Properties

Label 490.4.c.g
Level $490$
Weight $4$
Character orbit 490.c
Analytic conductor $28.911$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.9109359028\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \( x^{20} + 438 x^{18} + 80439 x^{16} + 8097428 x^{14} + 488971671 x^{12} + 18162509334 x^{10} + 407198911753 x^{8} + 5129420990112 x^{6} + \cdots + 9871083181584 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{23}\cdot 5^{2}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{19}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta_{6} q^{2} + \beta_{5} q^{3} - 4 q^{4} + \beta_{8} q^{5} - \beta_{2} q^{6} - 4 \beta_{6} q^{8} + (\beta_{3} - 16) q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + \beta_{6} q^{2} + \beta_{5} q^{3} - 4 q^{4} + \beta_{8} q^{5} - \beta_{2} q^{6} - 4 \beta_{6} q^{8} + (\beta_{3} - 16) q^{9} + \beta_{12} q^{10} + (\beta_{4} + 5) q^{11} - 4 \beta_{5} q^{12} + ( - \beta_{19} - \beta_{12} - \beta_{8} + \beta_{5} - \beta_{2}) q^{13} + (\beta_{18} - \beta_{13} - 3 \beta_{6} + \beta_{4} + \beta_{3} - 18) q^{15} + 16 q^{16} + (2 \beta_{19} + \beta_{16} - \beta_{11} - \beta_{10} - \beta_{8} + \beta_{5} + \beta_{2}) q^{17} + (\beta_{18} + \beta_{15} - \beta_{14} + \beta_{13} - 14 \beta_{6}) q^{18} + ( - \beta_{12} + \beta_{10} + 2 \beta_{8} + \beta_{7} - \beta_{5} + 3 \beta_{2} - \beta_1) q^{19} - 4 \beta_{8} q^{20} + (\beta_{18} + \beta_{15} + \beta_{14} - \beta_{13} + 5 \beta_{6}) q^{22} + (\beta_{18} + \beta_{17} - \beta_{15} - \beta_{14} + \beta_{13} - 19 \beta_{6} + \beta_{4} - \beta_{3} + 1) q^{23} + 4 \beta_{2} q^{24} + (\beta_{18} - \beta_{17} + 2 \beta_{15} + 2 \beta_{13} + \beta_{9} - 10 \beta_{6} + \beta_{3} - 23) q^{25} + (\beta_{16} - \beta_{12} + 2 \beta_{10} + 4 \beta_{8} - 2 \beta_{7} - 3 \beta_{5} - 2 \beta_{2} + 2 \beta_1) q^{26} + ( - 3 \beta_{19} + 3 \beta_{11} + 3 \beta_{10} - 6 \beta_{8} - 10 \beta_{5} + \cdots - 3 \beta_{2}) q^{27}+ \cdots + (3 \beta_{14} + 3 \beta_{13} - 22 \beta_{4} + 8 \beta_{3} + 34) q^{99}+O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 80 q^{4} - 316 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 80 q^{4} - 316 q^{9} + 104 q^{11} - 360 q^{15} + 320 q^{16} - 440 q^{25} - 216 q^{29} + 224 q^{30} + 1264 q^{36} - 504 q^{39} - 416 q^{44} + 1600 q^{46} + 952 q^{50} - 296 q^{51} + 1440 q^{60} - 1280 q^{64} + 2732 q^{65} - 1872 q^{71} - 5968 q^{74} - 6424 q^{79} + 2020 q^{81} + 428 q^{85} + 3616 q^{86} + 3568 q^{95} + 624 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{20} + 438 x^{18} + 80439 x^{16} + 8097428 x^{14} + 488971671 x^{12} + 18162509334 x^{10} + 407198911753 x^{8} + 5129420990112 x^{6} + \cdots + 9871083181584 \) : Copy content Toggle raw display

