LMFDB - Embedded newform 1400.2.bh.d.249.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(249,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("1400.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.bh (of order $6$, 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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1400.249
Dual form			1400.2.bh.d.849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{3} +(-2.59808 - 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(-1.73205 - 1.00000i) q^{3} +(-2.59808 - 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} -2.00000i q^{13} +(-2.59808 - 1.50000i) q^{17} +(4.00000 + 3.46410i) q^{21} +(2.59808 - 1.50000i) q^{23} +4.00000i q^{27} +6.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(6.92820 - 4.00000i) q^{33} +(-2.00000 + 3.46410i) q^{39} +5.00000 q^{41} -6.00000i q^{43} +(-7.79423 + 4.50000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(3.00000 + 5.19615i) q^{51} +(5.19615 + 3.00000i) q^{53} +(4.00000 - 6.92820i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-0.866025 - 2.50000i) q^{63} +(12.1244 + 7.00000i) q^{67} -6.00000 q^{69} +11.0000 q^{71} +(1.73205 + 1.00000i) q^{73} +(6.92820 - 8.00000i) q^{77} +(4.50000 + 7.79423i) q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000i q^{83} +(-10.3923 - 6.00000i) q^{87} +(5.50000 + 9.52628i) q^{89} +(-1.00000 + 5.19615i) q^{91} +(15.5885 - 9.00000i) q^{93} +11.0000i q^{97} -4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} - 8 q^{11} + 16 q^{21} + 24 q^{29} - 18 q^{31} - 8 q^{39} + 20 q^{41} + 26 q^{49} + 12 q^{51} + 16 q^{59} - 16 q^{61} - 24 q^{69} + 44 q^{71} + 18 q^{79} + 22 q^{81} + 22 q^{89} - 4 q^{91} - 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^9 - 8 * q^11 + 16 * q^21 + 24 * q^29 - 18 * q^31 - 8 * q^39 + 20 * q^41 + 26 * q^49 + 12 * q^51 + 16 * q^59 - 16 * q^61 - 24 * q^69 + 44 * q^71 + 18 * q^79 + 22 * q^81 + 22 * q^89 - 4 * q^91 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.73205	−	1.00000i	−1.00000	−	0.577350i	−0.0917517	−	0.995782i	$-0.529247\pi$
$3$	−1.73205	−	1.00000i	−1.00000	−	0.577350i	−0.908248	+	0.418432i	$0.862580\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	0.150675	−	0.988583i	$-0.451855\pi$
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	−0.780801	+	0.624780i	$0.785189\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	4.00000	+	3.46410i	0.872872	+	0.755929i
$22$		0			0
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			4.00000i			0.769800i
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	0.105869	+	0.994380i	$0.466238\pi$
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	−0.914093	+	0.405505i	$0.867096\pi$
$32$		0			0
$33$	6.92820	−	4.00000i	1.20605	−	0.696311i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$		−	6.00000i		−	0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.79423	+	4.50000i	−1.13691	+	0.656392i	−0.945662	−	0.325150i	$-0.894585\pi$
$47$	−7.79423	+	4.50000i	−1.13691	+	0.656392i	−0.191243	+	0.981543i	$0.561252\pi$
$48$		0			0
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$		0			0
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$		0			0
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	0.812447	−	0.583036i	$-0.198135\pi$
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	−0.0987002	+	0.995117i	$0.531468\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$	−0.866025	−	2.50000i	−0.109109	−	0.314970i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	12.1244	+	7.00000i	1.48123	+	0.855186i	0.999773	−	0.0212861i	$-0.00677610\pi$
$67$	12.1244	+	7.00000i	1.48123	+	0.855186i	0.481452	+	0.876472i	$0.340109\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$	11.0000			1.30546			0.652730	−	0.757591i	$-0.273624\pi$
$71$	11.0000			1.30546			0.652730	+	0.757591i	$0.273624\pi$
$72$		0			0
$73$	1.73205	+	1.00000i	0.202721	+	0.117041i	0.597924	−	0.801553i	$-0.295992\pi$
$73$	1.73205	+	1.00000i	0.202721	+	0.117041i	−0.395203	+	0.918594i	$0.629326\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.92820	−	8.00000i	0.789542	−	0.911685i
$78$		0			0
$79$	4.50000	+	7.79423i	0.506290	+	0.876919i	0.999974	+	0.00727784i	$0.00231663\pi$
$79$	4.50000	+	7.79423i	0.506290	+	0.876919i	−0.493684	+	0.869641i	$0.664350\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−10.3923	−	6.00000i	−1.11417	−	0.643268i
$88$		0			0
$89$	5.50000	+	9.52628i	0.582999	+	1.00978i	0.995122	+	0.0986553i	$0.0314541\pi$
$89$	5.50000	+	9.52628i	0.582999	+	1.00978i	−0.412123	+	0.911128i	$0.635213\pi$
$90$		0			0
$91$	−1.00000	+	5.19615i	−0.104828	+	0.544705i
$92$		0			0
$93$	15.5885	−	9.00000i	1.61645	−	0.933257i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			11.0000i			1.11688i	0.829545	+	0.558440i	$0.188600\pi$
$97$			11.0000i			1.11688i	−0.829545	+	0.558440i	$0.811400\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$		0			0
$103$	12.9904	−	7.50000i	1.27998	−	0.738997i	0.303136	−	0.952947i	$-0.401966\pi$
