LMFDB - Embedded newform 252.2.bf.b.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(19,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("252.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bf (of order $6$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
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			199.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	252.199
Dual form			252.2.bf.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -2.00000 q^{4} +(2.44949 - 1.41421i) q^{5} +(-0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+1.41421i q^{2} -2.00000 q^{4} +(2.44949 - 1.41421i) q^{5} +(-0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +(2.00000 + 3.46410i) q^{10} +(4.89898 + 2.82843i) q^{11} +5.19615i q^{13} +(-3.67423 - 0.707107i) q^{14} +4.00000 q^{16} +(-2.44949 - 1.41421i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-4.89898 + 2.82843i) q^{20} +(-4.00000 + 6.92820i) q^{22} +(2.44949 - 1.41421i) q^{23} +(1.50000 - 2.59808i) q^{25} -7.34847 q^{26} +(1.00000 - 5.19615i) q^{28} +(0.500000 - 0.866025i) q^{31} +5.65685i q^{32} +(2.00000 - 3.46410i) q^{34} +(2.44949 + 7.07107i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(6.12372 - 3.53553i) q^{38} +(-4.00000 - 6.92820i) q^{40} -5.65685i q^{41} +5.19615i q^{43} +(-9.79796 - 5.65685i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-2.44949 - 4.24264i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(3.67423 + 2.12132i) q^{50} -10.3923i q^{52} +(2.44949 - 4.24264i) q^{53} +16.0000 q^{55} +(7.34847 + 1.41421i) q^{56} +(2.44949 - 4.24264i) q^{59} +(6.00000 - 3.46410i) q^{61} +(1.22474 + 0.707107i) q^{62} -8.00000 q^{64} +(7.34847 + 12.7279i) q^{65} +(-7.50000 - 4.33013i) q^{67} +(4.89898 + 2.82843i) q^{68} +(-10.0000 + 3.46410i) q^{70} +2.82843i q^{71} +(1.50000 + 0.866025i) q^{73} +(6.12372 - 3.53553i) q^{74} +(5.00000 + 8.66025i) q^{76} +(-9.79796 + 11.3137i) q^{77} +(1.50000 - 0.866025i) q^{79} +(9.79796 - 5.65685i) q^{80} +8.00000 q^{82} -14.6969 q^{83} -8.00000 q^{85} -7.34847 q^{86} +(8.00000 - 13.8564i) q^{88} +(9.79796 - 5.65685i) q^{89} +(-13.5000 - 2.59808i) q^{91} +(-4.89898 + 2.82843i) q^{92} +(6.00000 - 3.46410i) q^{94} +(-12.2474 - 7.07107i) q^{95} +(3.67423 - 9.19239i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} - 2 q^{7}+O(q^{10}) $ 4 * q - 8 * q^4 - 2 * q^7	$ 4 q - 8 q^{4} - 2 q^{7} + 8 q^{10} + 16 q^{16} - 10 q^{19} - 16 q^{22} + 6 q^{25} + 4 q^{28} + 2 q^{31} + 8 q^{34} - 10 q^{37} - 16 q^{40} + 8 q^{46} - 26 q^{49} + 64 q^{55} + 24 q^{61} - 32 q^{64} - 30 q^{67} - 40 q^{70} + 6 q^{73} + 20 q^{76} + 6 q^{79} + 32 q^{82} - 32 q^{85} + 32 q^{88} - 54 q^{91} + 24 q^{94}+O(q^{100}) $ 4 * q - 8 * q^4 - 2 * q^7 + 8 * q^10 + 16 * q^16 - 10 * q^19 - 16 * q^22 + 6 * q^25 + 4 * q^28 + 2 * q^31 + 8 * q^34 - 10 * q^37 - 16 * q^40 + 8 * q^46 - 26 * q^49 + 64 * q^55 + 24 * q^61 - 32 * q^64 - 30 * q^67 - 40 * q^70 + 6 * q^73 + 20 * q^76 + 6 * q^79 + 32 * q^82 - 32 * q^85 + 32 * q^88 - 54 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$		0			0
$3$		0			0
$4$	−2.00000			−1.00000
$5$	2.44949	−	1.41421i	1.09545	−	0.632456i	0.160424	−	0.987048i	$-0.448714\pi$
$5$	2.44949	−	1.41421i	1.09545	−	0.632456i	0.935021	+	0.354593i	$0.115380\pi$
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	2.00000	+	3.46410i	0.632456	+	1.09545i
$11$	4.89898	+	2.82843i	1.47710	+	0.852803i	0.999665	−	0.0258656i	$-0.00823419\pi$
$11$	4.89898	+	2.82843i	1.47710	+	0.852803i	0.477432	+	0.878668i	$0.341568\pi$
$12$		0			0
$13$			5.19615i			1.44115i	0.693375	+	0.720577i	$0.256123\pi$
$13$			5.19615i			1.44115i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−3.67423	−	0.707107i	−0.981981	−	0.188982i
$15$		0			0
$16$	4.00000			1.00000
$17$	−2.44949	−	1.41421i	−0.594089	−	0.342997i	0.172624	−	0.984988i	$-0.444775\pi$
$17$	−2.44949	−	1.41421i	−0.594089	−	0.342997i	−0.766712	+	0.641991i	$0.778109\pi$
$18$		0			0
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$	−4.89898	+	2.82843i	−1.09545	+	0.632456i
$21$		0			0
$22$	−4.00000	+	6.92820i	−0.852803	+	1.47710i
$23$	2.44949	−	1.41421i	0.510754	−	0.294884i	−0.222390	−	0.974958i	$-0.571386\pi$
$23$	2.44949	−	1.41421i	0.510754	−	0.294884i	0.733144	+	0.680074i	$0.238052\pi$
$24$		0			0
$25$	1.50000	−	2.59808i	0.300000	−	0.519615i
$26$	−7.34847			−1.44115
$27$		0			0
$28$	1.00000	−	5.19615i	0.188982	−	0.981981i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$			5.65685i			1.00000i
$33$		0			0
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$	2.44949	+	7.07107i	0.414039	+	1.19523i
$36$		0			0
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	0.584002	−	0.811752i	$-0.301486\pi$
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	−0.994999	+	0.0998840i	$0.968153\pi$
$38$	6.12372	−	3.53553i	0.993399	−	0.573539i
$39$		0			0
$40$	−4.00000	−	6.92820i	−0.632456	−	1.09545i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$			5.19615i			0.792406i	0.918163	+	0.396203i	$0.129672\pi$
$43$			5.19615i			0.792406i	−0.918163	+	0.396203i	$0.870328\pi$
$44$	−9.79796	−	5.65685i	−1.47710	−	0.852803i
$45$		0			0
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−2.44949	−	4.24264i	−0.357295	−	0.618853i	0.630213	−	0.776422i	$-0.282968\pi$
$47$	−2.44949	−	4.24264i	−0.357295	−	0.618853i	−0.987508	+	0.157569i	$0.949634\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	3.67423	+	2.12132i	0.519615	+	0.300000i
$51$		0			0
$52$		−	10.3923i		−	1.44115i
$53$	2.44949	−	4.24264i	0.336463	−	0.582772i	−0.647302	−	0.762234i	$-0.724103\pi$
$53$	2.44949	−	4.24264i	0.336463	−	0.582772i	0.983765	+	0.179463i	$0.0574359\pi$
$54$		0			0
$55$	16.0000			2.15744
$56$	7.34847	+	1.41421i	0.981981	+	0.188982i
$57$		0			0
$58$		0			0
$59$	2.44949	−	4.24264i	0.318896	−	0.552345i	−0.661362	−	0.750067i	$-0.730021\pi$
$59$	2.44949	−	4.24264i	0.318896	−	0.552345i	0.980258	+	0.197722i	$0.0633545\pi$
$60$		0			0
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	0.832240	+	0.554416i	$0.187058\pi$
$62$	1.22474	+	0.707107i	0.155543	+	0.0898027i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	7.34847	+	12.7279i	0.911465	+	1.57870i
$66$		0			0
$67$	−7.50000	−	4.33013i	−0.916271	−	0.529009i	−0.0338274	−	0.999428i	$-0.510770\pi$
$67$	−7.50000	−	4.33013i	−0.916271	−	0.529009i	−0.882443	+	0.470418i	$0.844103\pi$
$68$	4.89898	+	2.82843i	0.594089	+	0.342997i
$69$		0			0
$70$	−10.0000	+	3.46410i	−1.19523	+	0.414039i
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$		0			0
$73$	1.50000	+	0.866025i	0.175562	+	0.101361i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	1.50000	+	0.866025i	0.175562	+	0.101361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	6.12372	−	3.53553i	0.711868	−	0.410997i
$75$		0			0
$76$	5.00000	+	8.66025i	0.573539	+	0.993399i
$77$	−9.79796	+	11.3137i	−1.11658	+	1.28932i
$78$		0			0
$79$	1.50000	−	0.866025i	0.168763	−	0.0974355i	−0.413239	−	0.910622i	$-0.635603\pi$