\(\beta_{1}\)\(=\) \( ( 3519121 \nu^{18} + 1334144649 \nu^{16} + 201019280850 \nu^{14} + 15229196603546 \nu^{12} + 582862578889557 \nu^{10} + \cdots - 66\!\cdots\!40 ) / 53\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{2}\)\(=\) \( ( 27474940397 \nu^{18} + 11148705388355 \nu^{16} + \cdots + 90\!\cdots\!76 ) / 42\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{3}\)\(=\) \( ( - 27474940397 \nu^{18} - 11148705388355 \nu^{16} + \cdots + 97\!\cdots\!84 ) / 42\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{4}\)\(=\) \( ( 8937738269222 \nu^{18} + \cdots + 28\!\cdots\!16 ) / 28\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{5}\)\(=\) \( ( - 72357165941987 \nu^{19} + \cdots + 79\!\cdots\!04 \nu ) / 74\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{6}\)\(=\) \( ( - 72357165941987 \nu^{19} + \cdots + 15\!\cdots\!44 \nu ) / 37\!\cdots\!20 \) Copy content Toggle raw display
\(\beta_{7}\)\(=\) \( ( 74\!\cdots\!81 \nu^{19} + \cdots - 95\!\cdots\!24 ) / 27\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{8}\)\(=\) \( ( - 74\!\cdots\!81 \nu^{19} + \cdots - 12\!\cdots\!96 ) / 27\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{9}\)\(=\) \( ( - 36\!\cdots\!07 \nu^{19} + \cdots + 30\!\cdots\!60 ) / 82\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{10}\)\(=\) \( ( - 15\!\cdots\!79 \nu^{19} + \cdots - 45\!\cdots\!00 ) / 92\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{11}\)\(=\) \( ( - 135496097 \nu^{19} - 54531944529 \nu^{17} - 8946618728514 \nu^{15} - 773368268872522 \nu^{13} + \cdots + 34\!\cdots\!52 \nu ) / 76\!\cdots\!80 \) Copy content Toggle raw display
\(\beta_{12}\)\(=\) \( ( - 25\!\cdots\!97 \nu^{19} + \cdots + 67\!\cdots\!52 ) / 13\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{13}\)\(=\) \( ( 20\!\cdots\!05 \nu^{19} + \cdots + 85\!\cdots\!84 ) / 99\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{14}\)\(=\) \( ( - 20\!\cdots\!05 \nu^{19} + \cdots + 85\!\cdots\!84 ) / 99\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{15}\)\(=\) \( ( - 34\!\cdots\!71 \nu^{19} + \cdots + 33\!\cdots\!28 ) / 16\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{16}\)\(=\) \( ( 39\!\cdots\!47 \nu^{19} + \cdots + 94\!\cdots\!56 ) / 13\!\cdots\!40 \) Copy content Toggle raw display
\(\beta_{17}\)\(=\) \( ( - 47\!\cdots\!03 \nu^{19} + \cdots - 60\!\cdots\!20 ) / 16\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{18}\)\(=\) \( ( - 55\!\cdots\!86 \nu^{19} + \cdots - 33\!\cdots\!28 ) / 16\!\cdots\!60 \) Copy content Toggle raw display
\(\beta_{19}\)\(=\) \( ( - 11\!\cdots\!95 \nu^{19} + \cdots - 19\!\cdots\!00 ) / 27\!\cdots\!80 \) Copy content Toggle raw display
\(\nu\)\(=\) \( ( \beta_{6} - 2\beta_{5} ) / 2 \) Copy content Toggle raw display
\(\nu^{2}\)\(=\) \( \beta_{3} + \beta_{2} - 44 \) Copy content Toggle raw display
\(\nu^{3}\)\(=\) \( ( 6 \beta_{19} + 3 \beta_{18} + 3 \beta_{15} - 3 \beta_{14} + 3 \beta_{13} - 6 \beta_{11} - 6 \beta_{10} + 12 \beta_{8} - 124 \beta_{6} + 134 \beta_{5} + 6 \beta_{2} ) / 2 \) Copy content Toggle raw display
\(\nu^{4}\)\(=\) \( - 9 \beta_{18} + 18 \beta_{17} + 9 \beta_{15} - 3 \beta_{14} + 15 \beta_{13} + 12 \beta_{12} - 12 \beta_{10} - 18 \beta_{9} + 12 \beta_{7} + 18 \beta_{6} + 12 \beta_{5} + 6 \beta_{4} - 103 \beta_{3} - 124 \beta_{2} - 36 \beta _1 + 3116 \) Copy content Toggle raw display
