LMFDB - Embedded newform 1400.2.q.b.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(401,1400)]

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, 0, 2]))

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

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

chi := DirichletCharacter("1400.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Embedding invariants

Embedding label			401.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1400.401
Dual form			1400.2.q.b.1201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{11} -2.00000 q^{13} +(1.50000 + 2.59808i) q^{17} +(4.00000 - 3.46410i) q^{21} +(-1.50000 + 2.59808i) q^{23} -4.00000 q^{27} -6.00000 q^{29} +(-4.50000 - 7.79423i) q^{31} +(-4.00000 + 6.92820i) q^{33} +(2.00000 + 3.46410i) q^{39} +5.00000 q^{41} -6.00000 q^{43} +(-4.50000 + 7.79423i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} +(-4.00000 - 6.92820i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(-2.50000 - 0.866025i) q^{63} +(-7.00000 - 12.1244i) q^{67} +6.00000 q^{69} +11.0000 q^{71} +(1.00000 + 1.73205i) q^{73} +(8.00000 - 6.92820i) q^{77} +(-4.50000 + 7.79423i) q^{79} +(5.50000 + 9.52628i) q^{81} -6.00000 q^{83} +(6.00000 + 10.3923i) q^{87} +(-5.50000 + 9.52628i) q^{89} +(-1.00000 - 5.19615i) q^{91} +(-9.00000 + 15.5885i) q^{93} -11.0000 q^{97} +4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + q^7 - q^9	$ 2 q - 2 q^{3} + q^{7} - q^{9} - 4 q^{11} - 4 q^{13} + 3 q^{17} + 8 q^{21} - 3 q^{23} - 8 q^{27} - 12 q^{29} - 9 q^{31} - 8 q^{33} + 4 q^{39} + 10 q^{41} - 12 q^{43} - 9 q^{47} - 13 q^{49} + 6 q^{51} + 6 q^{53} - 8 q^{59} - 8 q^{61} - 5 q^{63} - 14 q^{67} + 12 q^{69} + 22 q^{71} + 2 q^{73} + 16 q^{77} - 9 q^{79} + 11 q^{81} - 12 q^{83} + 12 q^{87} - 11 q^{89} - 2 q^{91} - 18 q^{93} - 22 q^{97} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + q^7 - q^9 - 4 * q^11 - 4 * q^13 + 3 * q^17 + 8 * q^21 - 3 * q^23 - 8 * q^27 - 12 * q^29 - 9 * q^31 - 8 * q^33 + 4 * q^39 + 10 * q^41 - 12 * q^43 - 9 * q^47 - 13 * q^49 + 6 * q^51 + 6 * q^53 - 8 * q^59 - 8 * q^61 - 5 * q^63 - 14 * q^67 + 12 * q^69 + 22 * q^71 + 2 * q^73 + 16 * q^77 - 9 * q^79 + 11 * q^81 - 12 * q^83 + 12 * q^87 - 11 * q^89 - 2 * q^91 - 18 * q^93 - 22 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$	4.00000	−	3.46410i	0.872872	−	0.755929i
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−4.50000	−	7.79423i	−0.808224	−	1.39988i	−0.914093	−	0.405505i	$-0.867096\pi$
$31$	−4.50000	−	7.79423i	−0.808224	−	1.39988i	0.105869	−	0.994380i	$-0.466238\pi$
$32$		0			0
$33$	−4.00000	+	6.92820i	−0.696311	+	1.20605i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$		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
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	0.325150	+	0.945662i	$0.394585\pi$
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	−0.981543	+	0.191243i	$0.938748\pi$
$48$		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
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		0			0
$63$	−2.50000	−	0.866025i	−0.314970	−	0.109109i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$		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
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.00000	−	6.92820i	0.911685	−	0.789542i
$78$		0			0
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	0.493684	+	0.869641i	$0.335650\pi$
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	−0.999974	+	0.00727784i	$0.997683\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$		0			0
$89$	−5.50000	+	9.52628i	−0.582999	+	1.00978i	0.412123	+	0.911128i	$0.364787\pi$
$89$	−5.50000	+	9.52628i	−0.582999	+	1.00978i	−0.995122	+	0.0986553i	$0.968546\pi$
$90$		0			0
$91$	−1.00000	−	5.19615i	−0.104828	−	0.544705i
$92$		0			0
$93$	−9.00000	+	15.5885i	−0.933257	+	1.61645i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.0000			−1.11688			−0.558440	−	0.829545i	$-0.688600\pi$
$97$	−11.0000			−1.11688			−0.558440	+	0.829545i	$0.688600\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$		0			0
$103$	−7.50000	+	12.9904i	−0.738997	+	1.27998i	0.213950	+	0.976845i	$0.431367\pi$