$103$	12.9904	−	7.50000i	1.27998	−	0.738997i	0.976845	+	0.213950i	$0.0686331\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.92820	+	4.00000i	−0.669775	+	0.386695i	−0.795991	−	0.605308i	$-0.793050\pi$
$107$	−6.92820	+	4.00000i	−0.669775	+	0.386695i	0.126217	+	0.992003i	$0.459717\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			15.0000i			1.41108i	0.708669	+	0.705541i	$0.249296\pi$
$113$			15.0000i			1.41108i	−0.708669	+	0.705541i	$0.750704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.73205	−	1.00000i	0.160128	−	0.0924500i
$118$		0			0
$119$	6.00000	+	5.19615i	0.550019	+	0.476331i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	−8.66025	−	5.00000i	−0.780869	−	0.450835i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		0			0
$129$	−6.00000	+	10.3923i	−0.528271	+	0.914991i
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.7224	+	8.50000i	1.25782	+	0.726204i	0.972651	−	0.232273i	$-0.0746161\pi$
$137$	14.7224	+	8.50000i	1.25782	+	0.726204i	0.285171	+	0.958477i	$0.407949\pi$
$138$		0			0
$139$	6.00000			0.508913			0.254457	−	0.967084i	$-0.418103\pi$
$139$	6.00000			0.508913			0.254457	+	0.967084i	$0.418103\pi$
$140$		0			0
$141$	18.0000			1.51587
$142$		0			0
$143$	6.92820	+	4.00000i	0.579365	+	0.334497i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.66025	−	11.0000i	−0.714286	−	0.907265i
$148$		0			0
$149$	−10.0000	−	17.3205i	−0.819232	−	1.41895i	−0.906249	−	0.422744i	$-0.861067\pi$
$149$	−10.0000	−	17.3205i	−0.819232	−	1.41895i	0.0870170	−	0.996207i	$-0.472267\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$		0			0
$153$		−	3.00000i		−	0.242536i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.66025	+	5.00000i	0.691164	+	0.399043i	0.804048	−	0.594565i	$-0.202676\pi$
$157$	8.66025	+	5.00000i	0.691164	+	0.399043i	−0.112884	+	0.993608i	$0.536009\pi$
$158$		0			0
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$		0			0
$163$	−20.7846	+	12.0000i	−1.62798	+	0.939913i	−0.643280	+	0.765631i	$0.722427\pi$
$163$	−20.7846	+	12.0000i	−1.62798	+	0.939913i	−0.984696	+	0.174282i	$0.944240\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$		0			0
$172$		0			0
$173$	13.8564	−	8.00000i	1.05348	−	0.608229i	0.129861	−	0.991532i	$-0.458547\pi$
$173$	13.8564	−	8.00000i	1.05348	−	0.608229i	0.923622	+	0.383304i	$0.125214\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.8564	+	8.00000i	−1.04151	+	0.601317i
$178$		0			0
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$		0			0
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$			16.0000i			1.18275i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	10.3923	−	6.00000i	0.759961	−	0.438763i
$188$		0			0
$189$	2.00000	−	10.3923i	0.145479	−	0.755929i
$190$		0			0
$191$	6.50000	+	11.2583i	0.470323	+	0.814624i	0.999424	−	0.0339349i	$-0.0108039\pi$
$191$	6.50000	+	11.2583i	0.470323	+	0.814624i	−0.529101	+	0.848559i	$0.677471\pi$
$192$		0			0
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	0.335993	−	0.941865i	$-0.390928\pi$
$193$	−4.33013	−	2.50000i	−0.311689	−	0.179954i	−0.647682	+	0.761911i	$0.724262\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	−0.206184	−	0.978513i	$-0.566105\pi$
$199$	10.5000	−	18.1865i	0.744325	−	1.28921i	0.950509	−	0.310696i	$-0.100562\pi$
$200$		0			0
$201$	−14.0000	−	24.2487i	−0.987484	−	1.71037i
$202$		0			0
$203$	−15.5885	−	3.00000i	−1.09410	−	0.210559i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.59808	+	1.50000i	0.180579	+	0.104257i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$		0			0
$213$	−19.0526	−	11.0000i	−1.30546	−	0.753708i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	15.5885	−	18.0000i	1.05821	−	1.22192i
$218$		0			0
$219$	−2.00000	−	3.46410i	−0.135147	−	0.234082i
$220$		0			0
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		0			0
$223$			11.0000i			0.736614i	0.929704	+	0.368307i	$0.120063\pi$
$223$			11.0000i			0.736614i	−0.929704	+	0.368307i	$0.879937\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.0526	−	11.0000i	−1.26456	−	0.730096i	−0.290609	−	0.956842i	$-0.593858\pi$
$227$	−19.0526	−	11.0000i	−1.26456	−	0.730096i	−0.973954	+	0.226746i	$0.927191\pi$
$228$		0			0
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	0.703060	−	0.711131i	$-0.251817\pi$
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	−0.967387	+	0.253302i	$0.918483\pi$
$230$		0			0
$231$	−20.0000	+	6.92820i	−1.31590	+	0.455842i
$232$		0			0
$233$	−19.0526	+	11.0000i	−1.24817	+	0.720634i	−0.970745	−	0.240112i	$-0.922816\pi$
$233$	−19.0526	+	11.0000i	−1.24817	+	0.720634i	−0.277429	+	0.960746i	$0.589482\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	18.0000i		−	1.16923i
$238$		0			0
$239$	−11.0000			−0.711531			−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000			−0.711531			−0.355765	+	0.934575i	$0.615780\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$		0			0