$79$	1.50000	−	0.866025i	0.168763	−	0.0974355i	0.582003	+	0.813187i	$0.302269\pi$
$80$	9.79796	−	5.65685i	1.09545	−	0.632456i
$81$		0			0
$82$	8.00000			0.883452
$83$	−14.6969			−1.61320			−0.806599	−	0.591099i	$-0.798694\pi$
$83$	−14.6969			−1.61320			−0.806599	+	0.591099i	$0.798694\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$	−7.34847			−0.792406
$87$		0			0
$88$	8.00000	−	13.8564i	0.852803	−	1.47710i
$89$	9.79796	−	5.65685i	1.03858	−	0.599625i	0.119150	−	0.992876i	$-0.461983\pi$
$89$	9.79796	−	5.65685i	1.03858	−	0.599625i	0.919431	+	0.393251i	$0.128650\pi$
$90$		0			0
$91$	−13.5000	−	2.59808i	−1.41518	−	0.272352i
$92$	−4.89898	+	2.82843i	−0.510754	+	0.294884i
$93$		0			0
$94$	6.00000	−	3.46410i	0.618853	−	0.357295i
$95$	−12.2474	−	7.07107i	−1.25656	−	0.725476i
$96$		0			0
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	3.67423	−	9.19239i	0.371154	−	0.928571i
$99$		0			0
$100$	−3.00000	+	5.19615i	−0.300000	+	0.519615i
$101$	−9.79796	−	5.65685i	−0.974933	−	0.562878i	−0.0741967	−	0.997244i	$-0.523639\pi$
$101$	−9.79796	−	5.65685i	−0.974933	−	0.562878i	−0.900737	+	0.434366i	$0.856973\pi$
$102$		0			0
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$	14.6969			1.44115
$105$		0			0
$106$	6.00000	+	3.46410i	0.582772	+	0.336463i
$107$	2.44949	−	1.41421i	0.236801	−	0.136717i	−0.376905	−	0.926252i	$-0.623012\pi$
$107$	2.44949	−	1.41421i	0.236801	−	0.136717i	0.613706	+	0.789535i	$0.289678\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$			22.6274i			2.15744i
$111$		0			0
$112$	−2.00000	+	10.3923i	−0.188982	+	0.981981i
$113$	−14.6969			−1.38257			−0.691286	−	0.722581i	$-0.742955\pi$
$113$	−14.6969			−1.38257			−0.691286	+	0.722581i	$0.742955\pi$
$114$		0			0
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$		0			0
$117$		0			0
$118$	6.00000	+	3.46410i	0.552345	+	0.318896i
$119$	4.89898	−	5.65685i	0.449089	−	0.518563i
$120$		0			0
$121$	10.5000	+	18.1865i	0.954545	+	1.65332i
$122$	4.89898	+	8.48528i	0.443533	+	0.768221i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$			5.65685i			0.505964i
$126$		0			0
$127$			15.5885i			1.38325i	0.722256	+	0.691626i	$0.243105\pi$
$127$			15.5885i			1.38325i	−0.722256	+	0.691626i	$0.756895\pi$
$128$		−	11.3137i		−	1.00000i
$129$		0			0
$130$	−18.0000	+	10.3923i	−1.57870	+	0.911465i
$131$	−9.79796	−	16.9706i	−0.856052	−	1.48272i	−0.875666	−	0.482917i	$-0.839577\pi$
$131$	−9.79796	−	16.9706i	−0.856052	−	1.48272i	0.0196143	−	0.999808i	$-0.493756\pi$
$132$		0			0
$133$	12.5000	−	4.33013i	1.08389	−	0.375470i
$134$	6.12372	−	10.6066i	0.529009	−	0.916271i
$135$		0			0
$136$	−4.00000	+	6.92820i	−0.342997	+	0.594089i
$137$	−4.89898	+	8.48528i	−0.418548	+	0.724947i	−0.995794	−	0.0916241i	$-0.970794\pi$
$137$	−4.89898	+	8.48528i	−0.418548	+	0.724947i	0.577246	+	0.816571i	$0.304128\pi$
$138$		0			0
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$	−4.89898	−	14.1421i	−0.414039	−	1.19523i
$141$		0			0
$142$	−4.00000			−0.335673
$143$	−14.6969	+	25.4558i	−1.22902	+	2.12872i
$144$		0			0
$145$		0			0
$146$	−1.22474	+	2.12132i	−0.101361	+	0.175562i
$147$		0			0
$148$	5.00000	+	8.66025i	0.410997	+	0.711868i
$149$	4.89898	+	8.48528i	0.401340	+	0.695141i	0.993888	−	0.110394i	$-0.0352112\pi$
$149$	4.89898	+	8.48528i	0.401340	+	0.695141i	−0.592548	+	0.805535i	$0.701878\pi$
$150$		0			0
$151$	15.0000	+	8.66025i	1.22068	+	0.704761i	0.965064	−	0.262016i	$-0.0843873\pi$
$151$	15.0000	+	8.66025i	1.22068	+	0.704761i	0.255619	+	0.966778i	$0.417721\pi$
$152$	−12.2474	+	7.07107i	−0.993399	+	0.573539i
$153$		0			0
$154$	−16.0000	−	13.8564i	−1.28932	−	1.11658i
$155$		−	2.82843i		−	0.227185i
$156$		0			0
$157$	6.00000	+	3.46410i	0.478852	+	0.276465i	0.719938	−	0.694038i	$-0.244170\pi$
$157$	6.00000	+	3.46410i	0.478852	+	0.276465i	−0.241086	+	0.970504i	$0.577504\pi$
$158$	1.22474	+	2.12132i	0.0974355	+	0.168763i
$159$		0			0
$160$	8.00000	+	13.8564i	0.632456	+	1.09545i
$161$	2.44949	+	7.07107i	0.193047	+	0.557278i
$162$		0			0
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	−0.612866	−	0.790186i	$-0.709984\pi$
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	0.377888	+	0.925851i	$0.376650\pi$
$164$			11.3137i			0.883452i
$165$		0			0
$166$		−	20.7846i		−	1.61320i
$167$	14.6969			1.13728			0.568642	−	0.822585i	$-0.307469\pi$
$167$	14.6969			1.13728			0.568642	+	0.822585i	$0.307469\pi$
$168$		0			0
$169$	−14.0000			−1.07692
$170$		−	11.3137i		−	0.867722i
$171$		0			0
$172$		−	10.3923i		−	0.792406i
$173$	17.1464	−	9.89949i	1.30362	−	0.752645i	0.322596	−	0.946537i	$-0.395445\pi$
$173$	17.1464	−	9.89949i	1.30362	−	0.752645i	0.981023	+	0.193892i	$0.0621112\pi$
$174$		0			0
$175$	6.00000	+	5.19615i	0.453557	+	0.392792i
$176$	19.5959	+	11.3137i	1.47710	+	0.852803i
$177$		0			0
$178$	8.00000	+	13.8564i	0.599625	+	1.03858i
$179$	−2.44949	−	1.41421i	−0.183083	−	0.105703i	0.405657	−	0.914025i	$-0.367043\pi$
$179$	−2.44949	−	1.41421i	−0.183083	−	0.105703i	−0.588741	+	0.808322i	$0.700376\pi$
$180$		0			0
$181$		−	5.19615i		−	0.386227i	−0.981176	−	0.193113i	$-0.938141\pi$
$181$		−	5.19615i		−	0.386227i	0.981176	−	0.193113i	$-0.0618586\pi$
$182$	3.67423	−	19.0919i	0.272352	−	1.41518i
$183$		0			0
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	−12.2474	−	7.07107i	−0.900450	−	0.519875i
$186$		0			0
$187$	−8.00000	−	13.8564i	−0.585018	−	1.01328i
$188$	4.89898	+	8.48528i	0.357295	+	0.618853i
$189$		0			0
$190$	10.0000	−	17.3205i	0.725476	−	1.25656i
$191$	17.1464	−	9.89949i	1.24067	−	0.716302i	0.271441	−	0.962455i	$-0.412500\pi$
$191$	17.1464	−	9.89949i	1.24067	−	0.716302i	0.969231	+	0.246153i	$0.0791665\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$		0			0
$195$		0			0
$196$	13.0000	+	5.19615i	0.928571	+	0.371154i
$197$	14.6969			1.04711			0.523557	−	0.851991i	$-0.324605\pi$
$197$	14.6969			1.04711			0.523557	+	0.851991i	$0.324605\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−7.34847	−	4.24264i	−0.519615	−	0.300000i
$201$		0			0
$202$	8.00000	−	13.8564i	0.562878	−	0.974933i
$203$		0			0
$204$		0			0
$205$	−8.00000	−	13.8564i	−0.558744	−	0.967773i
$206$	−1.22474	+	0.707107i	−0.0853320	+	0.0492665i
$207$		0			0
$208$			20.7846i			1.44115i
$209$		−	28.2843i		−	1.95646i
$210$		0			0
$211$		−	10.3923i		−	0.715436i	−0.933830	−	0.357718i	$-0.883555\pi$
$211$		−	10.3923i		−	0.715436i	0.933830	−	0.357718i	$-0.116445\pi$
$212$	−4.89898	+	8.48528i	−0.336463	+	0.582772i
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	7.34847	+	12.7279i	0.501161	+	0.868037i
$216$		0			0
$217$	2.00000	+	1.73205i	0.135769	+	0.117579i
$218$	−6.12372	−	3.53553i	−0.414751	−	0.239457i
$219$		0			0
$220$	−32.0000			−2.15744
$221$	7.34847	−	12.7279i	0.494312	−	0.856173i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	−14.6969	−	2.82843i	−0.981981	−	0.188982i
$225$		0			0
$226$		−	20.7846i		−	1.38257i