$103$	−7.50000	+	12.9904i	−0.738997	+	1.27998i	−0.952947	+	0.303136i	$0.901966\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	−0.992003	−	0.126217i	$-0.959717\pi$
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	0.605308	+	0.795991i	$0.293050\pi$
$108$		0			0
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$		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
$123$	−5.00000	−	8.66025i	−0.450835	−	0.780869i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	6.00000	+	10.3923i	0.528271	+	0.914991i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.50000	−	14.7224i	−0.726204	−	1.25782i	−0.958477	−	0.285171i	$-0.907949\pi$
$137$	−8.50000	−	14.7224i	−0.726204	−	1.25782i	0.232273	−	0.972651i	$-0.425384\pi$
$138$		0			0
$139$	−6.00000			−0.508913			−0.254457	−	0.967084i	$-0.581897\pi$
$139$	−6.00000			−0.508913			−0.254457	+	0.967084i	$0.581897\pi$
$140$		0			0
$141$	18.0000			1.51587
$142$		0			0
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	11.0000	+	8.66025i	0.907265	+	0.714286i
$148$		0			0
$149$	10.0000	−	17.3205i	0.819232	−	1.41895i	−0.0870170	−	0.996207i	$-0.527733\pi$
$149$	10.0000	−	17.3205i	0.819232	−	1.41895i	0.906249	−	0.422744i	$-0.138933\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	−0.910195	−	0.414181i	$-0.864068\pi$
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	0.0964061	−	0.995342i	$-0.469265\pi$
$152$		0			0
$153$	−3.00000			−0.242536
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$		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
$163$	12.0000	−	20.7846i	0.939913	−	1.62798i	0.174282	−	0.984696i	$-0.444240\pi$
$163$	12.0000	−	20.7846i	0.939913	−	1.62798i	0.765631	−	0.643280i	$-0.222427\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.00000	+	13.8564i	−0.608229	+	1.05348i	0.383304	+	0.923622i	$0.374786\pi$
$173$	−8.00000	+	13.8564i	−0.608229	+	1.05348i	−0.991532	+	0.129861i	$0.958547\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.00000	+	13.8564i	−0.601317	+	1.04151i
$178$		0			0
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$		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
$183$	16.0000			1.18275
$184$		0			0
$185$		0			0
$186$		0			0
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$		0			0
$189$	−2.00000	−	10.3923i	−0.145479	−	0.755929i
$190$		0			0
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	−0.529101	−	0.848559i	$-0.677471\pi$
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	0.999424	+	0.0339349i	$0.0108039\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	−0.950509	−	0.310696i	$-0.899438\pi$
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	0.206184	−	0.978513i	$-0.433895\pi$
$200$		0			0
$201$	−14.0000	+	24.2487i	−0.987484	+	1.71037i
$202$		0			0
$203$	−3.00000	−	15.5885i	−0.210559	−	1.09410i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.50000	−	2.59808i	−0.104257	−	0.180579i
$208$		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
$213$	−11.0000	−	19.0526i	−0.753708	−	1.30546i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	18.0000	−	15.5885i	1.22192	−	1.05821i
$218$		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
$223$	11.0000			0.736614			0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000			0.736614			0.368307	+	0.929704i	$0.379937\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.0000	+	19.0526i	0.730096	+	1.26456i	0.956842	+	0.290609i	$0.0938578\pi$
$227$	11.0000	+	19.0526i	0.730096	+	1.26456i	−0.226746	+	0.973954i	$0.572809\pi$
$228$		0			0
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	−0.703060	−	0.711131i	$-0.748183\pi$
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	0.967387	+	0.253302i	$0.0815167\pi$
$230$		0			0
$231$	−20.0000	−	6.92820i	−1.31590	−	0.455842i
$232$		0			0
$233$	11.0000	−	19.0526i	0.720634	−	1.24817i	−0.240112	−	0.970745i	$-0.577184\pi$
$233$	11.0000	−	19.0526i	0.720634	−	1.24817i	0.960746	−	0.277429i	$-0.0894825\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	18.0000			1.16923
$238$		0			0
