Properties

Label 31.4.a.b
Level $31$
Weight $4$
Character orbit 31.a
Self dual yes
Analytic conductor $1.829$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [31,4,Mod(1,31)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(31, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("31.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 31.a (trivial)

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: yes
Analytic conductor: \(1.82905921018\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 32x^{3} + 19x^{2} + 228x + 172 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-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 \(1,\beta_1,\beta_2,\beta_3,\beta_4\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + ( - \beta_1 + 1) q^{2} + ( - \beta_{4} + \beta_{3} - \beta_{2}) q^{3} + (\beta_{4} - 2 \beta_{3} + \beta_{2} - \beta_1 + 7) q^{4} + (2 \beta_{4} + \beta_{3} + \beta_{2} + 3 \beta_1 + 3) q^{5} + ( - \beta_{4} - \beta_{3} + 3 \beta_{2} + 4 \beta_1 + 4) q^{6} + (\beta_{3} - 3 \beta_{2} - \beta_1 + 1) q^{7} + (\beta_{4} - 3 \beta_{3} - 4 \beta_{2} - 7 \beta_1 + 4) q^{8} + ( - 6 \beta_{4} + 6 \beta_1 + 1) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + ( - \beta_1 + 1) q^{2} + ( - \beta_{4} + \beta_{3} - \beta_{2}) q^{3} + (\beta_{4} - 2 \beta_{3} + \beta_{2} - \beta_1 + 7) q^{4} + (2 \beta_{4} + \beta_{3} + \beta_{2} + 3 \beta_1 + 3) q^{5} + ( - \beta_{4} - \beta_{3} + 3 \beta_{2} + 4 \beta_1 + 4) q^{6} + (\beta_{3} - 3 \beta_{2} - \beta_1 + 1) q^{7} + (\beta_{4} - 3 \beta_{3} - 4 \beta_{2} - 7 \beta_1 + 4) q^{8} + ( - 6 \beta_{4} + 6 \beta_1 + 1) q^{9} + (2 \beta_{4} + 11 \beta_{3} - \beta_{2} - 37) q^{10} + ( - 5 \beta_{4} - 7 \beta_{3} + 3 \beta_{2} + 2 \beta_1 + 16) q^{11} + (\beta_{4} + 7 \beta_{3} - 5 \beta_{2} - 4 \beta_1 - 38) q^{12} + (7 \beta_{4} - \beta_{3} + 9 \beta_{2} + 2 \beta_1) q^{13} + (2 \beta_{4} - 9 \beta_{3} + 9 \beta_{2} + 5) q^{14} + (6 \beta_{4} + 4 \beta_{3} - 12 \beta_{2} - 16 \beta_1 - 22) q^{15} + ( - 2 \beta_{4} - 16 \beta_{3} + 2 \beta_{2} - 13 \beta_1 + 7) q^{16} + (14 \beta_{4} - 10 \beta_{3} + 2 \beta_{2} - 10 \beta_1 + 38) q^{17} + ( - 18 \beta_{4} + 12 \beta_{3} - 12 \beta_{2} + 5 \beta_1 - 59) q^{18} + ( - 8 \beta_{4} + 7 \beta_{3} + 11 \beta_{2} + 9 \beta_1 - 11) q^{19} + ( - \beta_{4} + 11 \beta_{3} + 18 \beta_{2} + 54 \beta_1 - 19) q^{20} + (6 \beta_{4} - 4 \beta_{2} + 12 \beta_1 + 30) q^{21} + ( - 19 \beta_{4} - \beta_{3} - 27 \beta_{2} - 36 \beta_1 - 12) q^{22} + ( - 12 \beta_{4} + 18 \beta_{3} - 18 \beta_{2} + 8 \beta_1 + 26) q^{23} + (21 \beta_{4} - \beta_{3} + 5 \beta_{2} + 28 \beta_1 - 8) q^{24} + (12 \beta_{4} - 23 \beta_{3} + 17 \beta_{2} - 3 \beta_1 + 106) q^{25} + (11 \beta_{4} + 29 \beta_{3} - 15 \beta_{2} - 2 \beta_1 - 16) q^{26} + ( - 16 \beta_{4} - 8 \beta_{3} + 8 \beta_{2} - 12 \beta_1 + 36) q^{27} + ( - 5 \beta_{4} + \beta_{3} - 10 \beta_{2} - 26 \beta_1 - 11) q^{28} + (9 \beta_{4} - \beta_{3} + 13 \beta_{2} - 16 \beta_1 + 110) q^{29} + (32 \beta_{4} - 60 \beta_{3} + 54 \beta_{2} + 20 \beta_1 + 138) q^{30} - 31 q^{31} + ( - 15 \beta_{4} - 28 \beta_{3} + 7 \beta_{2} - 11 \beta_1 + 95) q^{32} + ( - 46 \beta_{4} + 36 \beta_{3} - 24 \beta_{2} - 18 \beta_1 - 68) q^{33} + (28 \beta_{4} - 34 \beta_{3} - 90 \beta_1 + 82) q^{34} + ( - 16 \beta_{4} + 31 \beta_{3} - 41 \beta_{2} + \beta_1 - 39) q^{35} + (19 \beta_{4} - 2 \beta_{3} + 25 \beta_{2} + 65 \beta_1 - 65) q^{36} + (49 \beta_{4} + 21 \beta_{3} + 11 \beta_{2} - 24 \beta_1 - 68) q^{37} + ( - 18 \beta_{4} + 65 \beta_{3} - 25 \beta_{2} + 58 \beta_1 - 15) q^{38} + (24 \beta_{4} - 10 \beta_{3} + 10 \beta_{2} - 42 \beta_1 - 128) q^{39} + ( - 61 \beta_{4} + 96 \beta_{3} - 61 \beta_{2} + 82 \beta_1 - 330) q^{40} + ( - 66 \beta_{4} - 19 \beta_{3} - 39 \beta_{2} - \beta_1 + 53) q^{41} + (12 \beta_{3} + 2 \beta_{2} - 40 \beta_1 - 182) q^{42} + ( - 27 \beta_{4} - 27 \beta_{3} + 7 \beta_{2} + 74 \beta_1 - 54) q^{43} + (37 \beta_{4} - 99 \beta_{3} + 45 \beta_{2} - 16 \beta_1 + 300) q^{44} + (38 \beta_{4} - 83 \beta_{3} + 25 \beta_{2} + 3 \beta_1 + 27) q^{45} + ( - 14 \beta_{4} - 2 \beta_{3} + 52 \beta_{2} + 40 \beta_1 - 38) q^{46} + (40 \beta_{4} - 6 \beta_{3} + 50 \beta_{2} - 2 \beta_1 - 92) q^{47} + (5 \beta_{4} + 13 \beta_{3} + 21 \beta_{2} + 20 \beta_1 - 160) q^{48} + (17 \beta_{3} - 43 \beta_{2} + 29 \beta_1 - 184) q^{49} + (4 \beta_{4} - \beta_{3} - 65 \beta_{2} - 193 \beta_1 + 70) q^{50} + (74 \beta_{4} + 22 \beta_{3} - 26 \beta_{2} - 12 \beta_1 - 248) q^{51} + ( - 3 \beta_{4} + 17 \beta_{3} + 29 \beta_{2} + 90 \beta_1 + 38) q^{52} + ( - 13 \beta_{4} + 57 \beta_{3} + 11 \beta_{2} + 30 \beta_1 + 62) q^{53} + ( - 28 \beta_{4} - 16 \beta_{3} - 36 \beta_{2} - 44 \beta_1 + 268) q^{54} + (26 \beta_{4} - 56 \beta_{3} + 76 \beta_{2} + 158 \beta_1 - 182) q^{55} + (\beta_{4} - 8 \beta_{3} - 29 \beta_{2} + 10 \beta_1 + 288) q^{56} + ( - 92 \beta_{4} - 10 \beta_{3} + 30 \beta_{2} - 28 \beta_1 + 98) q^{57} + (33 \beta_{4} + 5 \beta_{3} - 3 \beta_{2} - 110 \beta_1 + 358) q^{58} + (2 \beta_{4} + 55 \beta_{3} + 51 \beta_{2} - 25 \beta_1 - 77) q^{59} + ( - 64 \beta_{4} + 50 \beta_{3} - 120 \beta_{2} - 228 \beta_1 - 124) q^{60} + (7 \beta_{4} + 27 \beta_{3} - 59 \beta_{2} + 58 \beta_1 + 44) q^{61} + (31 \beta_1 - 31) q^{62} + (24 \beta_{4} + 25 \beta_{3} - 15 \beta_{2} - 25 \beta_1 - 119) q^{63} + ( - 31 \beta_{4} + 71 \beta_{3} - 90 \beta_{2} - 81 \beta_1 + 148) q^{64} + (30 \beta_{4} - 48 \beta_{3} + 108 \beta_{2} - 16 \beta_1 + 382) q^{65} + ( - 38 \beta_{4} - 36 \beta_{3} + 92 \beta_{2} + 234 \beta_1 + 428) q^{66} + ( - 20 \beta_{4} - 