$227$	−4.89898	+	8.48528i	−0.325157	+	0.563188i	−0.981544	−	0.191236i	$-0.938750\pi$
$227$	−4.89898	+	8.48528i	−0.325157	+	0.563188i	0.656387	+	0.754424i	$0.272084\pi$
$228$		0			0
$229$	−16.5000	+	9.52628i	−1.09035	+	0.629514i	−0.933670	−	0.358135i	$-0.883413\pi$
$229$	−16.5000	+	9.52628i	−1.09035	+	0.629514i	−0.156681	+	0.987649i	$0.550079\pi$
$230$	9.79796	+	5.65685i	0.646058	+	0.373002i
$231$		0			0
$232$		0			0
$233$	12.2474	+	21.2132i	0.802357	+	1.38972i	0.918061	+	0.396439i	$0.129754\pi$
$233$	12.2474	+	21.2132i	0.802357	+	1.38972i	−0.115704	+	0.993284i	$0.536912\pi$
$234$		0			0
$235$	−12.0000	−	6.92820i	−0.782794	−	0.451946i
$236$	−4.89898	+	8.48528i	−0.318896	+	0.552345i
$237$		0			0
$238$	8.00000	+	6.92820i	0.518563	+	0.449089i
$239$			11.3137i			0.731823i	0.930650	+	0.365911i	$0.119243\pi$
$239$			11.3137i			0.731823i	−0.930650	+	0.365911i	$0.880757\pi$
$240$		0			0
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	0.0609515	−	0.998141i	$-0.480586\pi$
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	−0.833939	+	0.551856i	$0.813920\pi$
$242$	−25.7196	+	14.8492i	−1.65332	+	0.954545i
$243$		0			0
$244$	−12.0000	+	6.92820i	−0.768221	+	0.443533i
$245$	−19.5959	+	2.82843i	−1.25194	+	0.180702i
$246$		0			0
$247$	22.5000	−	12.9904i	1.43164	−	0.826558i
$248$	−2.44949	−	1.41421i	−0.155543	−	0.0898027i
$249$		0			0
$250$	−8.00000			−0.505964
$251$	14.6969			0.927663			0.463831	−	0.885924i	$-0.346474\pi$
$251$	14.6969			0.927663			0.463831	+	0.885924i	$0.346474\pi$
$252$		0			0
$253$	16.0000			1.00591
$254$	−22.0454			−1.38325
$255$		0			0
$256$	16.0000			1.00000
$257$	2.44949	−	1.41421i	0.152795	−	0.0882162i	−0.421653	−	0.906757i	$-0.638550\pi$
$257$	2.44949	−	1.41421i	0.152795	−	0.0882162i	0.574448	+	0.818541i	$0.305217\pi$
$258$		0			0
$259$	12.5000	−	4.33013i	0.776712	−	0.269061i
$260$	−14.6969	−	25.4558i	−0.911465	−	1.57870i
$261$		0			0
$262$	24.0000	−	13.8564i	1.48272	−	0.856052i
$263$	4.89898	+	2.82843i	0.302084	+	0.174408i	0.643379	−	0.765548i	$-0.277532\pi$
$263$	4.89898	+	2.82843i	0.302084	+	0.174408i	−0.341295	+	0.939956i	$0.610865\pi$
$264$		0			0
$265$		−	13.8564i		−	0.851192i
$266$	6.12372	+	17.6777i	0.375470	+	1.08389i
$267$		0			0
$268$	15.0000	+	8.66025i	0.916271	+	0.529009i
$269$	−9.79796	−	5.65685i	−0.597392	−	0.344904i	0.170623	−	0.985336i	$-0.445422\pi$
$269$	−9.79796	−	5.65685i	−0.597392	−	0.344904i	−0.768015	+	0.640432i	$0.778755\pi$
$270$		0			0
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	0.880812	+	0.473466i	$0.156997\pi$
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−9.79796	−	5.65685i	−0.594089	−	0.342997i
$273$		0			0
$274$	−12.0000	−	6.92820i	−0.724947	−	0.418548i
$275$	14.6969	−	8.48528i	0.886259	−	0.511682i
$276$		0			0
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	−0.982603	−	0.185720i	$-0.940538\pi$
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	0.652140	+	0.758099i	$0.273872\pi$
$278$		−	18.3848i		−	1.10265i
$279$		0			0
$280$	20.0000	−	6.92820i	1.19523	−	0.414039i
$281$	−14.6969			−0.876746			−0.438373	−	0.898793i	$-0.644445\pi$
$281$	−14.6969			−0.876746			−0.438373	+	0.898793i	$0.644445\pi$
$282$		0			0
$283$	−14.5000	+	25.1147i	−0.861936	+	1.49292i	0.00812260	+	0.999967i	$0.497414\pi$
$283$	−14.5000	+	25.1147i	−0.861936	+	1.49292i	−0.870058	+	0.492949i	$0.835919\pi$
$284$		−	5.65685i		−	0.335673i
$285$		0			0
$286$	−36.0000	−	20.7846i	−2.12872	−	1.22902i
$287$	14.6969	+	2.82843i	0.867533	+	0.166957i
$288$		0			0
$289$	−4.50000	−	7.79423i	−0.264706	−	0.458484i
$290$		0			0
$291$		0			0
$292$	−3.00000	−	1.73205i	−0.175562	−	0.101361i
$293$			11.3137i			0.660954i	0.943814	+	0.330477i	$0.107210\pi$
$293$			11.3137i			0.660954i	−0.943814	+	0.330477i	$0.892790\pi$
$294$		0			0
$295$		−	13.8564i		−	0.806751i
$296$	−12.2474	+	7.07107i	−0.711868	+	0.410997i
$297$		0			0
$298$	−12.0000	+	6.92820i	−0.695141	+	0.401340i
$299$	7.34847	+	12.7279i	0.424973	+	0.736075i
$300$		0			0
$301$	−13.5000	−	2.59808i	−0.778127	−	0.149751i
$302$	−12.2474	+	21.2132i	−0.704761	+	1.22068i
$303$		0			0
$304$	−10.0000	−	17.3205i	−0.573539	−	0.993399i
$305$	9.79796	−	16.9706i	0.561029	−	0.971732i
$306$		0			0
$307$	−1.00000			−0.0570730			−0.0285365	−	0.999593i	$-0.509085\pi$
$307$	−1.00000			−0.0570730			−0.0285365	+	0.999593i	$0.509085\pi$
$308$	19.5959	−	22.6274i	1.11658	−	1.28932i
$309$		0			0
$310$	4.00000			0.227185
$311$	9.79796	−	16.9706i	0.555591	−	0.962312i	−0.442266	−	0.896884i	$-0.645825\pi$
$311$	9.79796	−	16.9706i	0.555591	−	0.962312i	0.997857	−	0.0654284i	$-0.0208414\pi$
$312$		0			0
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.165406	−	0.986226i	$-0.447107\pi$
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.936799	+	0.349867i	$0.113773\pi$
$314$	−4.89898	+	8.48528i	−0.276465	+	0.478852i
$315$		0			0
$316$	−3.00000	+	1.73205i	−0.168763	+	0.0974355i
$317$	−9.79796	−	16.9706i	−0.550308	−	0.953162i	−0.998252	−	0.0591001i	$-0.981177\pi$
$317$	−9.79796	−	16.9706i	−0.550308	−	0.953162i	0.447944	−	0.894062i	$-0.352156\pi$
$318$		0			0
$319$		0			0
$320$	−19.5959	+	11.3137i	−1.09545	+	0.632456i
$321$		0			0
$322$	−10.0000	+	3.46410i	−0.557278	+	0.193047i
$323$			14.1421i			0.786889i
$324$		0			0
$325$	13.5000	+	7.79423i	0.748845	+	0.432346i
$326$	−2.44949	−	4.24264i	−0.135665	−	0.234978i
$327$		0			0
$328$	−16.0000			−0.883452
$329$	12.2474	−	4.24264i	0.675224	−	0.233904i
$330$		0			0
$331$	−25.5000	+	14.7224i	−1.40161	+	0.809218i	−0.994558	−	0.104188i	$-0.966776\pi$
$331$	−25.5000	+	14.7224i	−1.40161	+	0.809218i	−0.407049	+	0.913406i	$0.633442\pi$
$332$	29.3939			1.61320
$333$		0			0
$334$			20.7846i			1.13728i
$335$	−24.4949			−1.33830
$336$		0			0
$337$	29.0000			1.57973			0.789865	−	0.613280i	$-0.210150\pi$
$337$	29.0000			1.57973			0.789865	+	0.613280i	$0.210150\pi$
$338$		−	19.7990i		−	1.07692i
$339$		0			0
$340$	16.0000			0.867722
$341$	4.89898	−	2.82843i	0.265295	−	0.153168i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	14.6969			0.792406
$345$		0			0
$346$	14.0000	+	24.2487i	0.752645	+	1.30362i
$347$	−2.44949	−	1.41421i	−0.131495	−	0.0759190i	0.432809	−	0.901486i	$-0.357522\pi$
$347$	−2.44949	−	1.41421i	−0.131495	−	0.0759190i	−0.564305	+	0.825567i	$0.690856\pi$
$348$		0			0
$349$			20.7846i			1.11257i	0.830990	+	0.556287i	$0.187775\pi$
$349$			20.7846i			1.11257i	−0.830990	+	0.556287i	$0.812225\pi$
$350$	−7.34847	+	8.48528i	−0.392792	+	0.453557i
$351$		0			0
$352$	−16.0000	+	27.7128i	−0.852803	+	1.47710i
$353$	26.9444	+	15.5563i	1.43411	+	0.827981i	0.997431	−	0.0716387i	$-0.0228229\pi$
$353$	26.9444	+	15.5563i	1.43411	+	0.827981i	0.436674	+	0.899620i	$0.356156\pi$
$354$		0			0
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$	−19.5959	+	11.3137i	−1.03858	+	0.599625i
$357$		0			0
$358$	2.00000	−	3.46410i	0.105703	−	0.183083i
$359$	−19.5959	+	11.3137i	−1.03423	+	0.597115i	−0.918194	−	0.396130i	$-0.870353\pi$
