Properties

Level $15$
Weight $0$
Character 15.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.91310981628 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.314405793\) \(a_{3}=+0.577350269\) \(a_{4}=-0.901148997\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.181522269\) \(a_{7}=+0.384009822\) \(a_{8}=-0.597732259\) \(a_{9}=+0.333333333\) \(a_{10}=+0.140606545\)
\(a_{11}=+0.675337268\) \(a_{12}=-0.520278616\) \(a_{13}=-0.911605875\) \(a_{14}=+0.120734913\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.713218512\) \(a_{17}=+1.685749622\) \(a_{18}=+0.104801931\) \(a_{19}=+0.935058121\) \(a_{20}=-0.403006083\)
\(a_{21}=+0.221708174\) \(a_{22}=+0.212329950\) \(a_{23}=+1.208750710\) \(a_{24}=-0.345100881\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.286614168\) \(a_{27}=+0.192450090\) \(a_{28}=-0.346050066\) \(a_{29}=+1.579316894\) \(a_{30}=+0.081179227\)
\(a_{31}=-1.107993804\) \(a_{32}=+0.821972291\) \(a_{33}=+0.389906154\) \(a_{34}=+0.530009447\) \(a_{35}=+0.171734413\)
\(a_{36}=-0.300382999\) \(a_{37}=+0.241193436\) \(a_{38}=+0.293987690\) \(a_{39}=-0.526315897\) \(a_{40}=-0.267313993\)
\(a_{41}=-0.724451368\) \(a_{42}=+0.069706334\) \(a_{43}=+0.530102936\) \(a_{44}=-0.608579502\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.380038226\) \(a_{47}=-0.685699254\) \(a_{48}=+0.411776900\) \(a_{49}=-0.852536457\) \(a_{50}=+0.062881159\)
\(a_{51}=+0.973267998\) \(a_{52}=+0.821492720\) \(a_{53}=+0.164498283\) \(a_{54}=+0.060507423\) \(a_{55}=+0.302020008\)
\(a_{56}=-0.229535058\) \(a_{57}=+0.539856058\) \(a_{58}=+0.496546381\) \(a_{59}=-0.808351966\) \(a_{60}=-0.232675671\)
\(a_{61}=-0.573561755\) \(a_{62}=-0.348359671\) \(a_{63}=+0.128003274\) \(a_{64}=-0.454785662\) \(a_{65}=-0.407682541\)
\(a_{66}=+0.122588754\) \(a_{67}=+0.570074261\) \(a_{68}=-1.519111581\) \(a_{69}=+0.697872548\) \(a_{70}=+0.053994294\)
\(a_{71}=-0.370795901\) \(a_{72}=-0.199244086\) \(a_{73}=+1.372107249\) \(a_{74}=+0.075832614\) \(a_{75}=+0.115470054\)
\(a_{76}=-0.842626688\) \(a_{77}=+0.259336144\) \(a_{78}=-0.165476767\) \(a_{79}=+1.915101670\) \(a_{80}=+0.318961015\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.227771707\) \(a_{83}=-1.587479835\) \(a_{84}=-0.199792098\) \(a_{85}=+0.753890149\)
\(a_{86}=+0.166667434\) \(a_{87}=+0.911819034\) \(a_{88}=-0.403670871\) \(a_{89}=+0.525003668\) \(a_{90}=+0.046868848\)
\(a_{91}=-0.350065609\) \(a_{92}=-1.089264490\) \(a_{93}=-0.639700521\) \(a_{94}=-0.215587818\) \(a_{95}=+0.418170704\)
\(a_{96}=+0.474565923\) \(a_{97}=-1.533220260\) \(a_{98}=-0.268042401\) \(a_{99}=+0.225112423\) \(a_{100}=-0.180229799\)

Showing 100 of 180 available coefficients

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