28 \beta_{3} - 56 \beta_{2} - 108 \beta_1 - 364) q^{67} + ( - 168 \beta_{3} + 34 \beta_{2} - 166 \beta_1 + 756) q^{68} + ( - 92 \beta_{4} + 36 \beta_{3} - 64 \beta_{2} + 64 \beta_1 + 412) q^{69} + ( - 2 \beta_{4} - 59 \beta_{3} + 127 \beta_{2} + 138 \beta_1 - 39) q^{70} + (4 \beta_{4} - 75 \beta_{3} - 51 \beta_{2} + 71 \beta_1 + 51) q^{71} + (115 \beta_{4} + 105 \beta_{3} - 4 \beta_{2} + 23 \beta_1 - 464) q^{72} + (80 \beta_{4} - 24 \beta_{3} - 32 \beta_{2} + 4 \beta_1 + 78) q^{73} + (143 \beta_{4} + 27 \beta_{3} + 93 \beta_{2} + 114 \beta_1 + 232) q^{74} + ( - 27 \beta_{4} + 117 \beta_{3} - 101 \beta_{2} - 92 \beta_1 - 498) q^{75} + (35 \beta_{4} + 115 \beta_{3} + 16 \beta_{2} + 196 \beta_1 - 467) q^{76} + (22 \beta_{4} + 4 \beta_{3} - 110 \beta_1 - 178) q^{77} + (80 \beta_{4} - 74 \beta_{3} + 26 \beta_{2} + 74 \beta_1 + 364) q^{78} + ( - 38 \beta_{4} - 146 \beta_{3} + 70 \beta_{2} - 110 \beta_1 - 192) q^{79} + ( - 100 \beta_{4} + 85 \beta_{3} + 27 \beta_{2} + 282 \beta_1 - 907) q^{80} + (6 \beta_{4} + 36 \beta_{3} + 36 \beta_{2} - 114 \beta_1 + 37) q^{81} + ( - 150 \beta_{4} - 157 \beta_{3} - 25 \beta_{2} - 102 \beta_1 + 41) q^{82} + ( - 7 \beta_{4} - 65 \beta_{3} - 27 \beta_{2} + 18 \beta_1 + 288) q^{83} + (4 \beta_{4} - 50 \beta_{3} + 92 \beta_{2} + 136 \beta_1 + 208) q^{84} + ( - 80 \beta_{4} + 162 \beta_{3} + 26 \beta_{2} + 312 \beta_1 + 14) q^{85} + ( - 155 \beta_{4} + 115 \beta_{3} - 169 \beta_{2} - 20 \beta_1 - 1082) q^{86} + ( - 84 \beta_{4} + 58 \beta_{3} - 18 \beta_{2} + 18 \beta_1 - 92) q^{87} + (143 \beta_{4} - 87 \beta_{3} - 19 \beta_{2} - 400 \beta_1 + 202) q^{88} + (96 \beta_{4} + 86 \beta_{3} - 58 \beta_{2} - 164 \beta_1 + 692) q^{89} + ( - 10 \beta_{4} - 85 \beta_{3} - 181 \beta_{2} - 372 \beta_1 - 457) q^{90} + ( - 38 \beta_{4} - 24 \beta_{3} + 72 \beta_{2} - 52 \beta_1 - 374) q^{91} + (26 \beta_{4} + 88 \beta_{3} - 18 \beta_{2} + 32 \beta_1 - 500) q^{92} + (31 \beta_{4} - 31 \beta_{3} + 31 \beta_{2}) q^{93} + (76 \beta_{4} + 134 \beta_{3} - 70 \beta_{2} + 78 \beta_1 - 4) q^{94} + (188 \beta_{4} - 185 \beta_{3} + 159 \beta_{2} - 247 \beta_1 + 281) q^{95} + ( - 165 \beta_{4} + 137 \beta_{3} - 71 \beta_{2} + 4 \beta_1 - 226) q^{96} + (34 \beta_{4} + 51 \beta_{3} - 197 \beta_{2} - 179 \beta_1 + 123) q^{97} + ( - 12 \beta_{4} - 37 \beta_{3} + 91 \beta_{2} + 209 \beta_1 - 720) q^{98} + ( - 119 \beta_{4} + 83 \beta_{3} + 105 \beta_{2} + 230 \beta_1 + 700) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 3 q^{2} + 4 q^{3} + 29 q^{4} + 15 q^{5} + 24 q^{6} + 9 q^{7} + 12 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 3 q^{2} + 4 q^{3} + 29 q^{4} + 15 q^{5} + 24 q^{6} + 9 q^{7} + 12 q^{8} + 29 q^{9} - 187 q^{10} + 88 q^{11} - 190 q^{12} - 28 q^{13} + 3 q^{14} - 130 q^{15} + 9 q^{16} + 138 q^{17} - 225 