$359$	−19.5959	+	11.3137i	−1.03423	+	0.597115i	−0.116039	+	0.993245i	$0.537020\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	7.34847			0.386227
$363$		0			0
$364$	27.0000	+	5.19615i	1.41518	+	0.272352i
$365$	4.89898			0.256424
$366$		0			0
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	−0.973116	−	0.230317i	$-0.926024\pi$
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	0.686018	+	0.727585i	$0.259357\pi$
$368$	9.79796	−	5.65685i	0.510754	−	0.294884i
$369$		0			0
$370$	10.0000	−	17.3205i	0.519875	−	0.900450i
$371$	9.79796	+	8.48528i	0.508685	+	0.440534i
$372$		0			0
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	0.878680	−	0.477412i	$-0.158425\pi$
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	−0.852791	+	0.522253i	$0.825092\pi$
$374$	19.5959	−	11.3137i	1.01328	−	0.585018i
$375$		0			0
$376$	−12.0000	+	6.92820i	−0.618853	+	0.357295i
$377$		0			0
$378$		0			0
$379$		−	36.3731i		−	1.86836i	−0.356803	−	0.934179i	$-0.616133\pi$
$379$		−	36.3731i		−	1.86836i	0.356803	−	0.934179i	$-0.383867\pi$
$380$	24.4949	+	14.1421i	1.25656	+	0.725476i
$381$		0			0
$382$	14.0000	+	24.2487i	0.716302	+	1.24067i
$383$	−17.1464	−	29.6985i	−0.876142	−	1.51752i	−0.855542	−	0.517734i	$-0.826776\pi$
$383$	−17.1464	−	29.6985i	−0.876142	−	1.51752i	−0.0205998	−	0.999788i	$-0.506558\pi$
$384$		0			0
$385$	−8.00000	+	41.5692i	−0.407718	+	2.11856i
$386$	8.57321	+	4.94975i	0.436365	+	0.251936i
$387$		0			0
$388$		0			0
$389$	−12.2474	+	21.2132i	−0.620970	+	1.07555i	0.368335	+	0.929693i	$0.379928\pi$
$389$	−12.2474	+	21.2132i	−0.620970	+	1.07555i	−0.989305	+	0.145859i	$0.953405\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	−7.34847	+	18.3848i	−0.371154	+	0.928571i
$393$		0			0
$394$			20.7846i			1.04711i
$395$	2.44949	−	4.24264i	0.123247	−	0.213470i
$396$		0			0
$397$	−25.5000	+	14.7224i	−1.27981	+	0.738898i	−0.976813	−	0.214094i	$-0.931320\pi$
$397$	−25.5000	+	14.7224i	−1.27981	+	0.738898i	−0.302995	+	0.952992i	$0.597987\pi$
$398$	4.89898	+	2.82843i	0.245564	+	0.141776i
$399$		0			0
$400$	6.00000	−	10.3923i	0.300000	−	0.519615i
$401$	−2.44949	−	4.24264i	−0.122322	−	0.211867i	0.798361	−	0.602179i	$-0.205701\pi$
$401$	−2.44949	−	4.24264i	−0.122322	−	0.211867i	−0.920683	+	0.390312i	$0.872367\pi$
$402$		0			0
$403$	4.50000	+	2.59808i	0.224161	+	0.129419i
$404$	19.5959	+	11.3137i	0.974933	+	0.562878i
$405$		0			0
$406$		0			0
$407$		−	28.2843i		−	1.40200i
$408$		0			0
$409$	−25.5000	−	14.7224i	−1.26089	−	0.727977i	−0.287646	−	0.957737i	$-0.592873\pi$
$409$	−25.5000	−	14.7224i	−1.26089	−	0.727977i	−0.973247	+	0.229759i	$0.926206\pi$
$410$	19.5959	−	11.3137i	0.967773	−	0.558744i
$411$		0			0
$412$	−1.00000	−	1.73205i	−0.0492665	−	0.0853320i
$413$	9.79796	+	8.48528i	0.482126	+	0.417533i
$414$		0			0
$415$	−36.0000	+	20.7846i	−1.76717	+	1.02028i
$416$	−29.3939			−1.44115
$417$		0			0
$418$	40.0000			1.95646
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	23.0000			1.12095			0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000			1.12095			0.560476	+	0.828171i	$0.310618\pi$
$422$	14.6969			0.715436
$423$		0			0
$424$	−12.0000	−	6.92820i	−0.582772	−	0.336463i
$425$	−7.34847	+	4.24264i	−0.356453	+	0.205798i
$426$		0			0
$427$	6.00000	+	17.3205i	0.290360	+	0.838198i
$428$	−4.89898	+	2.82843i	−0.236801	+	0.136717i
$429$		0			0
$430$	−18.0000	+	10.3923i	−0.868037	+	0.501161i
$431$	12.2474	+	7.07107i	0.589939	+	0.340601i	0.765073	−	0.643943i	$-0.222703\pi$
$431$	12.2474	+	7.07107i	0.589939	+	0.340601i	−0.175134	+	0.984545i	$0.556036\pi$
$432$		0			0
$433$			5.19615i			0.249711i	0.992175	+	0.124856i	$0.0398468\pi$
$433$			5.19615i			0.249711i	−0.992175	+	0.124856i	$0.960153\pi$
$434$	−2.44949	+	2.82843i	−0.117579	+	0.135769i
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	−12.2474	−	7.07107i	−0.585875	−	0.338255i
$438$		0			0
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	0.909798	−	0.415051i	$-0.136236\pi$
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	−0.814344	+	0.580383i	$0.802903\pi$
$440$		−	45.2548i		−	2.15744i
$441$		0			0
$442$	18.0000	+	10.3923i	0.856173	+	0.494312i
$443$	−26.9444	+	15.5563i	−1.28017	+	0.739104i	−0.976879	−	0.213795i	$-0.931418\pi$
$443$	−26.9444	+	15.5563i	−1.28017	+	0.739104i	−0.303288	+	0.952899i	$0.598084\pi$
$444$		0			0
$445$	16.0000	−	27.7128i	0.758473	−	1.31371i
$446$		−	5.65685i		−	0.267860i
$447$		0			0
$448$	4.00000	−	20.7846i	0.188982	−	0.981981i
$449$	−14.6969			−0.693591			−0.346796	−	0.937941i	$-0.612730\pi$
$449$	−14.6969			−0.693591			−0.346796	+	0.937941i	$0.612730\pi$
$450$		0			0
$451$	16.0000	−	27.7128i	0.753411	−	1.30495i
$452$	29.3939			1.38257
$453$		0			0
$454$	−12.0000	−	6.92820i	−0.563188	−	0.325157i
$455$	−36.7423	+	12.7279i	−1.72251	+	0.596694i
$456$		0			0
$457$	3.50000	+	6.06218i	0.163723	+	0.283577i	0.936201	−	0.351465i	$-0.114316\pi$
$457$	3.50000	+	6.06218i	0.163723	+	0.283577i	−0.772478	+	0.635042i	$0.780983\pi$
$458$	−13.4722	−	23.3345i	−0.629514	−	1.09035i
$459$		0			0
$460$	−8.00000	+	13.8564i	−0.373002	+	0.646058i
$461$			11.3137i			0.526932i	0.964669	+	0.263466i	$0.0848657\pi$
$461$			11.3137i			0.526932i	−0.964669	+	0.263466i	$0.915134\pi$
$462$		0			0
$463$		−	5.19615i		−	0.241486i	−0.992684	−	0.120743i	$-0.961472\pi$
$463$		−	5.19615i		−	0.241486i	0.992684	−	0.120743i	$-0.0385276\pi$
$464$		0			0
$465$		0			0
$466$	−30.0000	+	17.3205i	−1.38972	+	0.802357i
$467$	−2.44949	−	4.24264i	−0.113349	−	0.196326i	0.803770	−	0.594941i	$-0.202824\pi$
$467$	−2.44949	−	4.24264i	−0.113349	−	0.196326i	−0.917119	+	0.398615i	$0.869491\pi$
$468$		0			0
$469$	15.0000	−	17.3205i	0.692636	−	0.799787i
$470$	9.79796	−	16.9706i	0.451946	−	0.782794i
$471$		0			0
$472$	−12.0000	−	6.92820i	−0.552345	−	0.318896i
$473$	−14.6969	+	25.4558i	−0.675766	+	1.17046i
$474$		0			0
$475$	−15.0000			−0.688247
$476$	−9.79796	+	11.3137i	−0.449089	+	0.518563i
$477$		0			0
$478$	−16.0000			−0.731823
$479$	17.1464	−	29.6985i	0.783440	−	1.35696i	−0.146486	−	0.989213i	$-0.546796\pi$
$479$	17.1464	−	29.6985i	0.783440	−	1.35696i	0.929926	−	0.367746i	$-0.119870\pi$
$480$		0			0
$481$	22.5000	−	12.9904i	1.02591	−	0.592310i
$482$	9.79796	−	16.9706i	0.446285	−	0.772988i
$483$		0			0
$484$	−21.0000	−	36.3731i	−0.954545	−	1.65332i
$485$		0			0
$486$		0			0
$487$	19.5000	+	11.2583i	0.883629	+	0.510164i	0.871853	−	0.489767i	$-0.162918\pi$
$487$	19.5000	+	11.2583i	0.883629	+	0.510164i	0.0117760	+	0.999931i	$0.496251\pi$
$488$	−9.79796	−	16.9706i	−0.443533	−	0.768221i
$489$		0			0
$490$	−4.00000	−	27.7128i	−0.180702	−	1.25194i
$491$		−	5.65685i		−	0.255290i	−0.991820	−	0.127645i	$-0.959258\pi$
$491$		−	5.65685i		−	0.255290i	0.991820	−	0.127645i	$-0.0407419\pi$
$492$		0			0
$493$		0			0
$494$	18.3712	+	31.8198i	0.826558	+	1.43164i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	−7.34847	−	1.41421i	−0.329624	−	0.0634361i
$498$		0			0
