Properties

Label 273.2.i.b
Level $273$
Weight $2$
Character orbit 273.i
Analytic conductor $2.180$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a primitive root of unity \(\zeta_{18}\). We also show the integral \(q\)-expansion of the trace form.

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(1\) \(-\zeta_{18}^{3}\)

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.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
79.1
−0.766044 0.642788i
0.939693 0.342020i
−0.173648 + 0.984808i
−0.766044 + 0.642788i
0.939693 + 0.342020i
−0.173648 0.984808i
−0.939693 + 1.62760i 0.500000 + 0.866025i −0.766044 1.32683i −1.43969 + 2.49362i −1.87939 2.47178 + 0.943555i −0.879385 −0.500000 + 0.866025i −2.70574 4.68647i
79.2 0.173648 0.300767i 0.500000 + 0.866025i 0.939693 + 1.62760i −0.326352 + 0.565258i 0.347296 −2.05303 + 1.66885i 1.34730 −0.500000 + 0.866025i 0.113341 + 0.196312i
79.3 0.766044 1.32683i 0.500000 + 0.866025i −0.173648 0.300767i 0.266044 0.460802i 1.53209 −0.418748 2.61240i 2.53209 −0.500000 + 0.866025i −0.407604 0.705990i
235.1 −0.939693 1.62760i 0.500000 0.866025i −0.766044 + 1.32683i −1.43969 2.49362i −1.87939 2.47178 0.943555i −0.879385 −0.500000 0.866025i −2.70574 + 4.68647i
235.2 0.173648 + 0.300767i 0.500000 0.866025i 0.939693 1.62760i −0.326352 0.565258i 0.347296 −2.05303 1.66885i 1.34730 −0.500000 0.866025i 0.113341 0.196312i
235.3 0.766044 + 1.32683i 0.500000 0.866025i −0.173648 + 0.300767i 0.266044 + 0.460802i 1.53209 −0.418748 + 2.61240i 2.53209 −0.500000 0.866025i −0.407604 + 0.705990i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 235.3
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 273.2.i.b 6
3.b odd 2 1 819.2.j.e 6
7.c even 3 1 inner 273.2.i.b 6
7.c even 3 1 1911.2.a.o 3
7.d odd 6 1 1911.2.a.p 3
21.g even 6 1 5733.2.a.z 3
21.h odd 6 1 819.2.j.e 6
21.h odd 6 1 5733.2.a.y 3
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
273.2.i.b 6 1.a even 1 1 trivial
273.2.i.b 6 7.c even 3 1 inner
819.2.j.e 6 3.b odd 2 1
819.2.j.e 6 21.h odd 6 1
1911.2.a.o 3 7.c even 3 1
1911.2.a.p 3 7.d odd 6 1
5733.2.a.y 3 21.h odd 6 1
5733.2.a.z 3 21.g even 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{6} + 3 T_{2}^{4} - 2 T_{2}^{3} + 9 T_{2}^{2} - 3 T_{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(273, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 3 T + 9 T^{2} - 2 T^{3} + 3 T^{4} + T^{6} \)
$3$ \( ( 1 - T + T^{2} )^{3} \)
$5$ \( 1 + 3 T^{2} + 2 T^{3} + 9 T^{4} + 3 T^{5} + T^{6} \)
$7$ \( 343 - 17 T^{3} + T^{6} \)
$11$ \( 1 + 3 T^{2} - 2 T^{3} + 9 T^{4} - 3 T^{5} + T^{6} \)
$13$ \( ( -1 + T )^{6} \)
$17$ \( 289 + 408 T + 423 T^{2} + 182 T^{3} + 57 T^{4} + 9 T^{5} + T^{6} \)
$19$ \( 9 + 27 T + 90 T^{2} - 21 T^{3} + 18 T^{4} + 3 T^{5} + T^{6} \)
$23$ \( 81 + 567 T + 3969 T^{2} + 18 T^{3} + 63 T^{4} + T^{6} \)
$29$ \( ( 289 - 51 T - 6 T^{2} + T^{3} )^{2} \)
$31$ \( 361 + 741 T + 1293 T^{2} + 430 T^{3} + 105 T^{4} + 12 T^{5} + T^{6} \)
$37$ \( 1 + 3 T^{2} - 2 T^{3} + 9 T^{4} - 3 T^{5} + T^{6} \)
$41$ \( ( -27 - 27 T + T^{3} )^{2} \)
$43$ \( ( -51 - 9 T + 6 T^{2} + T^{3} )^{2} \)
$47$ \( 576 + 864 T + 1440 T^{2} - 168 T^{3} + 72 T^{4} + 6 T^{5} + T^{6} \)
$53$ \( 9 + 9 T^{2} - 6 T^{3} + 9 T^{4} - 3 T^{5} + T^{6} \)
$59$ \( 239121 - 105624 T + 48123 T^{2} - 330 T^{3} + 225 T^{4} - 3 T^{5} + T^{6} \)
$61$ \( 1014049 + 72504 T + 20289 T^{2} + 934 T^{3} + 297 T^{4} + 15 T^{5} + T^{6} \)
$67$ \( 5329 - 3504 T + 2961 T^{2} + 286 T^{3} + 129 T^{4} - 9 T^{5} + T^{6} \)
$71$ \( ( 597 + 54 T - 21 T^{2} + T^{3} )^{2} \)
$73$ \( 5041 - 9159 T + 16641 T^{2} - 142 T^{3} + 129 T^{4} + T^{6} \)
$79$ \( 271441 + 51579 T + 22305 T^{2} - 3418 T^{3} + 477 T^{4} - 24 T^{5} + T^{6} \)
$83$ \( ( 53 + 45 T + 12 T^{2} + T^{3} )^{2} \)
$89$ \( 7921 - 3204 T + 2631 T^{2} + 718 T^{3} + 189 T^{4} + 15 T^{5} + T^{6} \)
$97$ \( ( 269 + 84 T - 21 T^{2} + T^{3} )^{2} \)
show more
show less