q^{18} - 43 q^{19} - 21 q^{20} + 170 q^{21} - 40 q^{22} + 206 q^{23} - 36 q^{24} + 466 q^{25} - 76 q^{26} + 172 q^{27} - 77 q^{28} + 474 q^{29} + 558 q^{30} - 155 q^{31} + 469 q^{32} - 236 q^{33} + 174 q^{34} - 79 q^{35} - 283 q^{36} - 508 q^{37} + 127 q^{38} - 792 q^{39} - 1242 q^{40} + 473 q^{41} - 994 q^{42} - 82 q^{43} + 1304 q^{44} + 15 q^{45} - 186 q^{46} - 644 q^{47} - 812 q^{48} - 776 q^{49} + 86 q^{50} - 1360 q^{51} + 318 q^{52} + 374 q^{53} + 1380 q^{54} - 798 q^{55} + 1516 q^{56} + 558 q^{57} + 1510 q^{58} - 541 q^{59} - 708 q^{60} + 440 q^{61} - 93 q^{62} - 663 q^{63} + 820 q^{64} + 1602 q^{65} + 2500 q^{66} - 1884 q^{67} + 3380 q^{68} + 2500 q^{69} - 169 q^{70} + 491 q^{71} - 2496 q^{72} + 302 q^{73} + 916 q^{74} - 2418 q^{75} - 2045 q^{76} - 1154 q^{77} + 1756 q^{78} - 1244 q^{79} - 3825 q^{80} - 127 q^{81} + 351 q^{82} + 1544 q^{83} + 1120 q^{84} + 802 q^{85} - 4802 q^{86} - 220 q^{87} - 38 q^{88} + 3056 q^{89} - 2647 q^{90} - 2042 q^{91} - 2452 q^{92} - 124 q^{93} + 124 q^{94} + 217 q^{95} - 650 q^{96} + 583 q^{97} - 3340 q^{98} + 3988 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{5} - 2x^{4} - 32x^{3} + 19x^{2} + 228x + 172 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( \nu \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( \nu^{4} + 16\nu^{3} - 56\nu^{2} - 365\nu + 106 ) / 104 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( -5\nu^{4} + 24\nu^{3} + 72\nu^{2} - 359\nu - 10 ) / 104 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( -11\nu^{4} + 32\nu^{3} + 304\nu^{2} - 457\nu - 1582 ) / 104 \) Copy content Toggle raw display
\(\nu\)\(=\) \( \beta_1 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta_{4} - 2\beta_{3} + \beta_{2} + \beta _1 + 14 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( 2\beta_{4} - 3\beta_{3} + 7\beta_{2} + 23\beta _1 + 23 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( 24\beta_{4} - 64\beta_{3} + 48\beta_{2} + 53\beta _1 + 310 \) Copy content Toggle raw display

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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
5.63560
3.63578
−0.929505
−2.15912
−4.18275
−4.63560 −7.37181 13.4888 19.0185 34.1727 −13.5109 −25.4436 27.3436 −88.1622
1.2 −2.63578 5.22185 −1.05267 10.8334 −13.7637 25.9132 23.8608 0.267763 −28.5544
1.3 1.92951 8.71716 −4.27701 −10.4546 16.8198 −5.68067 −23.6886 48.9889 −20.1722
1.4 3.15912 −0.0377000 1.98006 13.5012 −0.119099 −3.86558 −19.0177 −26.9986 42.6518
1.5 5.18275 −2.52950 18.8609 −17.8984 −13.1098 6.14402 56.2891 −20.6016 −92.7630
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.5
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(31\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 31.4.a.b 5
3.b odd 2 1 279.4.a.h 5
4.b odd 2 1 496.4.a.i 5