$499$	28.5000	−	16.4545i	1.27584	−	0.736604i	0.299755	−	0.954016i	$-0.403095\pi$
$499$	28.5000	−	16.4545i	1.27584	−	0.736604i	0.976080	+	0.217412i	$0.0697616\pi$
$500$		−	11.3137i		−	0.505964i
$501$		0			0
$502$			20.7846i			0.927663i
$503$	−29.3939			−1.31061			−0.655304	−	0.755365i	$-0.727460\pi$
$503$	−29.3939			−1.31061			−0.655304	+	0.755365i	$0.727460\pi$
$504$		0			0
$505$	−32.0000			−1.42398
$506$			22.6274i			1.00591i
$507$		0			0
$508$		−	31.1769i		−	1.38325i
$509$	−26.9444	+	15.5563i	−1.19429	+	0.689523i	−0.959276	−	0.282469i	$-0.908846\pi$
$509$	−26.9444	+	15.5563i	−1.19429	+	0.689523i	−0.235013	+	0.971992i	$0.575513\pi$
$510$		0			0
$511$	−3.00000	+	3.46410i	−0.132712	+	0.153243i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	2.00000	+	3.46410i	0.0882162	+	0.152795i
$515$	2.44949	+	1.41421i	0.107937	+	0.0623177i
$516$		0			0
$517$		−	27.7128i		−	1.21881i
$518$	6.12372	+	17.6777i	0.269061	+	0.776712i
$519$		0			0
$520$	36.0000	−	20.7846i	1.57870	−	0.911465i
$521$	−9.79796	−	5.65685i	−0.429256	−	0.247831i	0.269773	−	0.962924i	$-0.413051\pi$
$521$	−9.79796	−	5.65685i	−0.429256	−	0.247831i	−0.699030	+	0.715093i	$0.746385\pi$
$522$		0			0
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	0.975652	+	0.219326i	$0.0703858\pi$
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	−0.297884	+	0.954602i	$0.596281\pi$
$524$	19.5959	+	33.9411i	0.856052	+	1.48272i
$525$		0			0
$526$	−4.00000	+	6.92820i	−0.174408	+	0.302084i
$527$	−2.44949	+	1.41421i	−0.106701	+	0.0616041i
$528$		0			0
$529$	−7.50000	+	12.9904i	−0.326087	+	0.564799i
$530$	19.5959			0.851192
$531$		0			0
$532$	−25.0000	+	8.66025i	−1.08389	+	0.375470i
$533$	29.3939			1.27319
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$	−12.2474	+	21.2132i	−0.529009	+	0.916271i
$537$		0			0
$538$	8.00000	−	13.8564i	0.344904	−	0.597392i
$539$	−24.4949	−	31.1127i	−1.05507	−	1.34012i
$540$		0			0
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	0.505556	−	0.862794i	$-0.331288\pi$
$541$	−11.5000	−	19.9186i	−0.494424	−	0.856367i	−0.999979	+	0.00642713i	$0.997954\pi$
$542$	−34.2929	+	19.7990i	−1.47300	+	0.850439i
$543$		0			0
$544$	8.00000	−	13.8564i	0.342997	−	0.594089i
$545$			14.1421i			0.605783i
$546$		0			0
$547$			10.3923i			0.444343i	0.975008	+	0.222171i	$0.0713145\pi$
$547$			10.3923i			0.444343i	−0.975008	+	0.222171i	$0.928686\pi$
$548$	9.79796	−	16.9706i	0.418548	−	0.724947i
$549$		0			0
$550$	12.0000	+	20.7846i	0.511682	+	0.886259i
$551$		0			0
$552$		0			0
$553$	1.50000	+	4.33013i	0.0637865	+	0.184136i
$554$	−13.4722	−	7.77817i	−0.572379	−	0.330463i
$555$		0			0
$556$	26.0000			1.10265
$557$	9.79796	−	16.9706i	0.415153	−	0.719066i	−0.580292	−	0.814409i	$-0.697061\pi$
$557$	9.79796	−	16.9706i	0.415153	−	0.719066i	0.995444	+	0.0953429i	$0.0303948\pi$
$558$		0			0
$559$	−27.0000			−1.14198
$560$	9.79796	+	28.2843i	0.414039	+	1.19523i
$561$		0			0
$562$		−	20.7846i		−	0.876746i
$563$	−12.2474	+	21.2132i	−0.516168	+	0.894030i	0.483655	+	0.875259i	$0.339309\pi$
$563$	−12.2474	+	21.2132i	−0.516168	+	0.894030i	−0.999824	+	0.0187714i	$0.994025\pi$
$564$		0			0
$565$	−36.0000	+	20.7846i	−1.51453	+	0.874415i
$566$	−35.5176	−	20.5061i	−1.49292	−	0.861936i
$567$		0			0
$568$	8.00000			0.335673
$569$	−9.79796	−	16.9706i	−0.410752	−	0.711443i	0.584220	−	0.811595i	$-0.301400\pi$
$569$	−9.79796	−	16.9706i	−0.410752	−	0.711443i	−0.994972	+	0.100152i	$0.968067\pi$
$570$		0			0
$571$	10.5000	+	6.06218i	0.439411	+	0.253694i	0.703348	−	0.710846i	$-0.251688\pi$
$571$	10.5000	+	6.06218i	0.439411	+	0.253694i	−0.263937	+	0.964540i	$0.585021\pi$
$572$	29.3939	−	50.9117i	1.22902	−	2.12872i
$573$		0			0
$574$	−4.00000	+	20.7846i	−0.166957	+	0.867533i
$575$		−	8.48528i		−	0.353861i
$576$		0			0
$577$	−7.50000	−	4.33013i	−0.312229	−	0.180266i	0.335694	−	0.941971i	$-0.391029\pi$
$577$	−7.50000	−	4.33013i	−0.312229	−	0.180266i	−0.647924	+	0.761705i	$0.724362\pi$
$578$	11.0227	−	6.36396i	0.458484	−	0.264706i
$579$		0			0
$580$		0			0
$581$	7.34847	−	38.1838i	0.304866	−	1.58413i
$582$		0			0
$583$	24.0000	−	13.8564i	0.993978	−	0.573874i
$584$	2.44949	−	4.24264i	0.101361	−	0.175562i
$585$		0			0
$586$	−16.0000			−0.660954
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$	−5.00000			−0.206021
$590$	19.5959			0.806751
$591$		0			0
$592$	−10.0000	−	17.3205i	−0.410997	−	0.711868i
$593$	−34.2929	+	19.7990i	−1.40824	+	0.813047i	−0.995218	−	0.0976747i	$-0.968860\pi$
$593$	−34.2929	+	19.7990i	−1.40824	+	0.813047i	−0.413020	+	0.910722i	$0.635526\pi$
$594$		0			0
$595$	4.00000	−	20.7846i	0.163984	−	0.852086i
$596$	−9.79796	−	16.9706i	−0.401340	−	0.695141i
$597$		0			0
$598$	−18.0000	+	10.3923i	−0.736075	+	0.424973i
$599$	19.5959	+	11.3137i	0.800668	+	0.462266i	0.843705	−	0.536808i	$-0.180370\pi$
$599$	19.5959	+	11.3137i	0.800668	+	0.462266i	−0.0430370	+	0.999073i	$0.513703\pi$
$600$		0			0
$601$		−	25.9808i		−	1.05978i	−0.848067	−	0.529889i	$-0.822234\pi$
$601$		−	25.9808i		−	1.05978i	0.848067	−	0.529889i	$-0.177766\pi$
$602$	3.67423	−	19.0919i	0.149751	−	0.778127i
$603$		0			0
$604$	−30.0000	−	17.3205i	−1.22068	−	0.704761i
$605$	51.4393	+	29.6985i	2.09130	+	1.20742i
$606$		0			0
$607$	−23.5000	−	40.7032i	−0.953836	−	1.65209i	−0.737011	−	0.675881i	$-0.763763\pi$
$607$	−23.5000	−	40.7032i	−0.953836	−	1.65209i	−0.216825	−	0.976210i	$-0.569570\pi$
$608$	24.4949	−	14.1421i	0.993399	−	0.573539i
$609$		0			0
$610$	24.0000	+	13.8564i	0.971732	+	0.561029i
$611$	22.0454	−	12.7279i	0.891862	−	0.514917i
$612$		0			0
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	−0.972056	−	0.234751i	$-0.924572\pi$
$613$	−7.00000	+	12.1244i	−0.282727	+	0.489698i	0.689328	+	0.724449i	$0.257906\pi$
$614$		−	1.41421i		−	0.0570730i
$615$		0			0
$616$	32.0000	+	27.7128i	1.28932	+	1.11658i
$617$	29.3939			1.18335			0.591676	−	0.806176i	$-0.298466\pi$
$617$	29.3939			1.18335			0.591676	+	0.806176i	$0.298466\pi$
$618$		0			0
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	0.412341	+	0.911030i	$0.364711\pi$
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	−0.995145	+	0.0984169i	$0.968622\pi$
$620$			5.65685i			0.227185i
$621$		0			0
$622$	24.0000	+	13.8564i	0.962312	+	0.555591i
$623$	9.79796	+	28.2843i	0.392547	+	1.13319i
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$	15.9217	+	27.5772i	0.636358	+	1.10221i
$627$		0			0
$628$	−12.0000	−	6.92820i	−0.478852	−	0.276465i
$629$			14.1421i			0.563884i
$630$		0			0
$631$		−	10.3923i		−	0.413711i	−0.978371	−	0.206856i	$-0.933677\pi$
$631$		−	10.3923i		−	0.413711i	0.978371	−	0.206856i	$-0.0663230\pi$
$632$	−2.44949	−	4.24264i	−0.0974355	−	0.168763i
$633$		0			0
$634$	24.0000	−	13.8564i	0.953162	−	0.550308i
$635$	22.0454	+	38.1838i	0.874845	+	1.51528i
$636$		0			0
$637$	13.5000	−	33.7750i	0.534889	−	1.33821i
$638$		0			0
$639$		0			0
$640$	−16.0000	−	27.7128i	−0.632456	−	1.09545i