$243$	−8.66025	+	5.00000i	−0.555556	+	0.320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	−16.0000			−1.00991			−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000			−1.00991			−0.504956	+	0.863145i	$0.668491\pi$
$252$		0			0
$253$			12.0000i			0.754434i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	2.59808	+	1.50000i	0.160204	+	0.0924940i	0.577959	−	0.816066i	$-0.303849\pi$
$263$	2.59808	+	1.50000i	0.160204	+	0.0924940i	−0.417755	+	0.908560i	$0.637183\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	22.0000i		−	1.34638i
$268$		0			0
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	−0.894900	−	0.446267i	$-0.852753\pi$
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	0.833929	+	0.551872i	$0.186086\pi$
$270$		0			0
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	0.739921	−	0.672694i	$-0.234863\pi$
$271$	−3.50000	−	6.06218i	−0.212610	−	0.368251i	−0.952531	+	0.304443i	$0.901530\pi$
$272$		0			0
$273$	6.92820	−	8.00000i	0.419314	−	0.484182i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.92820	+	4.00000i	0.416275	+	0.240337i	0.693482	−	0.720473i	$-0.256075\pi$
$277$	6.92820	+	4.00000i	0.416275	+	0.240337i	−0.277207	+	0.960810i	$0.589409\pi$
$278$		0			0
$279$	−9.00000			−0.538816
$280$		0			0
$281$	−13.0000			−0.775515			−0.387757	−	0.921761i	$-0.626750\pi$
$281$	−13.0000			−0.775515			−0.387757	+	0.921761i	$0.626750\pi$
$282$		0			0
$283$	−1.73205	−	1.00000i	−0.102960	−	0.0594438i	0.447636	−	0.894216i	$-0.352266\pi$
$283$	−1.73205	−	1.00000i	−0.102960	−	0.0594438i	−0.550596	+	0.834772i	$0.685599\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.9904	−	2.50000i	−0.766798	−	0.147570i
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$	11.0000	−	19.0526i	0.644831	−	1.11688i
$292$		0			0
$293$			14.0000i			0.817889i	0.912559	+	0.408944i	$0.134103\pi$
$293$			14.0000i			0.817889i	−0.912559	+	0.408944i	$0.865897\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−13.8564	−	8.00000i	−0.804030	−	0.464207i
$298$		0			0
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		0			0
$301$	−3.00000	+	15.5885i	−0.172917	+	0.898504i
$302$		0			0
$303$	−13.8564	+	8.00000i	−0.796030	+	0.459588i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			24.0000i			1.36975i	0.728659	+	0.684876i	$0.240144\pi$
$307$			24.0000i			1.36975i	−0.728659	+	0.684876i	$0.759856\pi$
$308$		0			0
$309$	−30.0000			−1.70664
$310$		0			0
$311$	−0.500000	+	0.866025i	−0.0283524	+	0.0491078i	−0.879853	−	0.475245i	$-0.842359\pi$
$311$	−0.500000	+	0.866025i	−0.0283524	+	0.0491078i	0.851501	+	0.524353i	$0.175693\pi$
$312$		0			0
$313$	−26.8468	+	15.5000i	−1.51747	+	0.876112i	−0.517681	+	0.855574i	$0.673205\pi$
$313$	−26.8468	+	15.5000i	−1.51747	+	0.876112i	−0.999789	+	0.0205381i	$0.993462\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	−0.178908	−	0.983866i	$-0.557257\pi$
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	0.762598	+	0.646872i	$0.223923\pi$
$318$		0			0
$319$	−12.0000	+	20.7846i	−0.671871	+	1.16371i
$320$		0			0
$321$	16.0000			0.893033
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	24.2487	−	14.0000i	1.34096	−	0.774202i
$328$		0			0
$329$	22.5000	−	7.79423i	1.24047	−	0.429710i
$330$		0			0
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	0.892199	−	0.451643i	$-0.149162\pi$
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	−0.837234	+	0.546845i	$0.815829\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$			29.0000i			1.57973i	0.613280	+	0.789865i	$0.289850\pi$
$337$			29.0000i			1.57973i	−0.613280	+	0.789865i	$0.710150\pi$
$338$		0			0
$339$	15.0000	−	25.9808i	0.814688	−	1.41108i
$340$		0			0
$341$	−18.0000	−	31.1769i	−0.974755	−	1.68832i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.73205	+	1.00000i	0.0929814	+	0.0536828i	0.545770	−	0.837935i	$-0.316237\pi$
$347$	1.73205	+	1.00000i	0.0929814	+	0.0536828i	−0.452788	+	0.891618i	$0.649571\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	−12.9904	−	7.50000i	−0.691408	−	0.399185i	0.112731	−	0.993626i	$-0.464040\pi$
$353$	−12.9904	−	7.50000i	−0.691408	−	0.399185i	−0.804139	+	0.594441i	$0.797373\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−5.19615	−	15.0000i	−0.275010	−	0.793884i
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		0			0
$363$			10.0000i			0.524864i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	0.815966	−	0.578101i	$-0.196206\pi$
$367$	13.8564	+	8.00000i	0.723299	+	0.417597i	−0.0926670	+	0.995697i	$0.529539\pi$
$368$		0			0
$369$	2.50000	+	4.33013i	0.130145	+	0.225417i
$370$		0			0
$371$	−12.0000	−	10.3923i	−0.623009	−	0.539542i
$372$		0			0
$373$	5.19615	−	3.00000i	0.269047	−	0.155334i	−0.359408	−	0.933181i	$-0.617021\pi$
$373$	5.19615	−	3.00000i	0.269047	−	0.155334i	0.628454	+	0.777847i	$0.283688\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$		0			0
$381$	−8.00000	+	13.8564i	−0.409852	+	0.709885i
$382$		0			0
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.0427020	−	0.999088i	$-0.486403\pi$