\(\nu^{5}\)\(=\) \( ( - 870 \beta_{19} - 645 \beta_{18} - 150 \beta_{17} - 84 \beta_{16} - 285 \beta_{15} + 435 \beta_{14} - 435 \beta_{13} + 84 \beta_{12} + 1050 \beta_{11} + 870 \beta_{10} + 30 \beta_{9} - 1404 \beta_{8} + 13816 \beta_{6} + \cdots - 180 ) / 2 \) Copy content Toggle raw display
\(\nu^{6}\)\(=\) \( 1440 \beta_{18} - 2880 \beta_{17} - 1440 \beta_{15} + 798 \beta_{14} - 2082 \beta_{13} - 1986 \beta_{12} + 1986 \beta_{10} + 2880 \beta_{9} - 504 \beta_{8} - 2490 \beta_{7} - 2880 \beta_{6} - 1986 \beta_{5} + \cdots - 264200 \) Copy content Toggle raw display
\(\nu^{7}\)\(=\) \( ( 104442 \beta_{19} + 97461 \beta_{18} + 27048 \beta_{17} + 15036 \beta_{16} + 21861 \beta_{15} - 54957 \beta_{14} + 54957 \beta_{13} - 14028 \beta_{12} - 139542 \beta_{11} - 103434 \beta_{10} + \cdots + 37800 ) / 2 \) Copy content Toggle raw display
\(\nu^{8}\)\(=\) \( - 183159 \beta_{18} + 366318 \beta_{17} - 2016 \beta_{16} + 183159 \beta_{15} - 122769 \beta_{14} + 243549 \beta_{13} + 258840 \beta_{12} - 260856 \beta_{10} - 366318 \beta_{9} + \cdots + 25075520 \) Copy content Toggle raw display
\(\nu^{9}\)\(=\) \( ( - 12014790 \beta_{19} - 12939033 \beta_{18} - 3744810 \beta_{17} - 2039940 \beta_{16} - 1541793 \beta_{15} + 6684987 \beta_{14} - 6684987 \beta_{13} + 1798020 \beta_{12} + \cdots - 5698620 ) / 2 \) Copy content Toggle raw display
\(\nu^{10}\)\(=\) \( 21784770 \beta_{18} - 43569540 \beta_{17} + 544320 \beta_{16} - 21784770 \beta_{15} + 15981960 \beta_{14} - 27587580 \beta_{13} - 31523142 \beta_{12} + 32067462 \beta_{10} + \cdots - 2558015768 \) Copy content Toggle raw display
\(\nu^{11}\)\(=\) \( ( 1369209858 \beta_{19} + 1616821701 \beta_{18} + 474271908 \beta_{17} + 252379596 \beta_{16} + 104608581 \beta_{15} - 800185881 \beta_{14} + 800185881 \beta_{13} + \cdots + 756106560 ) / 2 \) Copy content Toggle raw display
\(\nu^{12}\)\(=\) \( - 2530666377 \beta_{18} + 5061332754 \beta_{17} - 95742864 \beta_{16} + 2530666377 \beta_{15} - 1945651587 \beta_{14} + 3115681167 \beta_{13} + 3746113188 \beta_{12} + \cdots + 273220924784 \) Copy content Toggle raw display
\(\nu^{13}\)\(=\) \( ( - 156017266782 \beta_{19} - 195674951745 \beta_{18} - 57704512710 \beta_{17} - 30048631620 \beta_{16} - 6968312793 \beta_{15} + 94826398719 \beta_{14} + \cdots - 94353319476 ) / 2 \) Copy content Toggle raw display
\(\nu^{14}\)\(=\) \( 291562384860 \beta_{18} - 583124769720 \beta_{17} + 14009649696 \beta_{16} - 291562384860 \beta_{15} + 229908518514 \beta_{14} - 353216251206 \beta_{13} + \cdots - 30043923835256 \) Copy content Toggle raw display
\(\nu^{15}\)\(=\) \( ( 17819049711354 \beta_{19} + 23256603957693 \beta_{18} + 6875331493680 \beta_{17} + 3516019770060 \beta_{16} + 460546818573 \beta_{15} + \cdots + 11398028569560 ) / 2 \) Copy content Toggle raw display
\(\nu^{16}\)\(=\) \( - 33513482589147 \beta_{18} + 67026965178294 \beta_{17} - 1861128384192 \beta_{16} + 33513482589147 \beta_{15} - 26797561369077 \beta_{14} + \cdots + 33\!\cdots\!16 \) Copy content Toggle raw display