$641$	2.44949	−	4.24264i	0.0967490	−	0.167574i	−0.813588	−	0.581442i	$-0.802489\pi$
$641$	2.44949	−	4.24264i	0.0967490	−	0.167574i	0.910337	+	0.413867i	$0.135822\pi$
$642$		0			0
$643$	29.0000			1.14365			0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000			1.14365			0.571824	+	0.820376i	$0.306236\pi$
$644$	−4.89898	−	14.1421i	−0.193047	−	0.557278i
$645$		0			0
$646$	−20.0000			−0.786889
$647$	9.79796	−	16.9706i	0.385198	−	0.667182i	−0.606599	−	0.795008i	$-0.707467\pi$
$647$	9.79796	−	16.9706i	0.385198	−	0.667182i	0.991797	+	0.127826i	$0.0408000\pi$
$648$		0			0
$649$	24.0000	−	13.8564i	0.942082	−	0.543912i
$650$	−11.0227	+	19.0919i	−0.432346	+	0.748845i
$651$		0			0
$652$	6.00000	−	3.46410i	0.234978	−	0.135665i
$653$	−9.79796	−	16.9706i	−0.383424	−	0.664109i	0.608125	−	0.793841i	$-0.291922\pi$
$653$	−9.79796	−	16.9706i	−0.383424	−	0.664109i	−0.991549	+	0.129732i	$0.958588\pi$
$654$		0			0
$655$	−48.0000	−	27.7128i	−1.87552	−	1.08283i
$656$		−	22.6274i		−	0.883452i
$657$		0			0
$658$	6.00000	+	17.3205i	0.233904	+	0.675224i
$659$		−	14.1421i		−	0.550899i	−0.961315	−	0.275450i	$-0.911173\pi$
$659$		−	14.1421i		−	0.550899i	0.961315	−	0.275450i	$-0.0888267\pi$
$660$		0			0
$661$	28.5000	+	16.4545i	1.10852	+	0.640005i	0.938446	−	0.345426i	$-0.112266\pi$
$661$	28.5000	+	16.4545i	1.10852	+	0.640005i	0.170075	+	0.985431i	$0.445599\pi$
$662$	−20.8207	−	36.0624i	−0.809218	−	1.40161i
$663$		0			0
$664$			41.5692i			1.61320i
$665$	24.4949	−	28.2843i	0.949871	−	1.09682i
$666$		0			0
$667$		0			0
$668$	−29.3939			−1.13728
$669$		0			0
$670$		−	34.6410i		−	1.33830i
$671$	39.1918			1.51298
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$			41.0122i			1.57973i
$675$		0			0
$676$	28.0000			1.07692
$677$	−4.89898	+	2.82843i	−0.188283	+	0.108705i	−0.591179	−	0.806541i	$-0.701337\pi$
$677$	−4.89898	+	2.82843i	−0.188283	+	0.108705i	0.402895	+	0.915246i	$0.368004\pi$
$678$		0			0
$679$		0			0
$680$			22.6274i			0.867722i
$681$		0			0
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	−31.8434	−	18.3848i	−1.21845	−	0.703474i	−0.253866	−	0.967239i	$-0.581702\pi$
$683$	−31.8434	−	18.3848i	−1.21845	−	0.703474i	−0.964587	+	0.263766i	$0.915035\pi$
$684$		0			0
$685$			27.7128i			1.05885i
$686$	22.0454	+	14.1421i	0.841698	+	0.539949i
$687$		0			0
$688$			20.7846i			0.792406i
$689$	22.0454	+	12.7279i	0.839863	+	0.484895i
$690$		0			0
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	0.814548	−	0.580097i	$-0.196985\pi$
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	−0.909652	+	0.415371i	$0.863652\pi$
$692$	−34.2929	+	19.7990i	−1.30362	+	0.752645i
$693$		0			0
$694$	2.00000	−	3.46410i	0.0759190	−	0.131495i
$695$	−31.8434	+	18.3848i	−1.20789	+	0.697374i
$696$		0			0
$697$	−8.00000	+	13.8564i	−0.303022	+	0.524849i
$698$	−29.3939			−1.11257
$699$		0			0
$700$	−12.0000	−	10.3923i	−0.453557	−	0.392792i
$701$	−44.0908			−1.66529			−0.832644	−	0.553809i	$-0.813174\pi$
$701$	−44.0908			−1.66529			−0.832644	+	0.553809i	$0.813174\pi$
$702$		0			0
$703$	−12.5000	+	21.6506i	−0.471446	+	0.816569i
$704$	−39.1918	−	22.6274i	−1.47710	−	0.852803i
$705$		0			0
$706$	−22.0000	+	38.1051i	−0.827981	+	1.43411i
$707$	19.5959	−	22.6274i	0.736980	−	0.850992i
$708$		0			0
$709$	−1.00000	−	1.73205i	−0.0375558	−	0.0650485i	0.846637	−	0.532172i	$-0.178624\pi$
$709$	−1.00000	−	1.73205i	−0.0375558	−	0.0650485i	−0.884192	+	0.467123i	$0.845291\pi$
$710$	−9.79796	+	5.65685i	−0.367711	+	0.212298i
$711$		0			0
$712$	−16.0000	−	27.7128i	−0.599625	−	1.03858i
$713$		−	2.82843i		−	0.105925i
$714$		0			0
$715$			83.1384i			3.10920i
$716$	4.89898	+	2.82843i	0.183083	+	0.105703i
$717$		0			0
$718$	−16.0000	−	27.7128i	−0.597115	−	1.03423i
$719$	19.5959	+	33.9411i	0.730804	+	1.26579i	0.956540	+	0.291602i	$0.0941882\pi$
$719$	19.5959	+	33.9411i	0.730804	+	1.26579i	−0.225735	+	0.974189i	$0.572478\pi$
$720$		0			0
$721$	−2.50000	+	0.866025i	−0.0931049	+	0.0322525i
$722$	−7.34847	−	4.24264i	−0.273482	−	0.157895i
$723$		0			0
$724$			10.3923i			0.386227i
$725$		0			0
$726$		0			0
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$	−7.34847	+	38.1838i	−0.272352	+	1.41518i
$729$		0			0
$730$			6.92820i			0.256424i
$731$	7.34847	−	12.7279i	0.271793	−	0.470759i
$732$		0			0
$733$	−7.50000	+	4.33013i	−0.277019	+	0.159937i	−0.632073	−	0.774909i	$-0.717796\pi$
$733$	−7.50000	+	4.33013i	−0.277019	+	0.159937i	0.355054	+	0.934846i	$0.384462\pi$
$734$	−13.4722	−	7.77817i	−0.497268	−	0.287098i
$735$		0			0
$736$	8.00000	+	13.8564i	0.294884	+	0.510754i
$737$	−24.4949	−	42.4264i	−0.902281	−	1.56280i
$738$		0			0
$739$	28.5000	+	16.4545i	1.04839	+	0.605288i	0.922198	−	0.386718i	$-0.126391\pi$
$739$	28.5000	+	16.4545i	1.04839	+	0.605288i	0.126191	+	0.992006i	$0.459725\pi$
$740$	24.4949	+	14.1421i	0.900450	+	0.519875i
$741$		0			0
$742$	−12.0000	+	13.8564i	−0.440534	+	0.508685i
$743$			45.2548i			1.66024i	0.557586	+	0.830119i	$0.311728\pi$
$743$			45.2548i			1.66024i	−0.557586	+	0.830119i	$0.688272\pi$
$744$		0			0
$745$	24.0000	+	13.8564i	0.879292	+	0.507659i
$746$	−1.22474	+	0.707107i	−0.0448411	+	0.0258890i
$747$		0			0
$748$	16.0000	+	27.7128i	0.585018	+	1.01328i
$749$	2.44949	+	7.07107i	0.0895024	+	0.258371i
$750$		0			0
$751$	−7.50000	+	4.33013i	−0.273679	+	0.158009i	−0.630558	−	0.776142i	$-0.717174\pi$
$751$	−7.50000	+	4.33013i	−0.273679	+	0.158009i	0.356879	+	0.934150i	$0.383841\pi$
$752$	−9.79796	−	16.9706i	−0.357295	−	0.618853i
$753$		0			0
$754$		0			0
$755$	48.9898			1.78292
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	51.4393			1.86836
$759$		0			0
$760$	−20.0000	+	34.6410i	−0.725476	+	1.25656i
$761$	17.1464	−	9.89949i	0.621558	−	0.358856i	−0.155918	−	0.987770i	$-0.549833\pi$
$761$	17.1464	−	9.89949i	0.621558	−	0.358856i	0.777475	+	0.628914i	$0.216500\pi$
$762$		0			0
$763$	−10.0000	−	8.66025i	−0.362024	−	0.313522i
$764$	−34.2929	+	19.7990i	−1.24067	+	0.716302i
$765$		0			0
$766$	42.0000	−	24.2487i	1.51752	−	0.876142i
$767$	22.0454	+	12.7279i	0.796014	+	0.459579i
$768$		0			0
$769$		−	15.5885i		−	0.562134i	−0.959688	−	0.281067i	$-0.909312\pi$
$769$		−	15.5885i		−	0.562134i	0.959688	−	0.281067i	$-0.0906883\pi$
$770$	−58.7878	−	11.3137i	−2.11856	−	0.407718i
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	−9.79796	−	5.65685i	−0.352408	−	0.203463i	0.313337	−	0.949642i	$-0.398553\pi$
$773$	−9.79796	−	5.65685i	−0.352408	−	0.203463i	−0.665745	+	0.746179i	$0.731886\pi$
$774$		0			0
$775$	−1.50000	−	2.59808i	−0.0538816	−	0.0933257i
$776$		0			0
$777$		0			0
$778$	−30.0000	−	17.3205i	−1.07555	−	0.620970i
$779$	−24.4949	+	14.1421i	−0.877621	+	0.506695i
$780$		0			0
$781$	−8.00000	+	13.8564i	−0.286263	+	0.495821i
$782$		−	11.3137i		−	0.404577i
$783$		0			0
$784$	−26.0000	−	10.3923i	−0.928571	−	0.371154i
$785$	19.5959			0.699408
$786$		0			0
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	−0.687481	−	0.726202i	$-0.741284\pi$