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.886586	+	0.462563i	$0.153070\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.19615	−	3.00000i	0.264135	−	0.152499i
$388$		0			0
$389$	17.0000	−	29.4449i	0.861934	−	1.49291i	−0.00812520	−	0.999967i	$-0.502586\pi$
$389$	17.0000	−	29.4449i	0.861934	−	1.49291i	0.870059	−	0.492947i	$-0.164080\pi$
$390$		0			0
$391$	−9.00000			−0.455150
$392$		0			0
$393$			24.0000i			1.21064i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	32.9090	−	19.0000i	1.65165	−	0.953583i	0.675261	−	0.737579i	$-0.264031\pi$
$397$	32.9090	−	19.0000i	1.65165	−	0.953583i	0.976392	−	0.216004i	$-0.0693024\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	15.5885	+	9.00000i	0.776516	+	0.448322i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$		0			0
$411$	−17.0000	−	29.4449i	−0.838548	−	1.45241i
$412$		0			0
$413$	−13.8564	+	16.0000i	−0.681829	+	0.787309i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−10.3923	−	6.00000i	−0.508913	−	0.293821i
$418$		0			0
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$		0			0
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$		0			0
$423$	−7.79423	−	4.50000i	−0.378968	−	0.218797i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.92820	+	20.0000i	0.335279	+	0.967868i
$428$		0			0
$429$	−8.00000	−	13.8564i	−0.386244	−	0.668994i
$430$		0			0
$431$	15.5000	−	26.8468i	0.746609	−	1.29316i	−0.202831	−	0.979214i	$-0.565014\pi$
$431$	15.5000	−	26.8468i	0.746609	−	1.29316i	0.949439	−	0.313950i	$-0.101653\pi$
$432$		0			0
$433$			21.0000i			1.00920i	0.863355	+	0.504598i	$0.168359\pi$
$433$			21.0000i			1.00920i	−0.863355	+	0.504598i	$0.831641\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	0.893843	+	0.448379i	$0.147999\pi$
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	−0.0586141	+	0.998281i	$0.518668\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$		0			0
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	−0.232377	−	0.972626i	$-0.574650\pi$
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	0.726130	+	0.687557i	$0.241317\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			40.0000i			1.89194i
$448$		0			0
$449$	27.0000			1.27421			0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000			1.27421			0.637104	+	0.770778i	$0.280132\pi$
$450$		0			0
$451$	−10.0000	+	17.3205i	−0.470882	+	0.815591i
$452$		0			0
$453$	34.6410	−	20.0000i	1.62758	−	0.939682i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.73205	+	1.00000i	−0.0810219	+	0.0467780i	−0.539964	−	0.841688i	$-0.681562\pi$
$457$	−1.73205	+	1.00000i	−0.0810219	+	0.0467780i	0.458942	+	0.888466i	$0.348229\pi$
$458$		0			0
$459$	6.00000	−	10.3923i	0.280056	−	0.485071i
$460$		0			0
$461$	24.0000			1.11779			0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000			1.11779			0.558896	+	0.829238i	$0.311225\pi$
$462$		0			0
$463$			11.0000i			0.511213i	0.966781	+	0.255607i	$0.0822752\pi$
$463$			11.0000i			0.511213i	−0.966781	+	0.255607i	$0.917725\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	25.9808	−	15.0000i	1.20225	−	0.694117i	0.241192	−	0.970477i	$-0.422462\pi$
$467$	25.9808	−	15.0000i	1.20225	−	0.694117i	0.961054	+	0.276360i	$0.0891283\pi$
$468$		0			0
$469$	−28.0000	−	24.2487i	−1.29292	−	1.11970i
$470$		0			0
$471$	−10.0000	−	17.3205i	−0.460776	−	0.798087i
$472$		0			0
$473$	20.7846	+	12.0000i	0.955677	+	0.551761i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			6.00000i			0.274721i
$478$		0			0
$479$	4.50000	−	7.79423i	0.205610	−	0.356127i	−0.744717	−	0.667381i	$-0.767415\pi$
$479$	4.50000	−	7.79423i	0.205610	−	0.356127i	0.950327	+	0.311253i	$0.100749\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	15.5885	+	3.00000i	0.709299	+	0.136505i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	19.9186	+	11.5000i	0.902597	+	0.521115i	0.878042	−	0.478584i	$-0.158850\pi$
$487$	19.9186	+	11.5000i	0.902597	+	0.521115i	0.0245553	+	0.999698i	$0.492183\pi$
$488$		0			0
$489$	48.0000			2.17064
$490$		0			0
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$		0			0
$493$	−15.5885	−	9.00000i	−0.702069	−	0.405340i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−28.5788	−	5.50000i	−1.28194	−	0.246709i
$498$		0			0
$499$	19.0000	+	32.9090i	0.850557	+	1.47321i	0.880707	+	0.473662i	$0.157068\pi$
$499$	19.0000	+	32.9090i	0.850557	+	1.47321i	−0.0301498	+	0.999545i	$0.509598\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	16.0000i		−	0.713405i	−0.934218	−	0.356702i	$-0.883901\pi$
$503$		−	16.0000i		−	0.713405i	0.934218	−	0.356702i	$-0.116099\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−15.5885	−	9.00000i	−0.692308	−	0.399704i
$508$		0			0
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$		0			0
$511$	−4.00000	−	3.46410i	−0.176950	−	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	36.0000i		−	1.58328i
$518$		0			0
$519$	−32.0000			−1.40464
$520$		0			0
$521$	−22.5000	+	38.9711i	−0.985743	+	1.70736i	−0.347155	+	0.937808i	$0.612852\pi$
$521$	−22.5000	+	38.9711i	−0.985743	+	1.70736i	−0.638588	+	0.769549i	$0.720481\pi$