\(\nu^{17}\)\(=\) \( ( - 20\!\cdots\!18 \beta_{19} + \cdots - 13\!\cdots\!00 ) / 2 \) Copy content Toggle raw display
\(\nu^{18}\)\(=\) \( 38\!\cdots\!94 \beta_{18} + \cdots - 38\!\cdots\!68 \) Copy content Toggle raw display
\(\nu^{19}\)\(=\) \( ( 23\!\cdots\!10 \beta_{19} + \cdots + 15\!\cdots\!76 ) / 2 \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
99.1
8.74678i
6.11026i
5.79189i
3.69313i
0.462233i
1.53777i
5.69313i
7.79189i
8.11026i
10.7468i
10.7468i
8.11026i
7.79189i
5.69313i
1.53777i
0.462233i
3.69313i
5.79189i
6.11026i
8.74678i
2.00000i 9.74678i −4.00000 −4.75591 10.1184i −19.4936 0 8.00000i −67.9997 −20.2367 + 9.51182i
99.2 2.00000i 7.11026i −4.00000 −6.02808 9.41606i −14.2205 0 8.00000i −23.5558 −18.8321 + 12.0562i
99.3 2.00000i 6.79189i −4.00000 10.7861 + 2.94297i −13.5838 0 8.00000i −19.1298 5.88595 21.5721i
99.4 2.00000i 4.69313i −4.00000 −1.54203 + 11.0735i −9.38627 0 8.00000i 4.97448 22.1470 + 3.08406i
99.5 2.00000i 0.537767i −4.00000 −8.93458 + 6.72110i −1.07553 0 8.00000i 26.7108 13.4422 + 17.8692i
99.6 2.00000i 0.537767i −4.00000 8.93458 6.72110i 1.07553 0 8.00000i 26.7108 −13.4422 17.8692i
99.7 2.00000i 4.69313i −4.00000 1.54203 11.0735i 9.38627 0 8.00000i 4.97448 −22.1470 3.08406i
99.8 2.00000i 6.79189i −4.00000 −10.7861 2.94297i 13.5838 0 8.00000i −19.1298 −5.88595 + 21.5721i
99.9 2.00000i 7.11026i −4.00000 6.02808 + 9.41606i 14.2205 0 8.00000i −23.5558 18.8321 12.0562i
99.10 2.00000i 9.74678i −4.00000 4.75591 + 10.1184i 19.4936 0 8.00000i −67.9997 20.2367 9.51182i
99.11 2.00000i 9.74678i −4.00000 4.75591 10.1184i 19.4936 0 8.00000i −67.9997 20.2367 + 9.51182i
99.12 2.00000i 7.11026i −4.00000 6.02808 9.41606i 14.2205 0 8.00000i −23.5558 18.8321 + 12.0562i
99.13 2.00000i 6.79189i −4.00000 −10.7861 + 2.94297i 13.5838 0 8.00000i −19.1298 −5.88595 21.5721i
99.14 2.00000i 4.69313i −4.00000 1.54203 + 11.0735i 9.38627 0 8.00000i 4.97448 −22.1470 + 3.08406i
99.15 2.00000i 0.537767i −4.00000 8.93458 + 6.72110i 1.07553 0 8.00000i 26.7108 −13.4422 + 17.8692i
99.16 2.00000i 0.537767i −4.00000 −8.93458 6.72110i −1.07553 0 8.00000i 26.7108 13.4422 17.8692i
99.17 2.00000i 4.69313i −4.00000 −1.54203 11.0735i −9.38627 0 8.00000i 4.97448 22.1470 3.08406i
99.18 2.00000i 6.79189i −4.00000 10.7861 2.94297i −13.5838 0 8.00000i −19.1298 5.88595 + 21.5721i
99.19 2.00000i 7.11026i −4.00000 −6.02808 + 9.41606i −14.2205 0 8.00000i −23.5558 −18.8321 12.0562i
99.20 2.00000i 9.74678i −4.00000 −4.75591 + 10.1184i −19.4936 0 8.00000i −67.9997 −20.2367 9.51182i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 99.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.b odd 2 1 inner
35.c odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 490.4.c.g 20
5.b even 2 1 inner 490.4.c.g 20
5.c odd 4 1 2450.4.a.db 10
5.c odd 4 1 2450.4.a.dc 10
7.b odd 2 1 inner 490.4.c.g 20
35.c odd 2 1 inner 490.4.c.g 20
35.f even 4 1 2450.4.a.db 10
35.f even 4 1 2450.4.a.dc 10
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