$239$	11.0000			0.711531			0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000			0.711531			0.355765	+	0.934575i	$0.384220\pi$
$240$		0			0
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$		0			0
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$		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
$253$	12.0000			0.754434
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	0.908560	−	0.417755i	$-0.137183\pi$
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	−0.816066	+	0.577959i	$0.803849\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	22.0000			1.34638
$268$		0			0
$269$	1.00000	+	1.73205i	0.0609711	+	0.105605i	0.894900	−	0.446267i	$-0.147247\pi$
$269$	1.00000	+	1.73205i	0.0609711	+	0.105605i	−0.833929	+	0.551872i	$0.813914\pi$
$270$		0			0
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	−0.952531	−	0.304443i	$-0.901530\pi$
$271$	−3.50000	+	6.06218i	−0.212610	+	0.368251i	0.739921	+	0.672694i	$0.234863\pi$
$272$		0			0
$273$	−8.00000	+	6.92820i	−0.484182	+	0.419314i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$		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
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	0.834772	−	0.550596i	$-0.185599\pi$
$283$	−1.00000	−	1.73205i	−0.0594438	−	0.102960i	−0.894216	+	0.447636i	$0.852266\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.50000	+	12.9904i	0.147570	+	0.766798i
$288$		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
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	8.00000	+	13.8564i	0.464207	+	0.804030i
$298$		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
$303$	8.00000	−	13.8564i	0.459588	−	0.796030i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−24.0000			−1.36975			−0.684876	−	0.728659i	$-0.740144\pi$
$307$	−24.0000			−1.36975			−0.684876	+	0.728659i	$0.740144\pi$
$308$		0			0
$309$	30.0000			1.70664
$310$		0			0
$311$	−0.500000	−	0.866025i	−0.0283524	−	0.0491078i	0.851501	−	0.524353i	$-0.175693\pi$
$311$	−0.500000	−	0.866025i	−0.0283524	−	0.0491078i	−0.879853	+	0.475245i	$0.842359\pi$
$312$		0			0
$313$	15.5000	−	26.8468i	0.876112	−	1.51747i	0.0205381	−	0.999789i	$-0.493462\pi$
$313$	15.5000	−	26.8468i	0.876112	−	1.51747i	0.855574	−	0.517681i	$-0.173205\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$		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
$327$	14.0000	−	24.2487i	0.774202	−	1.34096i
$328$		0			0
$329$	−22.5000	−	7.79423i	−1.24047	−	0.429710i
$330$		0			0
$331$	1.00000	−	1.73205i	0.0549650	−	0.0952021i	−0.837234	−	0.546845i	$-0.815829\pi$
$331$	1.00000	−	1.73205i	0.0549650	−	0.0952021i	0.892199	+	0.451643i	$0.149162\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−29.0000			−1.57973			−0.789865	−	0.613280i	$-0.789850\pi$
$337$	−29.0000			−1.57973			−0.789865	+	0.613280i	$0.789850\pi$
$338$		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
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	0.837935	−	0.545770i	$-0.183763\pi$
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	−0.891618	+	0.452788i	$0.850429\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$		0			0
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	15.0000	+	5.19615i	0.793884	+	0.275010i
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$		0			0
$363$	10.0000			0.524864
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$		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
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$	−8.00000	−	13.8564i	−0.409852	−	0.709885i
$382$		0			0
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$		0			0
$389$	−17.0000	−	29.4449i	−0.861934	−	1.49291i	−0.870059	−	0.492947i	$-0.835920\pi$
$389$	−17.0000	−	29.4449i	−0.861934	−	1.49291i	0.00812520	−	0.999967i	$-0.497414\pi$
$390$		0			0
$391$	−9.00000			−0.455150
$392$		0			0
$393$	24.0000			1.21064
$394$		0			0
$395$		0			0
$396$		0			0
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.216004	−	0.976392i	$-0.430698\pi$
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.737579	−	0.675261i	$-0.235969\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$	9.00000	+	15.5885i	0.448322	+	0.776516i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	0.939490	+	0.342578i	$0.111300\pi$
