LMFDB - Newform orbit 91.2.h.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [91,2,Mod(16,91)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(91, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("91.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$91 = 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	91.h (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1$ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

Coefficients of the $q$ -expansion are expressed in terms of a basis $1,\beta_1,\ldots,\beta_{11}$ for the coefficient ring described below. We also show the integral $q$ -expansion of the trace form.

$f(q)$	$=$	$q + ( - \beta_{11} + \beta_{5} + \beta_{3}) q^{2} + \beta_{11} q^{3} + ( - \beta_{10} - \beta_{6} + 1) q^{4} - \beta_{9} q^{5} + (\beta_{10} + \beta_{8} + 2 \beta_{7} + \cdots - 2) q^{6} + ( - \beta_{9} - \beta_{8} + \cdots + \beta_{2}) q^{7}+ \cdots + (2 \beta_{11} - 4 \beta_{5} + 2 \beta_{4} + \cdots - 3) q^{99}+O(q^{100})$ q + (-b11 + b5 + b3) * q^2 + b11 * q^3 + (-b10 - b6 + 1) * q^4 - b9 * q^5 + (b10 + b8 + 2b7 + b4 - 2) q^6 + (-b9 - b8 - b7 - b5 - b4 + b2) * q^7 + (b10 + b6 - b5 - 1) * q^8 + (-b8 + b6) * q^9 + (b9 - b7 + b5 + b1 + 1) * q^10 + (-b11 - b10 - b7 - b5 - b1 + 1) * q^11 + (2b11 - b10 + b9 - b7 + 1) q^12 + (b11 - b10 - b6 + b5 + b4 + b1) * q^13 + (-b11 - b5 - b4 - b3 - b2 - b1) * q^14 - b6 * q^15 + (2b11 + b10 + b6 - b5 - b4 - 2b3 - 2) * q^16 + (-b11 + b10 + b6 + b3 - 1) * q^17 + (b7 - b6 - 2b3 - b2 - 2b1) * q^18 + (2b8 - b7 + b6 - 2b3 + b2 + 2b1) q^19 + (-b11 + b9 + b8 + b4) * q^20 + (-b11 + b10 + b7 + 3b3 - b1 - 1) q^21 + (-2b11 - 2b8 + b5 - 2b4 + b1) q^22 + (b11 - b10 + 3b9 - b6 + 2b5 + b4 - b3 - 3b2 + 1) q^23 + (-2b11 + b10 - b9 + 2b7 - 2) * q^24 + (2b7 - 2b6 + b3 + b2 - b1) * q^25 + (2b10 + b9 + 2b8 + b7 + b6 + 2b5 + 2b4 - b2 - 2) * q^26 + (b10 - b9 + b6 + b5 + b2 - 1) * q^27 + (-b11 - b10 + b9 - b8 - 2b7 + b6 + b3 + b1 + 1) q^28 + (2b8 + b7 - b6 + b3 + 2b1) * q^29 + (-b7 + b6 + b3) * q^30 + (3b7 + b6 - 2b2 - 2b1) q^31 + (2b11 - b10 - b9 - b6 - 2b5 + b4 - 2b3 + b2 - 2) q^32 + (b8 + 3b7 + 2b3 + b2) * q^33 + (2b11 - 2b10 - 2b6 - b5 - b4 - 2b3 + 3) * q^34 + (b11 + b10 + b9 - b8 - b7 - b6 - 2b5 - b2 - 2b1 + 2) * q^35 + (-2b8 - 4b7 + b6 + 2b3 + b2) q^36 + (-b10 - 3b9 - b6 + 3b2 + 2) * q^37 + (-4b7 + b6 + b2 + 4b1) * q^38 + (-b11 - b10 + b9 - b8 - 5b7 + b6 + b5 + b1 + 1) q^39 + (b11 - b10 - 2b9 - b8 + b7 - b5 - b4 - b1 - 1) q^40 + (-2b7 + 2b6 - b3 - b2) * q^41 + (2b11 - 2b10 + b8 + 4b7 - 3b6 - b5 - b4 - b1 + 3) * q^42 + (b11 + 2b10 + 3b7 - 2b5 - 2b1 - 3) * q^43 + (-2b9 - b8 - 3b7 - 2b5 - b4 - 2b1 + 3) * q^44 + (b11 - b10 - 2b9 - b6 - b3 + 2b2 + 1) * q^45 + (-b11 + 2b10 - 2b9 + 2b6 + 3b4 + b3 + 2b2 - 4) q^46 + (-3b11 - 2b10 - 2b8 - 2b7 + 4b5 - 2b4 + 4b1 + 2) q^47 + (-b11 - b10 - b9 - 2b8 - 4b7 - b5 - 2b4 - b1 + 4) q^48 + (-b11 + 2b10 + b9 - b8 - b7 + b6 + 3b5 + b4 - b3 - 2b2 + 3b1) * q^49 + (2b7 + b6 + 4b3 - b2 - 3b1) q^50 + (-2b11 + 2b10 - b9 + b8 + 4b7 + b4 - 4) q^51 + (4b11 + b9 - b7 + b6 - b5 - 2b3 + b2 + b1 + 3) * q^52 + (-2b8 - 3b2 - b1) * q^53 + (2b11 - b10 + b9 - b6 + b4 - 2b3 - b2 + 3) * q^54 + (b8 + b7 + 2b6 - b3 - b1) q^55 + (-b9 + b8 + 2b7 - 2b6 + 2b5 + b4 - b3 + b2 + b1) q^56 + (2b11 - b9 - 2b5 - 2b4 - 2b3 + b2 + 3) * q^57 + (3b8 - b7 + 4b3 + 2b2 + 3b1) * q^58 + (-b11 - 2b10 + b9 - 2b6 - b5 - 2b4 + b3 - b2 - 1) q^59 + (b8 + 3b7 - 2b3 + b1) * q^60 + (2b7 - 2b6 + 5b3 - 2b2 - 6b1) q^61 + (-2b8 + b7 - b6 + 2b3 + 2b2 - b1) q^62 + (3b10 + b8 + b7 + b6 - 2b3 + 2b2 + 3b1 - 5) * q^63 + (-2b11 + b10 + 2b9 + b6 + 3b5 + 2b4 + 2b3 - 2b2 - 2) * q^64 + (-b11 - b10 + 2b9 + 2b8 - 2b7 - 2b6 + 2b4 + b2 + b1 + 1) q^65 + (2b8 + 5b7 - 2b6 + 