Properties

Level $15$
Weight $0$
Character 15.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.10450058521 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.400579108\) \(a_{3}=+0.577350269\) \(a_{4}=+0.961621837\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.808624725\) \(a_{7}=-0.798440616\) \(a_{8}=-0.053751654\) \(a_{9}=+0.333333333\) \(a_{10}=-0.626358018\)
\(a_{11}=+0.682343623\) \(a_{12}=+0.555192626\) \(a_{13}=+1.957529065\) \(a_{14}=-1.118279245\) \(a_{15}=-0.258198890\)
\(a_{16}=-1.036905280\) \(a_{17}=-1.181509755\) \(a_{18}=+0.466859703\) \(a_{19}=+0.239922047\) \(a_{20}=-0.430050359\)
\(a_{21}=-0.460979905\) \(a_{22}=+0.955676223\) \(a_{23}=+0.005549650\) \(a_{24}=-0.031033532\) \(a_{25}=+0.199951172\)
\(a_{26}=+2.741674311\) \(a_{27}=+0.192450090\) \(a_{28}=-0.767797932\) \(a_{29}=-0.638817249\) \(a_{30}=-0.361627971\)
\(a_{31}=-0.153468153\) \(a_{32}=-1.398516218\) \(a_{33}=+0.393951274\) \(a_{34}=-1.654797878\) \(a_{35}=+0.357073499\)
\(a_{36}=+0.320540612\) \(a_{37}=+0.669942758\) \(a_{38}=+0.336029806\) \(a_{39}=+1.130179933\) \(a_{40}=+0.024038470\)
\(a_{41}=-1.236810277\) \(a_{42}=-0.645638823\) \(a_{43}=+1.037840927\) \(a_{44}=+0.656156528\) \(a_{45}=-0.149071198\)
\(a_{46}=+0.007772724\) \(a_{47}=-0.549211530\) \(a_{48}=-0.598657543\) \(a_{49}=-0.362492583\) \(a_{50}=+0.280115822\)
\(a_{51}=-0.682144975\) \(a_{52}=+1.882402695\) \(a_{53}=+1.120735759\) \(a_{54}=+0.269541575\) \(a_{55}=-0.305153345\)
\(a_{56}=+0.042917504\) \(a_{57}=+0.138519058\) \(a_{58}=-0.894714092\) \(a_{59}=-0.090452175\) \(a_{60}=-0.248289691\)
\(a_{61}=-0.336636816\) \(a_{62}=-0.214944288\) \(a_{63}=-0.266146872\) \(a_{64}=-0.921827316\) \(a_{65}=-0.875433612\)
\(a_{66}=+0.551759924\) \(a_{67}=+0.922186160\) \(a_{68}=-1.136165580\) \(a_{69}=+0.003204092\) \(a_{70}=+0.500109682\)
\(a_{71}=+0.430773520\) \(a_{72}=-0.017917218\) \(a_{73}=-0.705286340\) \(a_{74}=+0.938307830\) \(a_{75}=+0.115470054\)
\(a_{76}=+0.230714279\) \(a_{77}=-0.544810863\) \(a_{78}=+1.582906402\) \(a_{79}=+1.043156610\) \(a_{80}=+0.463718138\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.732250634\) \(a_{83}=+0.896655100\) \(a_{84}=-0.443288342\) \(a_{85}=+0.528387225\)
\(a_{86}=+1.453578320\) \(a_{87}=-0.368821311\) \(a_{88}=-0.036677098\) \(a_{89}=-1.456932999\) \(a_{90}=-0.208786006\)
\(a_{91}=-1.562970713\) \(a_{92}=+0.005336664\) \(a_{93}=-0.088604879\) \(a_{94}=-0.769214195\) \(a_{95}=-0.107296401\)
\(a_{96}=-0.807433715\) \(a_{97}=+0.427271999\) \(a_{98}=-0.507699538\) \(a_{99}=+0.227447874\) \(a_{100}=+0.192324367\)

Showing 100 of 162 available coefficients

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