$409$	15.5000	+	26.8468i	0.766426	+	1.32749i	−0.173064	+	0.984911i	$0.555367\pi$
$410$		0			0
$411$	−17.0000	+	29.4449i	−0.838548	+	1.45241i
$412$		0			0
$413$	16.0000	−	13.8564i	0.787309	−	0.681829i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6.00000	+	10.3923i	0.293821	+	0.508913i
$418$		0			0
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$		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
$423$	−4.50000	−	7.79423i	−0.218797	−	0.378968i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−20.0000	−	6.92820i	−0.967868	−	0.335279i
$428$		0			0
$429$	8.00000	−	13.8564i	0.386244	−	0.668994i
$430$		0			0
$431$	15.5000	+	26.8468i	0.746609	+	1.29316i	0.949439	+	0.313950i	$0.101653\pi$
$431$	15.5000	+	26.8468i	0.746609	+	1.29316i	−0.202831	+	0.979214i	$0.565014\pi$
$432$		0			0
$433$	21.0000			1.00920			0.504598	−	0.863355i	$-0.331641\pi$
$433$	21.0000			1.00920			0.504598	+	0.863355i	$0.331641\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	0.0586141	+	0.998281i	$0.481332\pi$
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	−0.893843	+	0.448379i	$0.852001\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−40.0000			−1.89194
$448$		0			0
$449$	−27.0000			−1.27421			−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000			−1.27421			−0.637104	+	0.770778i	$0.719868\pi$
$450$		0			0
$451$	−10.0000	−	17.3205i	−0.470882	−	0.815591i
$452$		0			0
$453$	−20.0000	+	34.6410i	−0.939682	+	1.62758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	−0.888466	−	0.458942i	$-0.848229\pi$
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	0.841688	+	0.539964i	$0.181562\pi$
$458$		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
$463$	11.0000			0.511213			0.255607	−	0.966781i	$-0.417725\pi$
$463$	11.0000			0.511213			0.255607	+	0.966781i	$0.417725\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	15.0000	−	25.9808i	0.694117	−	1.20225i	−0.276360	−	0.961054i	$-0.589128\pi$
$467$	15.0000	−	25.9808i	0.694117	−	1.20225i	0.970477	−	0.241192i	$-0.0775384\pi$
$468$		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
$473$	12.0000	+	20.7846i	0.551761	+	0.955677i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.00000			−0.274721
$478$		0			0
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	0.744717	−	0.667381i	$-0.232585\pi$
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	−0.950327	+	0.311253i	$0.899251\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	3.00000	+	15.5885i	0.136505	+	0.709299i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$		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
$493$	−9.00000	−	15.5885i	−0.405340	−	0.702069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.50000	+	28.5788i	0.246709	+	1.28194i
$498$		0			0
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	0.0301498	+	0.999545i	$0.490402\pi$
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	−0.880707	+	0.473662i	$0.842932\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	9.00000	+	15.5885i	0.399704	+	0.692308i
$508$		0			0
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	−0.967811	−	0.251679i	$-0.919017\pi$
$509$	−6.00000	+	10.3923i	−0.265945	+	0.460631i	0.701866	+	0.712309i	$0.252351\pi$
$510$		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
$517$	36.0000			1.58328
$518$		0			0
$519$	32.0000			1.40464
$520$		0			0
$521$	−22.5000	−	38.9711i	−0.985743	−	1.70736i	−0.638588	−	0.769549i	$-0.720481\pi$
$521$	−22.5000	−	38.9711i	−0.985743	−	1.70736i	−0.347155	−	0.937808i	$-0.612852\pi$
$522$		0			0
$523$	−11.0000	+	19.0526i	−0.480996	+	0.833110i	−0.999762	−	0.0218062i	$-0.993058\pi$
$523$	−11.0000	+	19.0526i	−0.480996	+	0.833110i	0.518766	+	0.854916i	$0.326392\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.5000	−	23.3827i	0.588069	−	1.01857i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	8.00000			0.347170
$532$		0			0
$533$	−10.0000			−0.433148
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.00000	+	6.92820i	−0.172613	+	0.298974i