$522$		0			0
$523$	19.0526	−	11.0000i	0.833110	−	0.480996i	−0.0218062	−	0.999762i	$-0.506942\pi$
$523$	19.0526	−	11.0000i	0.833110	−	0.480996i	0.854916	+	0.518766i	$0.173608\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	23.3827	−	13.5000i	1.01857	−	0.588069i
$528$		0			0
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$		0			0
$531$	8.00000			0.347170
$532$		0			0
$533$		−	10.0000i		−	0.433148i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−6.92820	+	4.00000i	−0.298974	+	0.172613i
$538$		0			0
$539$	−22.0000	+	17.3205i	−0.947607	+	0.746047i
$540$		0			0
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	0.984325	+	0.176367i	$0.0564345\pi$
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	−0.339424	+	0.940633i	$0.610232\pi$
$542$		0			0
$543$	13.8564	+	8.00000i	0.594635	+	0.343313i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			40.0000i			1.71028i	0.518400	+	0.855138i	$0.326528\pi$
$547$			40.0000i			1.71028i	−0.518400	+	0.855138i	$0.673472\pi$
$548$		0			0
$549$	4.00000	−	6.92820i	0.170716	−	0.295689i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−7.79423	−	22.5000i	−0.331444	−	0.956797i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−31.1769	−	18.0000i	−1.32101	−	0.762684i	−0.337119	−	0.941462i	$-0.609452\pi$
$557$	−31.1769	−	18.0000i	−1.32101	−	0.762684i	−0.983890	+	0.178778i	$0.942786\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$	22.5167	+	13.0000i	0.948964	+	0.547885i	0.892759	−	0.450535i	$-0.148767\pi$
$563$	22.5167	+	13.0000i	0.948964	+	0.547885i	0.0562051	+	0.998419i	$0.482100\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−19.0526	+	22.0000i	−0.800132	+	0.923913i
$568$		0			0
$569$	−5.50000	−	9.52628i	−0.230572	−	0.399362i	0.727405	−	0.686209i	$-0.240726\pi$
$569$	−5.50000	−	9.52628i	−0.230572	−	0.399362i	−0.957977	+	0.286846i	$0.907393\pi$
$570$		0			0
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	−0.712735	−	0.701434i	$-0.752544\pi$
$571$	6.00000	−	10.3923i	0.251092	−	0.434904i	0.963827	+	0.266529i	$0.0858769\pi$
$572$		0			0
$573$		−	26.0000i		−	1.08617i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.1244	+	7.00000i	0.504744	+	0.291414i	0.730670	−	0.682730i	$-0.239208\pi$
$577$	12.1244	+	7.00000i	0.504744	+	0.291414i	−0.225927	+	0.974144i	$0.572541\pi$
$578$		0			0
$579$	5.00000	+	8.66025i	0.207793	+	0.359908i
$580$		0			0
$581$	−3.00000	+	15.5885i	−0.124461	+	0.646718i
$582$		0			0
$583$	−20.7846	+	12.0000i	−0.860811	+	0.496989i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	8.00000i		−	0.330195i	−0.986277	−	0.165098i	$-0.947206\pi$
$587$		−	8.00000i		−	0.330195i	0.986277	−	0.165098i	$-0.0527939\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$		0			0
$593$	−11.2583	+	6.50000i	−0.462324	+	0.266923i	−0.713021	−	0.701143i	$-0.752674\pi$
$593$	−11.2583	+	6.50000i	−0.462324	+	0.266923i	0.250697	+	0.968066i	$0.419340\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−36.3731	+	21.0000i	−1.48865	+	0.859473i
$598$		0			0
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$			14.0000i			0.570124i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	−0.253804	−	0.967256i	$-0.581682\pi$
$607$	11.2583	−	6.50000i	0.456962	−	0.263827i	0.710766	+	0.703429i	$0.248349\pi$
$608$		0			0
$609$	24.0000	+	20.7846i	0.972529	+	0.842235i
$610$		0			0
$611$	9.00000	+	15.5885i	0.364101	+	0.630641i
$612$		0			0
$613$	−22.5167	−	13.0000i	−0.909439	−	0.525065i	−0.0291886	−	0.999574i	$-0.509292\pi$
$613$	−22.5167	−	13.0000i	−0.909439	−	0.525065i	−0.880251	+	0.474509i	$0.842626\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			17.0000i			0.684394i	0.939628	+	0.342197i	$0.111171\pi$
$617$			17.0000i			0.684394i	−0.939628	+	0.342197i	$0.888829\pi$
$618$		0			0
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$		0			0
$621$	6.00000	+	10.3923i	0.240772	+	0.417029i
$622$		0			0
$623$	−9.52628	−	27.5000i	−0.381662	−	1.10176i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−15.0000			−0.597141			−0.298570	−	0.954388i	$-0.596510\pi$
$631$	−15.0000			−0.597141			−0.298570	+	0.954388i	$0.596510\pi$
$632$		0			0
$633$	−38.1051	−	22.0000i	−1.51454	−	0.874421i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	5.19615	−	13.0000i	0.205879	−	0.515079i
$638$		0			0
$639$	5.50000	+	9.52628i	0.217577	+	0.376854i
$640$		0			0
$641$	17.5000	−	30.3109i	0.691208	−	1.19721i	−0.280234	−	0.959932i	$-0.590412\pi$
$641$	17.5000	−	30.3109i	0.691208	−	1.19721i	0.971442	−	0.237276i	$-0.0762547\pi$
$642$		0			0
$643$		−	16.0000i		−	0.630978i	−0.948929	−	0.315489i	$-0.897831\pi$
$643$		−	16.0000i		−	0.630978i	0.948929	−	0.315489i	$-0.102169\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−41.5692	−	24.0000i	−1.63425	−	0.943537i	−0.982760	−	0.184884i	$-0.940809\pi$
$647$	−41.5692	−	24.0000i	−1.63425	−	0.943537i	−0.651494	−	0.758654i	$-0.725858\pi$
$648$		0			0
$649$	16.0000	+	27.7128i	0.628055	+	1.08782i
$650$		0			0
$651$	−45.0000	+	15.5885i	−1.76369	+	0.610960i
$652$		0			0