$787$	8.00000	−	13.8564i	0.285169	−	0.493928i	0.972650	+	0.232275i	$0.0746169\pi$
$788$	−29.3939			−1.04711
$789$		0			0
$790$	6.00000	+	3.46410i	0.213470	+	0.123247i
$791$	7.34847	−	38.1838i	0.261281	−	1.35766i
$792$		0			0
$793$	18.0000	+	31.1769i	0.639199	+	1.10712i
$794$	−20.8207	−	36.0624i	−0.738898	−	1.27981i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$		−	31.1127i		−	1.10207i	−0.834483	−	0.551034i	$-0.814233\pi$
$797$		−	31.1127i		−	1.10207i	0.834483	−	0.551034i	$-0.185767\pi$
$798$		0			0
$799$			13.8564i			0.490204i
$800$	14.6969	+	8.48528i	0.519615	+	0.300000i
$801$		0			0
$802$	6.00000	−	3.46410i	0.211867	−	0.122322i
$803$	4.89898	+	8.48528i	0.172881	+	0.299439i
$804$		0			0
$805$	16.0000	+	13.8564i	0.563926	+	0.488374i
$806$	−3.67423	+	6.36396i	−0.129419	+	0.224161i
$807$		0			0
$808$	−16.0000	+	27.7128i	−0.562878	+	0.974933i
$809$	2.44949	−	4.24264i	0.0861195	−	0.149163i	−0.819748	−	0.572724i	$-0.805887\pi$
$809$	2.44949	−	4.24264i	0.0861195	−	0.149163i	0.905868	+	0.423561i	$0.139220\pi$
$810$		0			0
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$		0			0
$813$		0			0
$814$	40.0000			1.40200
$815$	−4.89898	+	8.48528i	−0.171604	+	0.297226i
$816$		0			0
$817$	22.5000	−	12.9904i	0.787175	−	0.454476i
$818$	20.8207	−	36.0624i	0.727977	−	1.26089i
$819$		0			0
$820$	16.0000	+	27.7128i	0.558744	+	0.967773i
$821$	−17.1464	−	29.6985i	−0.598414	−	1.03648i	−0.993055	−	0.117649i	$-0.962464\pi$
$821$	−17.1464	−	29.6985i	−0.598414	−	1.03648i	0.394641	−	0.918835i	$-0.370869\pi$
$822$		0			0
$823$	−39.0000	−	22.5167i	−1.35945	−	0.784881i	−0.369904	−	0.929070i	$-0.620610\pi$
$823$	−39.0000	−	22.5167i	−1.35945	−	0.784881i	−0.989550	+	0.144188i	$0.953943\pi$
$824$	2.44949	−	1.41421i	0.0853320	−	0.0492665i
$825$		0			0
$826$	−12.0000	+	13.8564i	−0.417533	+	0.482126i
$827$			2.82843i			0.0983540i	0.998790	+	0.0491770i	$0.0156598\pi$
$827$			2.82843i			0.0983540i	−0.998790	+	0.0491770i	$0.984340\pi$
$828$		0			0
$829$	28.5000	+	16.4545i	0.989846	+	0.571488i	0.905228	−	0.424926i	$-0.139700\pi$
$829$	28.5000	+	16.4545i	0.989846	+	0.571488i	0.0846177	+	0.996413i	$0.473033\pi$
$830$	−29.3939	−	50.9117i	−1.02028	−	1.76717i
$831$		0			0
$832$		−	41.5692i		−	1.44115i
$833$	12.2474	+	15.5563i	0.424349	+	0.538996i
$834$		0			0
$835$	36.0000	−	20.7846i	1.24583	−	0.719281i
$836$			56.5685i			1.95646i
$837$		0			0
$838$		0			0
$839$	29.3939			1.01479			0.507395	−	0.861714i	$-0.330609\pi$
$839$	29.3939			1.01479			0.507395	+	0.861714i	$0.330609\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$			32.5269i			1.12095i
$843$		0			0
$844$			20.7846i			0.715436i
$845$	−34.2929	+	19.7990i	−1.17971	+	0.681106i
$846$		0			0
$847$	−52.5000	+	18.1865i	−1.80392	+	0.624897i
$848$	9.79796	−	16.9706i	0.336463	−	0.582772i
$849$		0			0
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$	−12.2474	−	7.07107i	−0.419837	−	0.242393i
$852$		0			0
$853$			15.5885i			0.533739i	0.963733	+	0.266869i	$0.0859892\pi$
$853$			15.5885i			0.533739i	−0.963733	+	0.266869i	$0.914011\pi$
$854$	−24.4949	+	8.48528i	−0.838198	+	0.290360i
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	4.89898	+	2.82843i	0.167346	+	0.0966172i	0.581334	−	0.813665i	$-0.302531\pi$
$857$	4.89898	+	2.82843i	0.167346	+	0.0966172i	−0.413988	+	0.910282i	$0.635864\pi$
$858$		0			0
$859$	−4.00000	−	6.92820i	−0.136478	−	0.236387i	0.789683	−	0.613515i	$-0.210245\pi$
$859$	−4.00000	−	6.92820i	−0.136478	−	0.236387i	−0.926161	+	0.377128i	$0.876912\pi$
$860$	−14.6969	−	25.4558i	−0.501161	−	0.868037i
$861$		0			0
$862$	−10.0000	+	17.3205i	−0.340601	+	0.589939i
$863$	24.4949	−	14.1421i	0.833816	−	0.481404i	−0.0213414	−	0.999772i	$-0.506794\pi$
$863$	24.4949	−	14.1421i	0.833816	−	0.481404i	0.855157	+	0.518368i	$0.173460\pi$
$864$		0			0
$865$	28.0000	−	48.4974i	0.952029	−	1.64896i
$866$	−7.34847			−0.249711
$867$		0			0
$868$	−4.00000	−	3.46410i	−0.135769	−	0.117579i
$869$	9.79796			0.332373
$870$		0			0
$871$	22.5000	−	38.9711i	0.762383	−	1.32049i
$872$	12.2474	+	7.07107i	0.414751	+	0.239457i
$873$		0			0
$874$	10.0000	−	17.3205i	0.338255	−	0.585875i
$875$	−14.6969	−	2.82843i	−0.496847	−	0.0956183i
$876$		0			0
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$	−4.89898	+	2.82843i	−0.165333	+	0.0954548i
$879$		0			0
$880$	64.0000			2.15744
$881$			53.7401i			1.81055i	0.424826	+	0.905275i	$0.360335\pi$
$881$			53.7401i			1.81055i	−0.424826	+	0.905275i	$0.639665\pi$
$882$		0			0
$883$		−	15.5885i		−	0.524593i	−0.964987	−	0.262297i	$-0.915520\pi$
$883$		−	15.5885i		−	0.524593i	0.964987	−	0.262297i	$-0.0844799\pi$
$884$	−14.6969	+	25.4558i	−0.494312	+	0.856173i
$885$		0			0
$886$	−22.0000	−	38.1051i	−0.739104	−	1.28017i
$887$	19.5959	+	33.9411i	0.657967	+	1.13963i	0.981141	+	0.193292i	$0.0619165\pi$
$887$	19.5959	+	33.9411i	0.657967	+	1.13963i	−0.323175	+	0.946339i	$0.604750\pi$
$888$		0			0
$889$	−40.5000	−	7.79423i	−1.35833	−	0.261410i
$890$	39.1918	+	22.6274i	1.31371	+	0.758473i
$891$		0			0
$892$	8.00000			0.267860
$893$	−12.2474	+	21.2132i	−0.409845	+	0.709873i
$894$		0			0
$895$	−8.00000			−0.267411
$896$	29.3939	+	5.65685i	0.981981	+	0.188982i
$897$		0			0
$898$		−	20.7846i		−	0.693591i
$899$		0			0
$900$		0			0
$901$	−12.0000	+	6.92820i	−0.399778	+	0.230812i
$902$	39.1918	+	22.6274i	1.30495	+	0.753411i
$903$		0			0
$904$			41.5692i			1.38257i
$905$	−7.34847	−	12.7279i	−0.244271	−	0.423090i
$906$		0			0
$907$	19.5000	+	11.2583i	0.647487	+	0.373827i	0.787493	−	0.616324i	$-0.211379\pi$
$907$	19.5000	+	11.2583i	0.647487	+	0.373827i	−0.140006	+	0.990151i	$0.544712\pi$
$908$	9.79796	−	16.9706i	0.325157	−	0.563188i
$909$		0			0
$910$	−18.0000	−	51.9615i	−0.596694	−	1.72251i
$911$			2.82843i			0.0937100i	0.998902	+	0.0468550i	$0.0149199\pi$
$911$			2.82843i			0.0937100i	−0.998902	+	0.0468550i	$0.985080\pi$
$912$		0			0
$913$	−72.0000	−	41.5692i	−2.38285	−	1.37574i
$914$	−8.57321	+	4.94975i	−0.283577	+	0.163723i
$915$		0			0
$916$	33.0000	−	19.0526i	1.09035	−	0.629514i
$917$	48.9898	−	16.9706i	1.61779	−	0.560417i
$918$		0			0
$919$	−43.5000	+	25.1147i	−1.43493	+	0.828459i	−0.997491	−	0.0707883i	$-0.977449\pi$
$919$	−43.5000	+	25.1147i	−1.43493	+	0.828459i	−0.437441	+	0.899247i	$0.644115\pi$
$920$	−19.5959	−	11.3137i	−0.646058	−	0.373002i
$921$		0			0
$922$	−16.0000			−0.526932
$923$	−14.6969			−0.483756
$924$		0			0
$925$	−15.0000			−0.493197
$926$	7.34847			0.241486
$927$		0			0
$928$		0			0
$929$	−12.2474	+	7.07107i	−0.401826	+	0.231994i	−0.687271	−	0.726401i	$-0.741192\pi$
$929$	−12.2474	+	7.07107i	−0.401826	+	0.231994i	0.285446	+	0.958395i	$0.407858\pi$
$930$		0			0
$931$	5.00000	+	34.6410i	0.163868	+	1.13531i
$932$	−24.4949	−	42.4264i	−0.802357	−	1.38972i
$933$		0			0
$934$	6.00000	−	3.46410i	0.196326	−	0.113349i
$935$	−39.1918	−	22.6274i	−1.28171	−	0.739996i
$936$		0			0
$937$			36.3731i			1.18826i	0.804370	+	0.594128i	$0.202503\pi$