5.b even 2 1 775.4.a.f 5
7.b odd 2 1 1519.4.a.c 5
8.b even 2 1 1984.4.a.r 5
8.d odd 2 1 1984.4.a.s 5
31.b odd 2 1 961.4.a.e 5
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
31.4.a.b 5 1.a even 1 1 trivial
279.4.a.h 5 3.b odd 2 1
496.4.a.i 5 4.b odd 2 1
775.4.a.f 5 5.b even 2 1
961.4.a.e 5 31.b odd 2 1
1519.4.a.c 5 7.b odd 2 1
1984.4.a.r 5 8.b even 2 1
1984.4.a.s 5 8.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{5} - 3T_{2}^{4} - 30T_{2}^{3} + 79T_{2}^{2} + 167T_{2} - 386 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(31))\). Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{5} - 3 T^{4} - 30 T^{3} + 79 T^{2} + \cdots - 386 \) Copy content Toggle raw display
$3$ \( T^{5} - 4 T^{4} - 74 T^{3} + 188 T^{2} + \cdots + 32 \) Copy content Toggle raw display
$5$ \( T^{5} - 15 T^{4} - 433 T^{3} + \cdots - 520516 \) Copy content Toggle raw display
$7$ \( T^{5} - 9 T^{4} - 429 T^{3} + \cdots + 47236 \) Copy content Toggle raw display
$11$ \( T^{5} - 88 T^{4} - 562 T^{3} + \cdots - 76793648 \) Copy content Toggle raw display
$13$ \( T^{5} + 28 T^{4} - 3850 T^{3} + \cdots + 85935616 \) Copy content Toggle raw display
$17$ \( T^{5} - 138 T^{4} + \cdots + 845793728 \) Copy content Toggle raw display
$19$ \( T^{5} + 43 T^{4} + \cdots - 885299824 \) Copy content Toggle raw display
$23$ \( T^{5} - 206 T^{4} + \cdots - 1477525504 \) Copy content Toggle raw display
$29$ \( T^{5} - 474 T^{4} + \cdots + 6492808496 \) Copy content Toggle raw display
$31$ \( (T + 31)^{5} \) Copy content Toggle raw display
$37$ \( T^{5} + 508 T^{4} + \cdots - 315180705232 \) Copy content Toggle raw display
$41$ \( T^{5} - 473 T^{4} + \cdots + 19192433688 \) Copy content Toggle raw display
$43$ \( T^{5} + 82 T^{4} + \cdots - 154176970896 \) Copy content Toggle raw display
$47$ \( T^{5} + 644 T^{4} + \cdots + 197408306432 \) Copy content Toggle raw display
$53$ \( T^{5} - 374 T^{4} + \cdots + 79406336128 \) Copy content Toggle raw display
$59$ \( T^{5} + 541 T^{4} + \cdots + 19804492743336 \) Copy content Toggle raw display
$61$ \( T^{5} - 440 T^{4} + \cdots + 922927740352 \) Copy content Toggle raw display
$67$ \( T^{5} + 1884 T^{4} + \cdots - 22262005628928 \) Copy content Toggle raw display
$71$ \( T^{5} - 491 T^{4} + \cdots - 69573929276736 \) Copy content Toggle raw display
$73$ \( T^{5} - 302 T^{4} + \cdots - 1852644259168 \) Copy content Toggle raw display
$79$ \( T^{5} + 1244 T^{4} + \cdots - 59985571648 \) Copy content Toggle raw display
$83$ \( T^{5} - 1544 T^{4} + \cdots + 657431598704 \) Copy content Toggle raw display
$89$ \( T^{5} - 3056 T^{4} + \cdots + 68090734165536 \) Copy content Toggle raw display
$97$ \( T^{5} - 583 T^{4} + \cdots - 31148274036888 \) Copy content Toggle raw display
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