142
$906$		0			0
$907$			22.9335i			0.761496i	0.924679	+	0.380748i	$0.124333\pi$
$907$			22.9335i			0.761496i	−0.924679	+	0.380748i	$0.875667\pi$
$908$	108.008			3.58439
$909$		0			0
$910$	1.93364	+	3.73147i	0.0640996	+	0.123697i
$911$			7.56337i			0.250586i	0.992120	+	0.125293i	$0.0399870\pi$
$911$			7.56337i			0.250586i	−0.992120	+	0.125293i	$0.960013\pi$
$912$		0			0
$913$			13.1636i			0.435651i
$914$			7.90431i			0.261451i
$915$		0			0
$916$	84.6948			2.79840
$917$	−22.7866	−	43.9726i	−0.752478	−	1.45210i
$918$		0			0
$919$		−	27.9586i		−	0.922269i	−0.887330	−	0.461134i	$-0.847443\pi$
$919$		−	27.9586i		−	0.922269i	0.887330	−	0.461134i	$-0.152557\pi$
$920$	−2.44971	+	34.3327i	−0.0807645	+	1.13192i
$921$		0			0
$922$		−	98.2333i		−	3.23514i
$923$			1.12162i			0.0369184i
$924$		0			0
$925$			35.8791i			1.17970i
$926$	50.9430			1.67409
$927$		0			0
$928$	−8.12294			−0.266649
$929$			11.3298i			0.371718i	0.982576	+	0.185859i	$0.0595067\pi$
$929$			11.3298i			0.371718i	−0.982576	+	0.185859i	$0.940493\pi$
$930$		0			0
$931$	4.56836	−	6.47277i	0.149722	−	0.212137i
$932$	36.2124			1.18618
$933$		0			0
$934$	31.3811			1.02682
$935$		−	4.22325i		−	0.138115i
$936$		0			0
$937$	−7.75154			−0.253232			−0.126616	−	0.991952i	$-0.540412\pi$
$937$	−7.75154			−0.253232			−0.126616	+	0.991952i	$0.540412\pi$
$938$	−11.1944	−	21.6025i	−0.365510	−	0.705348i
$939$		0			0
$940$			22.2657i			0.726228i
$941$	4.38019			0.142790			0.0713950	−	0.997448i	$-0.477255\pi$
$941$	4.38019			0.142790			0.0713950	+	0.997448i	$0.477255\pi$
$942$		0			0
$943$	−23.9183	−	1.70662i	−0.778889	−	0.0555753i
$944$		−	1.23812i		−	0.0402973i
$945$		0			0
$946$	−19.1447			−0.622448
$947$	−4.60985			−0.149800			−0.0749001	−	0.997191i	$-0.523864\pi$
$947$	−4.60985			−0.149800			−0.0749001	+	0.997191i	$0.523864\pi$
$948$		0			0
$949$	5.29849			0.171996
$950$	10.0271			0.325323
$951$		0			0
$952$	−42.4556	+	22.0005i	−1.37599	+	0.713039i
$953$			2.26047i			0.0732239i	0.999330	+	0.0366119i	$0.0116565\pi$
$953$			2.26047i			0.0732239i	−0.999330	+	0.0366119i	$0.988343\pi$
$954$		0			0
$955$			15.0116i			0.485762i
$956$	92.8076			3.00161
$957$		0			0
$958$	63.5499			2.05321
$959$	14.9760	+	28.9002i	0.483601	+	0.933235i
$960$		0			0
$961$	−16.0531			−0.517841
$962$	13.3078			0.429062
$963$		0			0
$964$	−38.4909			−1.23971
$965$	−3.86719			−0.124489
$966$		0			0
$967$	33.1820			1.06706			0.533530	−	0.845781i	$-0.320865\pi$
$967$	33.1820			1.06706			0.533530	+	0.845781i	$0.320865\pi$
$968$	−57.3027			−1.84178
$969$		0			0
$970$	−55.6731			−1.78756
$971$	13.1660			0.422517			0.211259	−	0.977430i	$-0.432244\pi$
$971$	13.1660			0.422517			0.211259	+	0.977430i	$0.432244\pi$
$972$		0			0
$973$	−16.7736	−	32.3690i	−0.537736	−	1.03770i
$974$	47.9794			1.53736
$975$		0			0
$976$	−38.3199			−1.22659
$977$		−	24.5200i		−	0.784463i	−0.919866	−	0.392232i	$-0.871703\pi$
$977$		−	24.5200i		−	0.784463i	0.919866	−	0.392232i	$-0.128297\pi$
$978$		0			0
$979$		−	5.78760i		−	0.184973i
$980$	21.3310	−	30.2232i	0.681394	−	0.965446i
$981$		0			0
$982$	−32.3516			−1.03238
$983$	−47.6949			−1.52123			−0.760615	−	0.649203i	$-0.775103\pi$
$983$	−47.6949			−1.52123			−0.760615	+	0.649203i	$0.775103\pi$
$984$		0			0
$985$	−20.1658			−0.642537
$986$	−16.8038			−0.535143
$987$		0			0
$988$		−	2.54616i		−	0.0810041i
$989$	32.1332	+	2.29277i	1.02178	+	0.0729058i