$538$		0			0
$539$	22.0000	+	17.3205i	0.947607	+	0.746047i
$540$		0			0
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	−0.339424	−	0.940633i	$-0.610232\pi$
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	0.984325	−	0.176367i	$-0.0564345\pi$
$542$		0			0
$543$	8.00000	+	13.8564i	0.343313	+	0.594635i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−40.0000			−1.71028			−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000			−1.71028			−0.855138	+	0.518400i	$0.826528\pi$
$548$		0			0
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−22.5000	−	7.79423i	−0.956797	−	0.331444i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.0000	+	31.1769i	0.762684	+	1.32101i	0.941462	+	0.337119i	$0.109452\pi$
$557$	18.0000	+	31.1769i	0.762684	+	1.32101i	−0.178778	+	0.983890i	$0.557214\pi$
$558$		0			0
$559$	12.0000			0.507546
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	0.998419	+	0.0562051i	$0.0179001\pi$
$563$	13.0000	+	22.5167i	0.547885	+	0.948964i	−0.450535	+	0.892759i	$0.648767\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−22.0000	+	19.0526i	−0.923913	+	0.800132i
$568$		0			0
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	−0.727405	−	0.686209i	$-0.759274\pi$
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	0.957977	+	0.286846i	$0.0926069\pi$
$570$		0			0
$571$	6.00000	+	10.3923i	0.251092	+	0.434904i	0.963827	−	0.266529i	$-0.0858769\pi$
$571$	6.00000	+	10.3923i	0.251092	+	0.434904i	−0.712735	+	0.701434i	$0.752544\pi$
$572$		0			0
$573$	−26.0000			−1.08617
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	0.682730	−	0.730670i	$-0.260792\pi$
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	−0.974144	+	0.225927i	$0.927459\pi$
$578$		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
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.00000			0.330195			0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000			0.330195			0.165098	+	0.986277i	$0.447206\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	18.0000	+	31.1769i	0.740421	+	1.28245i
$592$		0			0
$593$	6.50000	−	11.2583i	0.266923	−	0.462324i	−0.701143	−	0.713021i	$-0.747326\pi$
$593$	6.50000	−	11.2583i	0.266923	−	0.462324i	0.968066	+	0.250697i	$0.0806597\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−21.0000	+	36.3731i	−0.859473	+	1.48865i
$598$		0			0
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	0.759328	−	0.650708i	$-0.225528\pi$
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	−0.943193	+	0.332244i	$0.892194\pi$
$600$		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
$603$	14.0000			0.570124
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$		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
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.0000			−0.684394			−0.342197	−	0.939628i	$-0.611171\pi$
$617$	−17.0000			−0.684394			−0.342197	+	0.939628i	$0.611171\pi$
$618$		0			0
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$		0			0
$621$	6.00000	−	10.3923i	0.240772	−	0.417029i
$622$		0			0
$623$	−27.5000	−	9.52628i	−1.10176	−	0.381662i
$624$		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
$633$	−22.0000	−	38.1051i	−0.874421	−	1.51454i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	13.0000	−	5.19615i	0.515079	−	0.205879i
$638$		0			0
$639$	−5.50000	+	9.52628i	−0.217577	+	0.376854i
$640$		0			0
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	0.971442	+	0.237276i	$0.0762547\pi$
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	−0.280234	+	0.959932i	$0.590412\pi$
$642$		0			0
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.758654	+	0.651494i	$0.225858\pi$
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.184884	+	0.982760i	$0.440809\pi$
$648$		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
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.00000			−0.0780274
$658$		0			0
$659$	14.0000			0.545363			0.272681	−	0.962104i	$-0.412090\pi$
$659$	14.0000			0.545363			0.272681	+	0.962104i	$0.412090\pi$
$660$		0			0
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	−0.875993	−	0.482323i	$-0.839793\pi$