490.4.c.g 20 1.a even 1 1 trivial
490.4.c.g 20 5.b even 2 1 inner
490.4.c.g 20 7.b odd 2 1 inner
490.4.c.g 20 35.c odd 2 1 inner
2450.4.a.db 10 5.c odd 4 1
2450.4.a.db 10 35.f even 4 1
2450.4.a.dc 10 5.c odd 4 1
2450.4.a.dc 10 35.f even 4 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(490, [\chi])\):

\( T_{3}^{10} + 214T_{3}^{8} + 15801T_{3}^{6} + 479776T_{3}^{4} + 5017216T_{3}^{2} + 1411200 \) Copy content Toggle raw display
\( T_{19}^{10} - 25424 T_{19}^{8} + 218838208 T_{19}^{6} - 700579963008 T_{19}^{4} + 563374160025600 T_{19}^{2} - 86\!\cdots\!00 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( (T^{2} + 4)^{10} \) Copy content Toggle raw display
$3$ \( (T^{10} + 214 T^{8} + 15801 T^{6} + \cdots + 1411200)^{2} \) Copy content Toggle raw display
$5$ \( T^{20} + 220 T^{18} + \cdots + 93\!\cdots\!25 \) Copy content Toggle raw display
$7$ \( T^{20} \) Copy content Toggle raw display
$11$ \( (T^{5} - 26 T^{4} - 4311 T^{3} + \cdots + 575456)^{4} \) Copy content Toggle raw display
$13$ \( (T^{10} + 10588 T^{8} + \cdots + 39\!\cdots\!00)^{2} \) Copy content Toggle raw display
$17$ \( (T^{10} + 30812 T^{8} + \cdots + 62\!\cdots\!48)^{2} \) Copy content Toggle raw display
$19$ \( (T^{10} - 25424 T^{8} + \cdots - 86\!\cdots\!00)^{2} \) Copy content Toggle raw display
$23$ \( (T^{10} + 50380 T^{8} + \cdots + 46\!\cdots\!00)^{2} \) Copy content Toggle raw display
$29$ \( (T^{5} + 54 T^{4} - 36631 T^{3} + \cdots - 11338881824)^{4} \) Copy content Toggle raw display
$31$ \( (T^{10} - 136452 T^{8} + \cdots - 55\!\cdots\!72)^{2} \) Copy content Toggle raw display
$37$ \( (T^{10} + 392632 T^{8} + \cdots + 72\!\cdots\!00)^{2} \) Copy content Toggle raw display
$41$ \( (T^{10} - 292810 T^{8} + \cdots - 37\!\cdots\!08)^{2} \) Copy content Toggle raw display
$43$ \( (T^{10} + 488720 T^{8} + \cdots + 20\!\cdots\!64)^{2} \) Copy content Toggle raw display
$47$ \( (T^{10} + 685110 T^{8} + \cdots + 39\!\cdots\!00)^{2} \) Copy content Toggle raw display
$53$ \( (T^{10} + 876316 T^{8} + \cdots + 12\!\cdots\!24)^{2} \) Copy content Toggle raw display
$59$ \( (T^{10} - 839716 T^{8} + \cdots - 15\!\cdots\!28)^{2} \) Copy content Toggle raw display
$61$ \( (T^{10} - 1935830 T^{8} + \cdots - 54\!\cdots\!00)^{2} \) Copy content Toggle raw display
$67$ \( (T^{10} + 3004412 T^{8} + \cdots + 38\!\cdots\!96)^{2} \) Copy content Toggle raw display
$71$ \( (T^{5} + 468 T^{4} + \cdots + 19001196779392)^{4} \) Copy content Toggle raw display
$73$ \( (T^{10} + 1652086 T^{8} + \cdots + 25\!\cdots\!52)^{2} \) Copy content Toggle raw display
$79$ \( (T^{5} + 1606 T^{4} + \cdots + 44582270876640)^{4} \) Copy content Toggle raw display
$83$ \( (T^{10} + 2087232 T^{8} + \cdots + 12\!\cdots\!48)^{2} \) Copy content Toggle raw display
$89$ \( (T^{10} - 2860022 T^{8} + \cdots - 20\!\cdots\!00)^{2} \) Copy content Toggle raw display
$97$ \( (T^{10} + 780572 T^{8} + \cdots + 17\!\cdots\!68)^{2} \) Copy content Toggle raw display
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