$653$	25.9808	−	15.0000i	1.01671	−	0.586995i	0.103558	−	0.994623i	$-0.466977\pi$
$653$	25.9808	−	15.0000i	1.01671	−	0.586995i	0.913148	+	0.407628i	$0.133644\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			2.00000i			0.0780274i
$658$		0			0
$659$	−14.0000			−0.545363			−0.272681	−	0.962104i	$-0.587910\pi$
$659$	−14.0000			−0.545363			−0.272681	+	0.962104i	$0.587910\pi$
$660$		0			0
$661$	−22.0000	+	38.1051i	−0.855701	+	1.48212i	0.0202925	+	0.999794i	$0.493540\pi$
$661$	−22.0000	+	38.1051i	−0.855701	+	1.48212i	−0.875993	+	0.482323i	$0.839793\pi$
$662$		0			0
$663$	10.3923	−	6.00000i	0.403604	−	0.233021i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	15.5885	−	9.00000i	0.603587	−	0.348481i
$668$		0			0
$669$	11.0000	−	19.0526i	0.425285	−	0.736614i
$670$		0			0
$671$	32.0000			1.23535
$672$		0			0
$673$		−	43.0000i		−	1.65753i	−0.559598	−	0.828764i	$-0.689045\pi$
$673$		−	43.0000i		−	1.65753i	0.559598	−	0.828764i	$-0.310955\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.19615	−	3.00000i	0.199704	−	0.115299i	−0.396813	−	0.917899i	$-0.629884\pi$
$677$	5.19615	−	3.00000i	0.199704	−	0.115299i	0.596518	+	0.802600i	$0.296551\pi$
$678$		0			0
$679$	5.50000	−	28.5788i	0.211071	−	1.09676i
$680$		0			0
$681$	22.0000	+	38.1051i	0.843042	+	1.46019i
$682$		0			0
$683$	12.1244	+	7.00000i	0.463926	+	0.267848i	0.713693	−	0.700458i	$-0.247021\pi$
$683$	12.1244	+	7.00000i	0.463926	+	0.267848i	−0.249768	+	0.968306i	$0.580354\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			16.0000i			0.610438i
$688$		0			0
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$		0			0
$693$	10.3923	+	2.00000i	0.394771	+	0.0759737i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−12.9904	−	7.50000i	−0.492046	−	0.284083i
$698$		0			0
$699$	44.0000			1.66423
$700$		0			0
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.8564	+	16.0000i	−0.521124	+	0.601742i
$708$		0			0
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	0.781086	−	0.624423i	$-0.214666\pi$
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	−0.931309	+	0.364229i	$0.881333\pi$
$710$		0			0
$711$	−4.50000	+	7.79423i	−0.168763	+	0.292306i
$712$		0			0
$713$			27.0000i			1.01116i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	19.0526	+	11.0000i	0.711531	+	0.410803i
$718$		0			0
$719$	14.5000	+	25.1147i	0.540759	+	0.936622i	0.998861	+	0.0477220i	$0.0151961\pi$
$719$	14.5000	+	25.1147i	0.540759	+	0.936622i	−0.458102	+	0.888900i	$0.651471\pi$
$720$		0			0
$721$	−37.5000	+	12.9904i	−1.39657	+	0.483787i
$722$		0			0
$723$	31.1769	−	18.0000i	1.15948	−	0.669427i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	29.0000i		−	1.07555i	−0.843088	−	0.537775i	$-0.819265\pi$
$727$		−	29.0000i		−	1.07555i	0.843088	−	0.537775i	$-0.180735\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−9.00000	+	15.5885i	−0.332877	+	0.576560i
$732$		0			0
$733$	12.1244	−	7.00000i	0.447823	−	0.258551i	−0.259087	−	0.965854i	$-0.583422\pi$
$733$	12.1244	−	7.00000i	0.447823	−	0.258551i	0.706910	+	0.707303i	$0.250088\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−48.4974	+	28.0000i	−1.78643	+	1.03139i
$738$		0			0
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	27.0000i		−	0.990534i	−0.868741	−	0.495267i	$-0.835070\pi$
$743$		−	27.0000i		−	0.990534i	0.868741	−	0.495267i	$-0.164930\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.19615	−	3.00000i	0.190117	−	0.109764i
$748$		0			0
$749$	20.0000	−	6.92820i	0.730784	−	0.253151i
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$		0			0
$753$	27.7128	+	16.0000i	1.00991	+	0.583072i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			34.0000i			1.23575i	0.786276	+	0.617876i	$0.212006\pi$
$757$			34.0000i			1.23575i	−0.786276	+	0.617876i	$0.787994\pi$
$758$		0			0
$759$	12.0000	−	20.7846i	0.435572	−	0.754434i
$760$		0			0
$761$	21.5000	+	37.2391i	0.779374	+	1.34992i	0.932303	+	0.361679i	$0.117796\pi$
$761$	21.5000	+	37.2391i	0.779374	+	1.34992i	−0.152928	+	0.988237i	$0.548870\pi$
$762$		0			0
$763$	24.2487	−	28.0000i	0.877862	−	1.01367i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.8564	−	8.00000i	−0.500326	−	0.288863i
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	36.0000			1.29651
$772$		0			0
$773$	17.3205	+	10.0000i	0.622975	+	0.359675i	0.778027	−	0.628231i	$-0.216221\pi$
$773$	17.3205	+	10.0000i	0.622975	+	0.359675i	−0.155051	+	0.987906i	$0.549554\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−22.0000	+	38.1051i	−0.787222	+	1.36351i
$782$		0			0
$783$			24.0000i			0.857690i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	6.92820	+	4.00000i	0.246964	+	0.142585i	0.618373	−	0.785885i	$-0.287792\pi$
$787$	6.92820	+	4.00000i	0.246964	+	0.142585i	−0.371409	+	0.928469i	$0.621125\pi$
$788$		0			0
$789$	−3.00000	−	5.19615i	−0.106803	−	0.184988i
$790$		0			0
$791$	7.50000	−	38.9711i	0.266669	−	1.38565i
$792$		0			0
$793$	−13.8564	+	8.00000i	−0.492055	+	0.284088i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$		0			0