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	0.0202925	−	0.999794i	$-0.493540\pi$
$662$		0			0
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$		0			0
$669$	−11.0000	−	19.0526i	−0.425285	−	0.736614i
$670$		0			0
$671$	32.0000			1.23535
$672$		0			0
$673$	−43.0000			−1.65753			−0.828764	−	0.559598i	$-0.810955\pi$
$673$	−43.0000			−1.65753			−0.828764	+	0.559598i	$0.810955\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$		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
$683$	7.00000	+	12.1244i	0.267848	+	0.463926i	0.968306	−	0.249768i	$-0.0803543\pi$
$683$	7.00000	+	12.1244i	0.267848	+	0.463926i	−0.700458	+	0.713693i	$0.747021\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−16.0000			−0.610438
$688$		0			0
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	−0.577325	−	0.816514i	$-0.695903\pi$
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	0.995785	+	0.0917209i	$0.0292368\pi$
$692$		0			0
$693$	2.00000	+	10.3923i	0.0759737	+	0.394771i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	7.50000	+	12.9904i	0.284083	+	0.492046i
$698$		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
$707$	−16.0000	+	13.8564i	−0.601742	+	0.521124i
$708$		0			0
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	−0.781086	−	0.624423i	$-0.785334\pi$
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	0.931309	+	0.364229i	$0.118667\pi$
$710$		0			0
$711$	−4.50000	−	7.79423i	−0.168763	−	0.292306i
$712$		0			0
$713$	27.0000			1.01116
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−11.0000	−	19.0526i	−0.410803	−	0.711531i
$718$		0			0
$719$	−14.5000	+	25.1147i	−0.540759	+	0.936622i	0.458102	+	0.888900i	$0.348529\pi$
$719$	−14.5000	+	25.1147i	−0.540759	+	0.936622i	−0.998861	+	0.0477220i	$0.984804\pi$
$720$		0			0
$721$	−37.5000	−	12.9904i	−1.39657	−	0.483787i
$722$		0			0
$723$	−18.0000	+	31.1769i	−0.669427	+	1.15948i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	29.0000			1.07555			0.537775	−	0.843088i	$-0.319265\pi$
$727$	29.0000			1.07555			0.537775	+	0.843088i	$0.319265\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−9.00000	−	15.5885i	−0.332877	−	0.576560i
$732$		0			0
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−28.0000	+	48.4974i	−1.03139	+	1.78643i
$738$		0			0
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−27.0000			−0.990534			−0.495267	−	0.868741i	$-0.664930\pi$
$743$	−27.0000			−0.990534			−0.495267	+	0.868741i	$0.664930\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$		0			0
$749$	−20.0000	−	6.92820i	−0.730784	−	0.253151i
$750$		0			0
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$		0			0
$753$	16.0000	+	27.7128i	0.583072	+	1.00991i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$		0			0
$759$	−12.0000	−	20.7846i	−0.435572	−	0.754434i
$760$		0			0
$761$	21.5000	−	37.2391i	0.779374	−	1.34992i	−0.152928	−	0.988237i	$-0.548870\pi$
$761$	21.5000	−	37.2391i	0.779374	−	1.34992i	0.932303	−	0.361679i	$-0.117796\pi$
$762$		0			0
$763$	−28.0000	+	24.2487i	−1.01367	+	0.877862i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.00000	+	13.8564i	0.288863	+	0.500326i
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	36.0000			1.29651
$772$		0			0
$773$	10.0000	+	17.3205i	0.359675	+	0.622975i	0.987906	−	0.155051i	$-0.0495542\pi$
$773$	10.0000	+	17.3205i	0.359675	+	0.622975i	−0.628231	+	0.778027i	$0.716221\pi$
$774$		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
$783$	24.0000			0.857690
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	0.785885	−	0.618373i	$-0.212208\pi$
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	−0.928469	+	0.371409i	$0.878875\pi$
$788$		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
$793$	8.00000	−	13.8564i	0.284088	−	0.492055i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$	−27.0000			−0.955191
$800$		0			0
$801$	−5.50000	−	9.52628i	−0.194333	−	0.336595i
$802$		0			0
$803$	4.00000	−	6.92820i	0.141157	−	0.244491i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.00000	−	3.46410i	0.0704033	−	0.121942i
$808$		0			0
