Properties

Level $463$
Weight $0$
Character 463.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 463 \)
Weight: \( 0 \)
Character: 463.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 0.828231596807 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.113848179\) \(a_{3}=-1.562413853\) \(a_{4}=-0.987038601\) \(a_{5}=+0.693664521\)
\(a_{6}=+0.177877970\) \(a_{7}=+0.718480022\) \(a_{8}=+0.226220726\) \(a_{9}=+1.441137096\) \(a_{10}=-0.078972447\)
\(a_{11}=-0.074155932\) \(a_{12}=+1.542162804\) \(a_{13}=+0.572923750\) \(a_{14}=-0.081797656\) \(a_{15}=-1.083791099\)
\(a_{16}=+0.961283775\) \(a_{17}=+0.182116974\) \(a_{18}=-0.164070829\) \(a_{19}=-1.406755902\) \(a_{20}=-0.684673664\)
\(a_{21}=-1.122563166\) \(a_{22}=+0.008442518\) \(a_{23}=-1.083772586\) \(a_{24}=-0.353450407\) \(a_{25}=-0.518829517\)
\(a_{26}=-0.065226329\) \(a_{27}=-0.689238723\) \(a_{28}=-0.709167477\) \(a_{29}=+0.809648776\) \(a_{30}=+0.123387639\)
\(a_{31}=-1.015209839\) \(a_{32}=-0.335661146\) \(a_{33}=+0.115862276\) \(a_{34}=-0.020733667\) \(a_{35}=+0.498384100\)
\(a_{36}=-1.422457955\) \(a_{37}=+0.295834705\) \(a_{38}=+0.160156620\) \(a_{39}=-0.895144013\) \(a_{40}=+0.156921298\)
\(a_{41}=-1.146449831\) \(a_{42}=+0.127801799\) \(a_{43}=-1.230515308\) \(a_{44}=+0.073194773\) \(a_{45}=+0.999665702\)
\(a_{46}=+0.123385542\) \(a_{47}=+1.408515058\) \(a_{48}=-1.501923119\) \(a_{49}=-0.483786504\) \(a_{50}=+0.059067803\)
\(a_{51}=-0.284542073\) \(a_{52}=-0.565497863\) \(a_{53}=-1.001763467\) \(a_{54}=+0.078468557\) \(a_{55}=-0.051439340\)
\(a_{56}=+0.162535068\) \(a_{57}=+2.197934927\) \(a_{58}=-0.092177052\) \(a_{59}=+0.206599995\) \(a_{60}=+1.069743645\)
\(a_{61}=-0.022637336\) \(a_{62}=+0.115579797\) \(a_{63}=+1.035428226\) \(a_{64}=-0.923069359\) \(a_{65}=+0.397416891\)
\(a_{66}=-0.013190718\) \(a_{67}=-0.959839034\) \(a_{68}=-0.179756508\) \(a_{69}=+1.693301321\) \(a_{70}=-0.056740124\)
\(a_{71}=+1.027359285\) \(a_{72}=+0.326015093\) \(a_{73}=-0.025679639\) \(a_{74}=-0.033680263\) \(a_{75}=+0.810626428\)
\(a_{76}=+1.388522359\) \(a_{77}=-0.053279556\) \(a_{78}=+0.101910528\) \(a_{79}=-1.298544923\) \(a_{80}=+0.666808479\)
\(a_{81}=-0.364260970\) \(a_{82}=+0.130521233\) \(a_{83}=-1.057089287\) \(a_{84}=+1.108013123\) \(a_{85}=+0.126328094\)
\(a_{86}=+0.140091908\) \(a_{87}=-1.265006466\) \(a_{88}=-0.016775600\) \(a_{89}=+1.766114744\) \(a_{90}=-0.113810142\)
\(a_{91}=+0.411634274\) \(a_{92}=+1.069725362\) \(a_{93}=+1.586177945\) \(a_{94}=-0.160356896\) \(a_{95}=-0.975816671\)
\(a_{96}=+0.524441639\) \(a_{97}=-0.970176736\) \(a_{98}=+0.055078244\) \(a_{99}=-0.106868898\) \(a_{100}=+0.512104763\)

Showing 100 of 1488 available coefficients

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