$799$	27.0000			0.955191
$800$		0			0
$801$	−5.50000	+	9.52628i	−0.194333	+	0.336595i
$802$		0			0
$803$	−6.92820	+	4.00000i	−0.244491	+	0.141157i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.46410	−	2.00000i	0.121942	−	0.0704033i
$808$		0			0
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	−0.764644	−	0.644453i	$-0.777085\pi$
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	0.940435	+	0.339975i	$0.110418\pi$
$810$		0			0
$811$	−10.0000			−0.351147			−0.175574	−	0.984466i	$-0.556178\pi$
$811$	−10.0000			−0.351147			−0.175574	+	0.984466i	$0.556178\pi$
$812$		0			0
$813$			14.0000i			0.491001i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−5.00000	+	1.73205i	−0.174714	+	0.0605228i
$820$		0			0
$821$	−10.0000	−	17.3205i	−0.349002	−	0.604490i	0.637070	−	0.770806i	$-0.280146\pi$
$821$	−10.0000	−	17.3205i	−0.349002	−	0.604490i	−0.986073	+	0.166316i	$0.946813\pi$
$822$		0			0
$823$	3.46410	+	2.00000i	0.120751	+	0.0697156i	0.559159	−	0.829060i	$-0.311124\pi$
$823$	3.46410	+	2.00000i	0.120751	+	0.0697156i	−0.438408	+	0.898776i	$0.644457\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	14.0000i		−	0.486828i	−0.969923	−	0.243414i	$-0.921733\pi$
$827$		−	14.0000i		−	0.486828i	0.969923	−	0.243414i	$-0.0782673\pi$
$828$		0			0
$829$	−16.0000	+	27.7128i	−0.555703	+	0.962506i	0.442145	+	0.896943i	$0.354217\pi$
$829$	−16.0000	+	27.7128i	−0.555703	+	0.962506i	−0.997848	+	0.0655624i	$0.979116\pi$
$830$		0			0
$831$	−8.00000	−	13.8564i	−0.277517	−	0.480673i
$832$		0			0
$833$	−12.9904	−	16.5000i	−0.450090	−	0.571691i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−31.1769	−	18.0000i	−1.07763	−	0.622171i
$838$		0			0
$839$	29.0000			1.00119			0.500596	−	0.865681i	$-0.333114\pi$
$839$	29.0000			1.00119			0.500596	+	0.865681i	$0.333114\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	22.5167	+	13.0000i	0.775515	+	0.447744i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	4.33013	+	12.5000i	0.148785	+	0.429505i
$848$		0			0
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	19.0526	+	11.0000i	0.650823	+	0.375753i	0.788771	−	0.614687i	$-0.210717\pi$
$857$	19.0526	+	11.0000i	0.650823	+	0.375753i	−0.137948	+	0.990439i	$0.544051\pi$
$858$		0			0
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$		0			0
$861$	20.0000	+	17.3205i	0.681598	+	0.590281i
$862$		0			0
$863$	−6.06218	+	3.50000i	−0.206359	+	0.119141i	−0.599618	−	0.800286i	$-0.704681\pi$
$863$	−6.06218	+	3.50000i	−0.206359	+	0.119141i	0.393259	+	0.919428i	$0.371348\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			16.0000i			0.543388i
$868$		0			0
$869$	−36.0000			−1.22122
$870$		0			0
$871$	14.0000	−	24.2487i	0.474372	−	0.821636i
$872$		0			0
$873$	−9.52628	+	5.50000i	−0.322416	+	0.186147i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.46410	−	2.00000i	0.116974	−	0.0675352i	−0.440371	−	0.897816i	$-0.645153\pi$
$877$	3.46410	−	2.00000i	0.116974	−	0.0675352i	0.557346	+	0.830281i	$0.311820\pi$
$878$		0			0
$879$	14.0000	−	24.2487i	0.472208	−	0.817889i
$880$		0			0
$881$	−37.0000			−1.24656			−0.623281	−	0.781998i	$-0.714201\pi$
$881$	−37.0000			−1.24656			−0.623281	+	0.781998i	$0.714201\pi$
$882$		0			0
$883$			2.00000i			0.0673054i	0.999434	+	0.0336527i	$0.0107140\pi$
$883$			2.00000i			0.0673054i	−0.999434	+	0.0336527i	$0.989286\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.3205	−	10.0000i	0.581566	−	0.335767i	−0.180190	−	0.983632i	$-0.557671\pi$
$887$	17.3205	−	10.0000i	0.581566	−	0.335767i	0.761755	+	0.647865i	$0.224338\pi$
$888$		0			0
$889$	−4.00000	+	20.7846i	−0.134156	+	0.697093i
$890$		0			0
$891$	22.0000	+	38.1051i	0.737028	+	1.27657i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$			12.0000i			0.400668i
$898$		0			0
$899$	−27.0000	+	46.7654i	−0.900500	+	1.55971i
$900$		0			0
$901$	−9.00000	−	15.5885i	−0.299833	−	0.519327i
$902$		0			0
$903$	20.7846	−	24.0000i	0.691669	−	0.798670i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	0.317441	−	0.948278i	$-0.397176\pi$
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	−0.662512	+	0.749051i	$0.730510\pi$
$908$		0			0
$909$	8.00000			0.265343
$910$		0			0
$911$	47.0000			1.55718			0.778590	−	0.627533i	$-0.215935\pi$
$911$	47.0000			1.55718			0.778590	+	0.627533i	$0.215935\pi$
$912$		0			0
$913$	20.7846	+	12.0000i	0.687870	+	0.397142i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.3923	+	30.0000i	0.343184	+	0.990687i
$918$		0			0
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	0.917961	−	0.396670i	$-0.129834\pi$
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	−0.802507	+	0.596643i	$0.796501\pi$
$920$		0			0
$921$	24.0000	−	41.5692i	0.790827	−	1.36975i
$922$		0			0
$923$		−	22.0000i		−	0.724139i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	12.9904	+	7.50000i	0.426660	+	0.246332i
$928$		0			0
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.73205	−	1.00000i	0.0567048	−	0.0327385i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$		0			0