$809$	−5.00000	−	8.66025i	−0.175791	−	0.304478i	0.764644	−	0.644453i	$-0.222915\pi$
$809$	−5.00000	−	8.66025i	−0.175791	−	0.304478i	−0.940435	+	0.339975i	$0.889582\pi$
$810$		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
$813$	14.0000			0.491001
$814$		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	−0.986073	−	0.166316i	$-0.946813\pi$
$821$	−10.0000	+	17.3205i	−0.349002	+	0.604490i	0.637070	+	0.770806i	$0.280146\pi$
$822$		0			0
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.0000			0.486828			0.243414	−	0.969923i	$-0.421733\pi$
$827$	14.0000			0.486828			0.243414	+	0.969923i	$0.421733\pi$
$828$		0			0
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	0.997848	+	0.0655624i	$0.0208842\pi$
$829$	16.0000	+	27.7128i	0.555703	+	0.962506i	−0.442145	+	0.896943i	$0.645783\pi$
$830$		0			0
$831$	−8.00000	+	13.8564i	−0.277517	+	0.480673i
$832$		0			0
$833$	−16.5000	−	12.9904i	−0.571691	−	0.450090i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	18.0000	+	31.1769i	0.622171	+	1.07763i
$838$		0			0
$839$	−29.0000			−1.00119			−0.500596	−	0.865681i	$-0.666886\pi$
$839$	−29.0000			−1.00119			−0.500596	+	0.865681i	$0.666886\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	13.0000	+	22.5167i	0.447744	+	0.775515i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.5000	−	4.33013i	−0.429505	−	0.148785i
$848$		0			0
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−38.0000			−1.30110			−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000			−1.30110			−0.650548	+	0.759465i	$0.725461\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	0.614687	−	0.788771i	$-0.289283\pi$
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	−0.990439	+	0.137948i	$0.955949\pi$
$858$		0			0
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$		0			0
$861$	20.0000	−	17.3205i	0.681598	−	0.590281i
$862$		0			0
$863$	3.50000	−	6.06218i	0.119141	−	0.206359i	−0.800286	−	0.599618i	$-0.795319\pi$
$863$	3.50000	−	6.06218i	0.119141	−	0.206359i	0.919428	+	0.393259i	$0.128652\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−16.0000			−0.543388
$868$		0			0
$869$	36.0000			1.22122
$870$		0			0
$871$	14.0000	+	24.2487i	0.474372	+	0.821636i
$872$		0			0
$873$	5.50000	−	9.52628i	0.186147	−	0.322416i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.00000	−	3.46410i	0.0675352	−	0.116974i	−0.830281	−	0.557346i	$-0.811820\pi$
$877$	2.00000	−	3.46410i	0.0675352	−	0.116974i	0.897816	+	0.440371i	$0.145153\pi$
$878$		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
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	−0.647865	−	0.761755i	$-0.724338\pi$
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	0.983632	+	0.180190i	$0.0576711\pi$
$888$		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
$897$	−12.0000			−0.400668
$898$		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
$903$	−24.0000	+	20.7846i	−0.798670	+	0.691669i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$		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
$913$	12.0000	+	20.7846i	0.397142	+	0.687870i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−30.0000	−	10.3923i	−0.990687	−	0.343184i
$918$		0			0
$919$	−3.50000	+	6.06218i	−0.115454	+	0.199973i	−0.917961	−	0.396670i	$-0.870166\pi$
$919$	−3.50000	+	6.06218i	−0.115454	+	0.199973i	0.802507	+	0.596643i	$0.203499\pi$
$920$		0			0
$921$	24.0000	+	41.5692i	0.790827	+	1.36975i
$922$		0			0
$923$	−22.0000			−0.724139
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−7.50000	−	12.9904i	−0.246332	−	0.426660i
$928$		0			0
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.00000	+	1.73205i	−0.0327385	+	0.0567048i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	−62.0000			−2.02329
$940$		0			0
$941$	13.0000	+	22.5167i	0.423788	+	0.734022i	0.996306	−	0.0858697i	$-0.0273669\pi$
$941$	13.0000	+	22.5167i	0.423788	+	0.734022i	−0.572518	+	0.819892i	$0.694034\pi$
$942$		0			0
$943$	−7.50000	+	12.9904i	−0.244234	+	0.423025i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	−24.0000			−0.778253
$952$		0			0