4b3 - 2b1) q^66 + (2b11 + 3b10 + 2b9 + 2b8 + 3b7 + b5 + 2b4 + b1 - 3) * q^67 + (-4b11 + 2b10 - b9 + 2b6 + b5 + b4 + 4b3 + b2 - 5) * q^68 + (-5b10 + b9 - b8 - 6b7 + b5 - b4 + b1 + 6) * q^69 + (-b11 - b9 - b8 + 2b7 + b6 + b5 - b4 + b3 - b1 - 4) q^70 + (-3b11 - 2b10 + b9 + 2b8 - 2b7 + 2b4 + 2) q^71 + (2b8 + 4b7 - b6 - 3b3 - b2 + 3b1) * q^72 + (-4b7 + b3 - 5b1) * q^73 + (-3b11 + b10 + 3b9 + b6 + 5b5 + 3b3 - 3b2 + 2) q^74 + (4b11 + 2b9 + b4 - 4b3 - 2b2) * q^75 + (-3b6 - b3 - 3b2 - b1) * q^76 + (-b10 - b9 + b8 - 3b7 + 2b6 - b5 + 2b4 - 4b3 + 2b2 + 3b1 + 1) * q^77 + (-2b11 - b9 - b6 - 6b3 - b2 + 2b1 + 1) q^78 + (-3b11 + 2b9 - b8 - 2b7 - b5 - b4 - b1 + 2) q^79 + (b11 + 2b10 - b9 - 2b8 + 2b7 - b5 - 2b4 - b1 - 2) * q^80 + (-2b11 - b10 - b9 - 3b8 - 3b4) q^81 + (-b8 - b7 - b6 - 4b3 + b2 + 3b1) * q^82 + (-b11 + b10 + b9 + b6 - 3b4 + b3 - b2 - 4) q^83 + (-4b11 + 2b10 - b9 + b8 + 2b7 + 3b6 + b5 + b4 + 6b3 + 2b2 - 5) * q^84 + (b11 - b10 - b9 - b8 - b4) * q^85 + (5b11 - b10 - b8 + 2b7 - 3b5 - b4 - 3b1 - 2) * q^86 + (6b11 + b9 - 2b5 + b4 - 6b3 - b2 - 4) q^87 + (b9 + 2b8 + b5 + 2b4 + b1) * q^88 + (5b11 + 4b10 + 4b6 - 8b5 - b4 - 5b3 - 4) q^89 + (-2b11 + 2b10 + 2b9 + 2b6 + 3b5 + b4 + 2b3 - 2b2 - 1) q^90 + (-b11 + b10 + 3b9 - b8 + 5b7 - b5 + 4b3 - b2 - b1 - 4) q^91 + (7b11 - b10 - b9 - b6 - 3b4 - 7b3 + b2 + 4) q^92 + (2b11 - b10 - b9 - b6 - 2b3 + b2 + 1) * q^93 + (-6b11 - b10 - 2b9 + b8 - 8b7 - 2b5 + b4 - 2b1 + 8) q^94 + (2b11 + 4b10 - 2b9 + 4b6 - 3b5 - 3b4 - 2b3 + 2b2 - 1) * q^95 + (-3b11 - 2b10 + b9 - 2b8 - 5b7 + b5 - 2b4 + b1 + 5) q^96 + (4b11 + 3b10 + b8 + 8b7 - 2b5 + b4 - 2b1 - 8) q^97 + (3b11 - 3b10 + b8 - 9b7 + b5 + 2b4 - 4b3 + 6) q^98 + (2b11 - 4b5 + 2b4 - 2b3 - 3) * q^99
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20}+ \cdots - 20 q^{99}+O(q^{100})$ 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