$939$	62.0000			2.02329
$940$		0			0
$941$	13.0000	−	22.5167i	0.423788	−	0.734022i	−0.572518	−	0.819892i	$-0.694034\pi$
$941$	13.0000	−	22.5167i	0.423788	−	0.734022i	0.996306	+	0.0858697i	$0.0273669\pi$
$942$		0			0
$943$	12.9904	−	7.50000i	0.423025	−	0.244234i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	−0.442659	−	0.896690i	$-0.645965\pi$
$947$	3.46410	−	2.00000i	0.112568	−	0.0649913i	0.555227	+	0.831699i	$0.312631\pi$
$948$		0			0
$949$	2.00000	−	3.46410i	0.0649227	−	0.112449i
$950$		0			0
$951$	−24.0000			−0.778253
$952$		0			0
$953$		−	10.0000i		−	0.323932i	−0.986796	−	0.161966i	$-0.948217\pi$
$953$		−	10.0000i		−	0.323932i	0.986796	−	0.161966i	$-0.0517835\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	41.5692	−	24.0000i	1.34374	−	0.775810i
$958$		0			0
$959$	−34.0000	−	29.4449i	−1.09792	−	0.950824i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$		0			0
$963$	−6.92820	−	4.00000i	−0.223258	−	0.128898i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	13.0000i		−	0.418052i	−0.977910	−	0.209026i	$-0.932971\pi$
$967$		−	13.0000i		−	0.418052i	0.977910	−	0.209026i	$-0.0670293\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	0.633768	−	0.773523i	$-0.281507\pi$
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	−0.986775	+	0.162098i	$0.948174\pi$
$972$		0			0
$973$	−15.5885	−	3.00000i	−0.499743	−	0.0961756i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	0.457864	−	0.889022i	$-0.348615\pi$
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	−0.540984	+	0.841033i	$0.681948\pi$
$978$		0			0
$979$	−44.0000			−1.40625
$980$		0			0
$981$	−14.0000			−0.446986
$982$		0			0
$983$	−41.5692	−	24.0000i	−1.32585	−	0.765481i	−0.341197	−	0.939992i	$-0.610832\pi$
$983$	−41.5692	−	24.0000i	−1.32585	−	0.765481i	−0.984655	+	0.174511i	$0.944166\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−46.7654	−	9.00000i	−1.48856	−	0.286473i
$988$		0			0
$989$	−9.00000	−	15.5885i	−0.286183	−	0.495684i
$990$		0			0
$991$	15.5000	−	26.8468i	0.492374	−	0.852816i	−0.507588	−	0.861600i	$-0.669463\pi$
$991$	15.5000	−	26.8468i	0.492374	−	0.852816i	0.999961	+	0.00878379i	$0.00279600\pi$
$992$		0			0
$993$		−	4.00000i		−	0.126936i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	38.1051	+	22.0000i	1.20680	+	0.696747i	0.962059	−	0.272841i	$-0.0879634\pi$
$997$	38.1051	+	22.0000i	1.20680	+	0.696747i	0.244742	+	0.969588i	$0.421297\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.d.249.1		4
5.2	odd	4		1400.2.q.b.1201.1	yes	2
5.3	odd	4		1400.2.q.f.1201.1	yes	2
5.4	even	2	inner	1400.2.bh.d.249.2		4
7.2	even	3	inner	1400.2.bh.d.849.2		4
35.2	odd	12		1400.2.q.b.401.1	✓	2
35.3	even	12		9800.2.a.bl.1.1		1
35.9	even	6	inner	1400.2.bh.d.849.1		4
35.17	even	12		9800.2.a.k.1.1		1
35.18	odd	12		9800.2.a.j.1.1		1
35.23	odd	12		1400.2.q.f.401.1	yes	2
35.32	odd	12		9800.2.a.bm.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.b.401.1	✓	2	35.2	odd	12
1400.2.q.b.1201.1	yes	2	5.2	odd	4
1400.2.q.f.401.1	yes	2	35.23	odd	12
1400.2.q.f.1201.1	yes	2	5.3	odd	4
1400.2.bh.d.249.1		4	1.1	even	1	trivial
1400.2.bh.d.249.2		4	5.4	even	2	inner
1400.2.bh.d.849.1		4	35.9	even	6	inner
1400.2.bh.d.849.2		4	7.2	even	3	inner
9800.2.a.j.1.1		1	35.18	odd	12
9800.2.a.k.1.1		1	35.17	even	12
9800.2.a.bl.1.1		1	35.3	even	12
9800.2.a.bm.1.1		1	35.32	odd	12

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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{3} +(-2.59808 - 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.00000i) q^{3} +(-2.59808 - 0.500000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} -2.00000i q^{13} +(-2.59808 - 1.50000i) q^{17} +(4.00000 + 3.46410i) q^{21} +(2.59808 - 1.50000i) q^{23} +4.00000i q^{27} +6.00000 q^{29} +(-4.50000 + 7.79423i) q^{31} +(6.92820 - 4.00000i) q^{33} +(-2.00000 + 3.46410i) q^{39} +5.00000 q^{41} -6.00000i q^{43} +(-7.79423 + 4.50000i) q^{47} +(6.50000 + 2.59808i) q^{49} +(3.00000 + 5.19615i) q^{51} +(5.19615 + 3.00000i) q^{53} +(4.00000 - 6.92820i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-0.866025 - 2.50000i) q^{63} +(12.1244 + 7.00000i) q^{67} -6.00000 q^{69} +11.0000 q^{71} +(1.73205 + 1.00000i) q^{73} +(6.92820 - 8.00000i) q^{77} +(4.50000 + 7.79423i) q^{79} +(5.50000 - 9.52628i) q^{81} -6.00000i q^{83} +(-10.3923 - 6.00000i) q^{87} +(5.50000 + 9.52628i) q^{89} +(-1.00000 + 5.19615i) q^{91} +(15.5885 - 9.00000i) q^{93} +11.0000i q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} - 8 q^{11} + 16 q^{21} + 24 q^{29} - 18 q^{31} - 8 q^{39} + 20 q^{41} + 26 q^{49} + 12 q^{51} + 16 q^{59} - 16 q^{61} - 24 q^{69} + 44 q^{71} + 18 q^{79} + 22 q^{81} + 22 q^{89} - 4 q^{91} - 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^9 - 8 * q^11 + 16 * q^21 + 24 * q^29 - 18 * q^31 - 8 * q^39 + 20 * q^41 + 26 * q^49 + 12 * q^51 + 16 * q^59 - 16 * q^61 - 24 * q^69 + 44 * q^71 + 18 * q^79 + 22 * q^81 + 22 * q^89 - 4 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more