Basic properties
Coefficient field
Field: $\mathbb{Q}(a)$
Degree: 2
Discriminant: $479 \cdot 4919$
Signature: $(2, 0)$
Is Galois: True
Field polynomial:
$x^{2} - x - 589050$
Field generator: $a$
Explicit formula
Show (-1384742489310021254894997497327602008379*a - 29109667357863906416025353168772901787784492755)*A^7*B + (1449542107307906627243304876432772764779*a + 57858828458630144596481406160891149590289744355)*A^4*B^3 + (119935548350558612607346051814237862230856192*a + 2117971759834753062100343813853695865225387862909440)*A^6*C + (-64799617997885372348307379105170756400*a - 28749161100766238180456052992118247802505251600)*A*B^5 + (-334272744425207755719061896401506832451379200*a - 17468086185480992925972214355332658910884988075417600)*A^3*B^2*C + (113160940226326219119353861969193304874591232*a + 4896407659068404068099853128059003276882243021358080)*A^4*B*D + 992959356415346480009338423094404674068298485760000*B^4*C + (19758598580718068761929471007261502627624779776000*a + 1152973267168272013793035782021492358438003363499212800000)*A^2*B*C^2 + (37312139962756694714481488092465467469209600*a + 9443304675419075777712556587735767176080014604902400)*A*B^3*D + (-4221644059179269523210735132023156123791628697600*a - 23851803761821168937062893212284929784033712021490892800)*A^3*C*D + (-320333702103205781914393432329864916294583294361600000*a - 21172972247919068556684011872161338659050945573036648038400000)*A*C^3 + (-200604133548354211962257009782526587777843200000*a - 239477168369468686562493072314528761367556707387965440000)*B^2*C*D + (-5672301031158859031659192085820665467931040153600*a - 744590597049320972905271825480057158329914530813339238400)*A*B*D^2 + (78306208917126605372035025847030196791822149222400000*a + 10903282489849133395297625521851855044288917266138755235840000)*C*D^2
(1594 bytes)
Selected eigenvalues $\lambda(l)$ of $T(l)$
$l$ $\lambda(l)$
$14$ (too large to render, please specify modulus or download to view)
Selected Fourier coefficients $c(F)$
\(\det(F)\) \(F\) $c(F)$
88
(1, 0, 22) $24978299391061927533358678345196375359301759489072966938354947474634033666560 a + 6822138607548316327229533142192922776659128187222598227838022563975853275678845440$
(2, 0, 11) $1502874188923233676888123760001680366425902804505643105221311860021760 a + 109785792736611066284217997275517008980703135804746059297841074198777862269440$
Select different
$\lambda(l)$ and $c(F)$ to display or specify a modulus $\mathfrak{m}$ to reduce them by
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