$937$			36.3731i			1.18826i	−0.804370	+	0.594128i	$0.797497\pi$
$938$	24.4949	+	21.2132i	0.799787	+	0.692636i
$939$		0			0
$940$	24.0000	+	13.8564i	0.782794	+	0.451946i
$941$	41.6413	+	24.0416i	1.35747	+	0.783735i	0.989282	−	0.146017i	$-0.0466455\pi$
$941$	41.6413	+	24.0416i	1.35747	+	0.783735i	0.368186	+	0.929752i	$0.379979\pi$
$942$		0			0
$943$	−8.00000	−	13.8564i	−0.260516	−	0.451227i
$944$	9.79796	−	16.9706i	0.318896	−	0.552345i
$945$		0			0
$946$	−36.0000	−	20.7846i	−1.17046	−	0.675766i
$947$	−4.89898	+	2.82843i	−0.159195	+	0.0919115i	−0.577481	−	0.816404i	$-0.695964\pi$
$947$	−4.89898	+	2.82843i	−0.159195	+	0.0919115i	0.418286	+	0.908315i	$0.362631\pi$
$948$		0			0
$949$	−4.50000	+	7.79423i	−0.146076	+	0.253011i
$950$		−	21.2132i		−	0.688247i
$951$		0			0
$952$	−16.0000	−	13.8564i	−0.518563	−	0.449089i
$953$	44.0908			1.42824			0.714121	−	0.700022i	$-0.246827\pi$
$953$	44.0908			1.42824			0.714121	+	0.700022i	$0.246827\pi$
$954$		0			0
$955$	28.0000	−	48.4974i	0.906059	−	1.56934i
$956$		−	22.6274i		−	0.731823i
$957$		0			0
$958$	42.0000	+	24.2487i	1.35696	+	0.783440i
$959$	−19.5959	−	16.9706i	−0.632785	−	0.548008i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	18.3712	+	31.8198i	0.592310	+	1.02591i
$963$		0			0
$964$	24.0000	+	13.8564i	0.772988	+	0.446285i
$965$		−	19.7990i		−	0.637352i
$966$		0			0
$967$		−	25.9808i		−	0.835485i	−0.908565	−	0.417742i	$-0.862821\pi$
$967$		−	25.9808i		−	0.835485i	0.908565	−	0.417742i	$-0.137179\pi$
$968$	51.4393	−	29.6985i	1.65332	−	0.954545i
$969$		0			0
$970$		0			0
$971$	−17.1464	−	29.6985i	−0.550255	−	0.953070i	−0.998256	−	0.0590366i	$-0.981197\pi$
$971$	−17.1464	−	29.6985i	−0.550255	−	0.953070i	0.448001	−	0.894033i	$-0.352136\pi$
$972$		0			0
$973$	6.50000	−	33.7750i	0.208380	−	1.08278i
$974$	−15.9217	+	27.5772i	−0.510164	+	0.883629i
$975$		0			0
$976$	24.0000	−	13.8564i	0.768221	−	0.443533i
$977$	9.79796	−	16.9706i	0.313464	−	0.542936i	−0.665645	−	0.746268i	$-0.731844\pi$
$977$	9.79796	−	16.9706i	0.313464	−	0.542936i	0.979110	+	0.203332i	$0.0651770\pi$
$978$		0			0
$979$	64.0000			2.04545
$980$	39.1918	−	5.65685i	1.25194	−	0.180702i
$981$		0			0
$982$	8.00000			0.255290
$983$	−12.2474	+	21.2132i	−0.390633	+	0.676596i	−0.992533	−	0.121975i	$-0.961077\pi$
$983$	−12.2474	+	21.2132i	−0.390633	+	0.676596i	0.601900	+	0.798571i	$0.294410\pi$
$984$		0			0
$985$	36.0000	−	20.7846i	1.14706	−	0.662253i
$986$		0			0
$987$		0			0
$988$	−45.0000	+	25.9808i	−1.43164	+	0.826558i
$989$	7.34847	+	12.7279i	0.233668	+	0.404724i
$990$		0			0
$991$	19.5000	+	11.2583i	0.619438	+	0.357633i	0.776650	−	0.629932i	$-0.216917\pi$
$991$	19.5000	+	11.2583i	0.619438	+	0.357633i	−0.157212	+	0.987565i	$0.550251\pi$
$992$	4.89898	+	2.82843i	0.155543	+	0.0898027i
$993$		0			0
$994$	2.00000	−	10.3923i	0.0634361	−	0.329624i
$995$		−	11.3137i		−	0.358669i
$996$		0			0
$997$	−16.5000	−	9.52628i	−0.522560	−	0.301700i	0.215421	−	0.976521i	$-0.430888\pi$
$997$	−16.5000	−	9.52628i	−0.522560	−	0.301700i	−0.737982	+	0.674821i	$0.764221\pi$
$998$	23.2702	+	40.3051i	0.736604	+	1.27584i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bf.b.199.2	yes	4
3.2	odd	2	inner	252.2.bf.b.199.1	yes	4
4.3	odd	2		252.2.bf.c.199.2	yes	4
7.3	odd	6		1764.2.b.c.1567.1		4
7.4	even	3		1764.2.b.d.1567.1		4
7.5	odd	6		252.2.bf.c.19.2	yes	4
12.11	even	2		252.2.bf.c.199.1	yes	4
21.5	even	6		252.2.bf.c.19.1	yes	4
21.11	odd	6		1764.2.b.d.1567.4		4
21.17	even	6		1764.2.b.c.1567.4		4
28.3	even	6		1764.2.b.d.1567.2		4
28.11	odd	6		1764.2.b.c.1567.2		4
28.19	even	6	inner	252.2.bf.b.19.1	✓	4
84.11	even	6		1764.2.b.c.1567.3		4
84.47	odd	6	inner	252.2.bf.b.19.2	yes	4
84.59	odd	6		1764.2.b.d.1567.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bf.b.19.1	✓	4	28.19	even	6	inner
252.2.bf.b.19.2	yes	4	84.47	odd	6	inner
252.2.bf.b.199.1	yes	4	3.2	odd	2	inner
252.2.bf.b.199.2	yes	4	1.1	even	1	trivial
252.2.bf.c.19.1	yes	4	21.5	even	6
252.2.bf.c.19.2	yes	4	7.5	odd	6
252.2.bf.c.199.1	yes	4	12.11	even	2
252.2.bf.c.199.2	yes	4	4.3	odd	2
1764.2.b.c.1567.1		4	7.3	odd	6
1764.2.b.c.1567.2		4	28.11	odd	6
1764.2.b.c.1567.3		4	84.11	even	6
1764.2.b.c.1567.4		4	21.17	even	6
1764.2.b.d.1567.1		4	7.4	even	3
1764.2.b.d.1567.2		4	28.3	even	6
1764.2.b.d.1567.3		4	84.59	odd	6
1764.2.b.d.1567.4		4	21.11	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(2.44949 - 1.41421i) q^{5} +(-0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(2.44949 - 1.41421i) q^{5} +(-0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +(2.00000 + 3.46410i) q^{10} +(4.89898 + 2.82843i) q^{11} +5.19615i q^{13} +(-3.67423 - 0.707107i) q^{14} +4.00000 q^{16} +(-2.44949 - 1.41421i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-4.89898 + 2.82843i) q^{20} +(-4.00000 + 6.92820i) q^{22} +(2.44949 - 1.41421i) q^{23} +(1.50000 - 2.59808i) q^{25} -7.34847 q^{26} +(1.00000 - 5.19615i) q^{28} +(0.500000 - 0.866025i) q^{31} +5.65685i q^{32} +(2.00000 - 3.46410i) q^{34} +(2.44949 + 7.07107i) q^{35} +(-2.50000 - 4.33013i) q^{37} +(6.12372 - 3.53553i) q^{38} +(-4.00000 - 6.92820i) q^{40} -5.65685i q^{41} +5.19615i q^{43} +(-9.79796 - 5.65685i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-2.44949 - 4.24264i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(3.67423 + 2.12132i) q^{50} -10.3923i q^{52} +(2.44949 - 4.24264i) q^{53} +16.0000 q^{55} +(7.34847 + 1.41421i) q^{56} +(2.44949 - 4.24264i) q^{59} +(6.00000 - 3.46410i) q^{61} +(1.22474 + 0.707107i) q^{62} -8.00000 q^{64} +(7.34847 + 12.7279i) q^{65} +(-7.50000 - 4.33013i) q^{67} +(4.89898 + 2.82843i) q^{68} +(-10.0000 + 3.46410i) q^{70} +2.82843i q^{71} +(1.50000 + 0.866025i) q^{73} +(6.12372 - 3.53553i) q^{74} +(5.00000 + 8.66025i) q^{76} +(-9.79796 + 11.3137i) q^{77} +(1.50000 - 0.866025i) q^{79} +(9.79796 - 5.65685i) q^{80} +8.00000 q^{82} -14.6969 q^{83} -8.00000 q^{85} -7.34847 q^{86} +(8.00000 - 13.8564i) q^{88} +(9.79796 - 5.65685i) q^{89} +(-13.5000 - 2.59808i) q^{91} +(-4.89898 + 2.82843i) q^{92} +(6.00000 - 3.46410i) q^{94} +(-12.2474 - 7.07107i) q^{95} +(3.67423 - 9.19239i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} - 2 q^{7}+O(q^{10}) \) 4 * q - 8 * q^4 - 2 * q^7	\( 4 q - 8 q^{4} - 2 q^{7} + 8 q^{10} + 16 q^{16} - 10 q^{19} - 16 q^{22} + 6 q^{25} + 4 q^{28} + 2 q^{31} + 8 q^{34} - 10 q^{37} - 16 q^{40} + 8 q^{46} - 26 q^{49} + 64 q^{55} + 24 q^{61} - 32 q^{64} - 30 q^{67} - 40 q^{70} + 6 q^{73} + 20 q^{76} + 6 q^{79} + 32 q^{82} - 32 q^{85} + 32 q^{88} - 54 q^{91} + 24 q^{94}+O(q^{100}) \) 4 * q - 8 * q^4 - 2 * q^7 + 8 * q^10 + 16 * q^16 - 10 * q^19 - 16 * q^22 + 6 * q^25 + 4 * q^28 + 2 * q^31 + 8 * q^34 - 10 * q^37 - 16 * q^40 + 8 * q^46 - 26 * q^49 + 64 * q^55 + 24 * q^61 - 32 * q^64 - 30 * q^67 - 40 * q^70 + 6 * q^73 + 20 * q^76 + 6 * q^79 + 32 * q^82 - 32 * q^85 + 32 * q^88 - 54 * q^91 + 24 * q^94

Introduction

L-functions

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