Basis of coefficient ring in terms of a root $\nu$ of $x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1$ x^12 - x^11 + 7*x^10 - 2*x^9 + 33*x^8 - 11*x^7 + 55*x^6 + 17*x^5 + 47*x^4 + x^3 + 8*x^2 + x + 1 :

$\beta_{1}$	$=$	$\nu$ v
$\beta_{2}$	$=$	$( - 29696 \nu^{11} - 478424 \nu^{10} + 682506 \nu^{9} - 3846008 \nu^{8} + 2684563 \nu^{7} + \cdots - 2119374 ) / 3318773$ (-29696v^11 - 478424v^10 + 682506v^9 - 3846008v^8 + 2684563v^7 - 16878368v^6 + 16008568v^5 - 31119861v^4 + 8363982v^3 - 14058754v^2 + 5624108*v - 2119374) / 3318773
$\beta_{3}$	$=$	$( - 73788 \nu^{11} - 498559 \nu^{10} + 495146 \nu^{9} - 4188508 \nu^{8} + 1631143 \nu^{7} + \cdots - 2229034 ) / 3318773$ (-73788v^11 - 498559v^10 + 495146v^9 - 4188508v^8 + 1631143v^7 - 18206928v^6 + 16328192v^5 - 34289666v^4 + 8704710v^3 - 14803002v^2 + 21668998*v - 2229034) / 3318773
$\beta_{4}$	$=$	$( - 109660 \nu^{11} + 153752 \nu^{10} - 747485 \nu^{9} + 406680 \nu^{8} - 3276280 \nu^{7} + \cdots - 6198231 ) / 3318773$ (-109660v^11 + 153752v^10 - 747485v^9 + 406680v^8 - 3276280v^7 + 2259680v^6 - 4702740v^5 - 2183844v^4 - 1984215v^3 - 450388v^2 - 133032*v - 6198231) / 3318773
$\beta_{5}$	$=$	$( 439315 \nu^{11} - 329655 \nu^{10} + 2921453 \nu^{9} - 131145 \nu^{8} + 14090715 \nu^{7} + \cdots + 572347 ) / 3318773$ (439315v^11 - 329655v^10 + 2921453v^9 - 131145v^8 + 14090715v^7 - 1556185v^6 + 21902645v^5 + 12171095v^4 + 22831649v^3 + 2423530v^2 + 646135*v + 572347) / 3318773
$\beta_{6}$	$=$	$( 566698 \nu^{11} - 1732988 \nu^{10} + 5617249 \nu^{9} - 9944902 \nu^{8} + 24340355 \nu^{7} + \cdots - 6707921 ) / 3318773$ (566698v^11 - 1732988v^10 + 5617249v^9 - 9944902v^8 + 24340355v^7 - 46353032v^6 + 58565408v^5 - 63065800v^4 + 27901335v^3 - 44235433v^2 + 12588213*v - 6707921) / 3318773
$\beta_{7}$	$=$	$( - 572347 \nu^{11} + 1011662 \nu^{10} - 4336084 \nu^{9} + 4066147 \nu^{8} - 19018596 \nu^{7} + \cdots + 3392561 ) / 3318773$ (-572347v^11 + 1011662v^10 - 4336084v^9 + 4066147v^8 - 19018596v^7 + 20386532v^6 - 33035270v^5 + 12172746v^4 - 14729214v^3 + 22259302v^2 - 2155246*v + 3392561) / 3318773
$\beta_{8}$	$=$	$( - 1035034 \nu^{11} + 1869572 \nu^{10} - 7924683 \nu^{9} + 7725614 \nu^{8} - 34760912 \nu^{7} + \cdots + 6345807 ) / 3318773$ (-1035034v^11 + 1869572v^10 - 7924683v^9 + 7725614v^8 - 34760912v^7 + 38513384v^6 - 61367800v^5 + 26529336v^4 - 27474213v^3 + 41650219v^2 - 4177460*v + 6345807) / 3318773
$\beta_{9}$	$=$	$( 1166290 \nu^{11} - 1650363 \nu^{10} + 8811506 \nu^{9} - 5639321 \nu^{8} + 40119354 \nu^{7} + \cdots + 566698 ) / 3318773$ (1166290v^11 - 1650363v^10 + 8811506v^9 - 5639321v^8 + 40119354v^7 - 27397018v^6 + 72699666v^5 - 1266529v^4 + 44802131v^3 - 8054629v^2 + 7274619*v + 566698) / 3318773
$\beta_{10}$	$=$	$( - 2686072 \nu^{11} + 3882058 \nu^{10} - 19974443 \nu^{9} + 13501144 \nu^{8} - 90433689 \nu^{7} + \cdots - 1035561 ) / 3318773$ (-2686072v^11 + 3882058v^10 - 19974443v^9 + 13501144v^8 - 90433689v^7 + 66981583v^6 - 158252610v^5 + 11027874v^4 - 96392052v^3 + 33752077v^2 - 15484451*v - 1035561) / 3318773
$\beta_{11}$	$=$	$\nu^{11} - \nu^{10} + 7\nu^{9} - 2\nu^{8} + 33\nu^{7} - 11\nu^{6} + 55\nu^{5} + 17\nu^{4} + 47\nu^{3} + \nu^{2} + 8\nu + 1$ v^11 - v^10 + 7v^9 - 2v^8 + 33v^7 - 11v^6 + 55v^5 + 17v^4 + 47v^3 + v^2 + 8v + 1