$953$	−10.0000			−0.323932			−0.161966	−	0.986796i	$-0.551783\pi$
$953$	−10.0000			−0.323932			−0.161966	+	0.986796i	$0.551783\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	24.0000	−	41.5692i	0.775810	−	1.34374i
$958$		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
$963$	−4.00000	−	6.92820i	−0.128898	−	0.223258i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	13.0000			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−11.0000	+	19.0526i	−0.353007	+	0.611426i	−0.986775	−	0.162098i	$-0.948174\pi$
$971$	−11.0000	+	19.0526i	−0.353007	+	0.611426i	0.633768	+	0.773523i	$0.281507\pi$
$972$		0			0
$973$	−3.00000	−	15.5885i	−0.0961756	−	0.499743i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	0.889022	−	0.457864i	$-0.151385\pi$
$977$	1.50000	+	2.59808i	0.0479893	+	0.0831198i	−0.841033	+	0.540984i	$0.818052\pi$
$978$		0			0
$979$	44.0000			1.40625
$980$		0			0
$981$	−14.0000			−0.446986
$982$		0			0
$983$	−24.0000	−	41.5692i	−0.765481	−	1.32585i	−0.939992	−	0.341197i	$-0.889168\pi$
$983$	−24.0000	−	41.5692i	−0.765481	−	1.32585i	0.174511	−	0.984655i	$-0.444166\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	9.00000	+	46.7654i	0.286473	+	1.48856i
$988$		0			0
$989$	9.00000	−	15.5885i	0.286183	−	0.495684i
$990$		0			0
$991$	15.5000	+	26.8468i	0.492374	+	0.852816i	0.999961	−	0.00878379i	$-0.00279600\pi$
$991$	15.5000	+	26.8468i	0.492374	+	0.852816i	−0.507588	+	0.861600i	$0.669463\pi$
$992$		0			0
$993$	−4.00000			−0.126936
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−22.0000	−	38.1051i	−0.696747	−	1.20680i	−0.969588	−	0.244742i	$-0.921297\pi$
$997$	−22.0000	−	38.1051i	−0.696747	−	1.20680i	0.272841	−	0.962059i	$-0.412037\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.b.401.1	✓	2	1.1	even	1	trivial
1400.2.q.b.1201.1	yes	2	7.4	even	3	inner
1400.2.q.f.401.1	yes	2	5.4	even	2
1400.2.q.f.1201.1	yes	2	35.4	even	6
1400.2.bh.d.249.1		4	35.18	odd	12
1400.2.bh.d.249.2		4	35.32	odd	12
1400.2.bh.d.849.1		4	5.2	odd	4
1400.2.bh.d.849.2		4	5.3	odd	4
9800.2.a.j.1.1		1	35.9	even	6
9800.2.a.k.1.1		1	7.5	odd	6
9800.2.a.bl.1.1		1	35.19	odd	6
9800.2.a.bm.1.1		1	7.2	even	3

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.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{3} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{11} -2.00000 q^{13} +(1.50000 + 2.59808i) q^{17} +(4.00000 - 3.46410i) q^{21} +(-1.50000 + 2.59808i) q^{23} -4.00000 q^{27} -6.00000 q^{29} +(-4.50000 - 7.79423i) q^{31} +(-4.00000 + 6.92820i) q^{33} +(2.00000 + 3.46410i) q^{39} +5.00000 q^{41} -6.00000 q^{43} +(-4.50000 + 7.79423i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(3.00000 - 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} +(-4.00000 - 6.92820i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(-2.50000 - 0.866025i) q^{63} +(-7.00000 - 12.1244i) q^{67} +6.00000 q^{69} +11.0000 q^{71} +(1.00000 + 1.73205i) q^{73} +(8.00000 - 6.92820i) q^{77} +(-4.50000 + 7.79423i) q^{79} +(5.50000 + 9.52628i) q^{81} -6.00000 q^{83} +(6.00000 + 10.3923i) q^{87} +(-5.50000 + 9.52628i) q^{89} +(-1.00000 - 5.19615i) q^{91} +(-9.00000 + 15.5885i) q^{93} -11.0000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + q^7 - q^9	\( 2 q - 2 q^{3} + q^{7} - q^{9} - 4 q^{11} - 4 q^{13} + 3 q^{17} + 8 q^{21} - 3 q^{23} - 8 q^{27} - 12 q^{29} - 9 q^{31} - 8 q^{33} + 4 q^{39} + 10 q^{41} - 12 q^{43} - 9 q^{47} - 13 q^{49} + 6 q^{51} + 6 q^{53} - 8 q^{59} - 8 q^{61} - 5 q^{63} - 14 q^{67} + 12 q^{69} + 22 q^{71} + 2 q^{73} + 16 q^{77} - 9 q^{79} + 11 q^{81} - 12 q^{83} + 12 q^{87} - 11 q^{89} - 2 q^{91} - 18 q^{93} - 22 q^{97} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + q^7 - q^9 - 4 * q^11 - 4 * q^13 + 3 * q^17 + 8 * q^21 - 3 * q^23 - 8 * q^27 - 12 * q^29 - 9 * q^31 - 8 * q^33 + 4 * q^39 + 10 * q^41 - 12 * q^43 - 9 * q^47 - 13 * q^49 + 6 * q^51 + 6 * q^53 - 8 * q^59 - 8 * q^61 - 5 * q^63 - 14 * q^67 + 12 * q^69 + 22 * q^71 + 2 * q^73 + 16 * q^77 - 9 * q^79 + 11 * q^81 - 12 * q^83 + 12 * q^87 - 11 * q^89 - 2 * q^91 - 18 * q^93 - 22 * q^97 + 8 * q^99

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