$990$		0			0
$991$	15.9512			0.506706			0.253353	−	0.967374i	$-0.418467\pi$
$991$	15.9512			0.506706			0.253353	+	0.967374i	$0.418467\pi$
$992$			25.5961i			0.812677i
$993$		0			0
$994$	12.8037	−	6.63487i	0.406110	−	0.210445i
$995$	−11.2985			−0.358186
$996$		0			0
$997$			27.8959i			0.883473i	0.897145	+	0.441736i	$0.145637\pi$
$997$			27.8959i			0.883473i	−0.897145	+	0.441736i	$0.854363\pi$
$998$	21.7126			0.687301
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1449.2.h.e.1126.3		12
3.2	odd	2		483.2.h.c.160.11	yes	12
7.6	odd	2	inner	1449.2.h.e.1126.1		12
21.20	even	2		483.2.h.c.160.10	yes	12
23.22	odd	2	inner	1449.2.h.e.1126.2		12
69.68	even	2		483.2.h.c.160.12	yes	12
161.160	even	2	inner	1449.2.h.e.1126.4		12
483.482	odd	2		483.2.h.c.160.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.c.160.9	✓	12	483.482	odd	2
483.2.h.c.160.10	yes	12	21.20	even	2
483.2.h.c.160.11	yes	12	3.2	odd	2
483.2.h.c.160.12	yes	12	69.68	even	2
1449.2.h.e.1126.1		12	7.6	odd	2	inner
1449.2.h.e.1126.2		12	23.22	odd	2	inner
1449.2.h.e.1126.3		12	1.1	even	1	trivial
1449.2.h.e.1126.4		12	161.160	even	2	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:	\( N \)	\(=\)	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1449.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.51820 q^{2} +4.34132 q^{4} +1.21729 q^{5} +(2.34908 - 1.21729i) q^{7} -5.89592 q^{8} +O(q^{10})\)	\(q-2.51820 q^{2} +4.34132 q^{4} +1.21729 q^{5} +(2.34908 - 1.21729i) q^{7} -5.89592 q^{8} -3.06538 q^{10} -1.13179i q^{11} -0.518199i q^{13} +(-5.91546 + 3.06538i) q^{14} +6.16445 q^{16} +3.06538 q^{17} +1.13179 q^{19} +5.28466 q^{20} +2.85008i q^{22} +(0.341325 - 4.78367i) q^{23} -3.51820 q^{25} +1.30493i q^{26} +(10.1981 - 5.28466i) q^{28} +2.17687 q^{29} -6.85952i q^{31} -3.73147 q^{32} -7.71925 q^{34} +(2.85952 - 1.48180i) q^{35} -10.1981i q^{37} -2.85008 q^{38} -7.17706 q^{40} -5.00000i q^{41} +6.71726i q^{43} -4.91348i q^{44} +(-0.859523 + 12.0462i) q^{46} +4.21327i q^{47} +(4.03640 - 5.71905i) q^{49} +8.85952 q^{50} -2.24967i q^{52} +5.41447i q^{53} -1.37772i q^{55} +(-13.8500 + 7.17706i) q^{56} -5.48180 q^{58} -0.200848i q^{59} -6.21627 q^{61} +17.2736i q^{62} -2.93232 q^{64} -0.630799i q^{65} +3.65188i q^{67} +13.3078 q^{68} +(-7.20085 + 3.73147i) q^{70} -2.16445 q^{71} +10.2248i q^{73} +25.6809i q^{74} +4.91348 q^{76} +(-1.37772 - 2.65868i) q^{77} -8.59454i q^{79} +7.50394 q^{80} +12.5910i q^{82} -11.6307 q^{83} +3.73147 q^{85} -16.9154i q^{86} +6.67296i q^{88} +5.11366 q^{89} +(-0.630799 - 1.21729i) q^{91} +(1.48180 - 20.7675i) q^{92} -10.6099i q^{94} +1.37772 q^{95} +18.1619 q^{97} +(-10.1645 + 14.4017i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 36 q^{4} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 + 36 * q^4 + 24 * q^8	\( 12 q - 4 q^{2} + 36 q^{4} + 24 q^{8} + 68 q^{16} - 12 q^{23} - 16 q^{25} + 16 q^{29} + 44 q^{32} - 8 q^{35} + 32 q^{46} - 4 q^{49} + 64 q^{50} - 92 q^{58} + 112 q^{64} - 28 q^{70} - 20 q^{71} + 52 q^{77} - 44 q^{85} + 44 q^{92} - 52 q^{95} - 116 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 + 68 * q^16 - 12 * q^23 - 16 * q^25 + 16 * q^29 + 44 * q^32 - 8 * q^35 + 32 * q^46 - 4 * q^49 + 64 * q^50 - 92 * q^58 + 112 * q^64 - 28 * q^70 - 20 * q^71 + 52 * q^77 - 44 * q^85 + 44 * q^92 - 52 * q^95 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more