Display $\nu^j$ in terms of $\beta_i$

$\nu$	$=$	$\beta_1$ b1
$\nu^{2}$	$=$	$-\beta_{8} + 2\beta_{7} - \beta_{4} - 2$ -b8 + 2*b7 - b4 - 2
$\nu^{3}$	$=$	$-\beta_{11} + \beta_{9} + 5\beta_{5} + \beta_{3} - \beta_{2}$ -b11 + b9 + 5*b5 + b3 - b2
$\nu^{4}$	$=$	$5\beta_{8} - 8\beta_{7} + \beta_{6} - \beta_{2} - \beta_1$ 5b8 - 8b7 + b6 - b2 - b1
$\nu^{5}$	$=$	$5\beta_{11} - \beta_{10} - 7\beta_{9} + \beta_{8} - \beta_{7} - 24\beta_{5} + \beta_{4} - 24\beta _1 + 1$ 5b11 - b10 - 7b9 + b8 - b7 - 24b5 + b4 - 24b1 + 1
$\nu^{6}$	$=$	$\beta_{11} - 7\beta_{10} - 9\beta_{9} - 7\beta_{6} - 11\beta_{5} + 24\beta_{4} - \beta_{3} + 9\beta_{2} + 36$ b11 - 7b10 - 9b9 - 7b6 - 11b5 + 24b4 - b3 + 9b2 + 36
$\nu^{7}$	$=$	$-11\beta_{8} + 12\beta_{7} - 9\beta_{6} - 24\beta_{3} + 40\beta_{2} + 117\beta_1$ -11b8 + 12b7 - 9b6 - 24b3 + 40b2 + 117b1
$\nu^{8}$	$=$	$- 11 \beta_{11} + 40 \beta_{10} + 60 \beta_{9} - 117 \beta_{8} + 170 \beta_{7} + 85 \beta_{5} + \cdots - 170$ -11b11 + 40b10 + 60b9 - 117b8 + 170b7 + 85b5 - 117b4 + 85b1 - 170
$\nu^{9}$	$=$	$- 117 \beta_{11} + 60 \beta_{10} + 217 \beta_{9} + 60 \beta_{6} + 581 \beta_{5} - 85 \beta_{4} + \cdots - 99$ -117b11 + 60b10 + 217b9 + 60b6 + 581b5 - 85b4 + 117b3 - 217b2 - 99
$\nu^{10}$	$=$	$581\beta_{8} - 828\beta_{7} + 217\beta_{6} + 85\beta_{3} - 362\beta_{2} - 571\beta_1$ 581b8 - 828b7 + 217b6 + 85b3 - 362b2 - 571b1
$\nu^{11}$	$=$	$581 \beta_{11} - 362 \beta_{10} - 1160 \beta_{9} + 571 \beta_{8} - 695 \beta_{7} - 2933 \beta_{5} + \cdots + 695$ 581b11 - 362b10 - 1160b9 + 571b8 - 695b7 - 2933b5 + 571b4 - 2933b1 + 695

Display $\beta_i$ in terms of $\nu^j$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$ .

$n$	$15$	$66$
$\chi(n)$	$-1 + \beta_{7}$	$-1 + \beta_{7}$

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment:embeddings in the coefficient field

gp:mfembed(f)

Label

\iota_m(\nu)

a_{2}

a_{3}

a_{4}

a_{5}

a_{6}

a_{7}

a_{8}

a_{9}

a_{10}

16.1

−0.181721	−	0.314749i
1.16700	+	2.02131i
0.756174	+	1.30973i
−0.437442	−	0.757672i
−1.02197	−	1.77010i
0.217953	+	0.377506i
−0.181721	+	0.314749i
1.16700	−	2.02131i
0.756174	−	1.30973i
−0.437442	+	0.757672i
−1.02197	+	1.77010i
0.217953	−	0.377506i

−2.38804

1.37574

−

2.38285i

3.70272

−0.491140

0.850679i

−3.28532

5.69033i

−0.911766

−

2.48368i

−4.06616

−2.28532

−

3.95828i

1.17286

−

2.03145i

16.2

−1.90556

−0.214224

0.371047i

1.63116

0.736565

−

1.27577i

0.408216

−

0.707051i

1.58334

2.11968i

0.702849

1.40822

2.43910i

−1.40357

2.43105i

16.3

−0.851125

−0.330612

0.572636i

−1.27559

−1.72074

2.98041i

0.281392

−

0.487385i

−2.57273

−

0.617304i

2.78793

1.28139

2.21944i

1.46456

−

2.53670i

16.4

−0.268125

0.571504

−

0.989875i

−1.92811

1.28088

−

2.21854i

−0.153235

0.265410i

1.80416

−

1.93520i

1.05323

0.846765

1.46664i

−0.343436

0.594848i

16.5

1.55469

0.244626

−

0.423704i

0.417051

0.595756

−

1.03188i

0.380316

−

0.658727i

−2.44127

1.01990i

−2.46099

1.38032

2.39078i

0.926214

−

1.60425i

16.6

1.85816

−1.14703

1.98672i

1.45276

0.0986811

−

0.170921i

−2.13137

3.69165i

1.03826

−

2.43352i

−1.01686

−1.13137

−

1.95960i

0.183365

−

0.317598i

74.1