Properties

Level $39$
Weight $0$
Character 39.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 39 = 3 \cdot 13 \)
Weight: \( 0 \)
Character: 39.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.2241472473 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.205539911\) \(a_{3}=-0.577350269\) \(a_{4}=+0.453326477\) \(a_{5}=+1.112702774\)
\(a_{6}=+0.696018792\) \(a_{7}=-1.522665750\) \(a_{8}=+0.659036750\) \(a_{9}=+0.333333333\) \(a_{10}=-1.341407603\)
\(a_{11}=-1.552006656\) \(a_{12}=-0.261728163\) \(a_{13}=+0.277350098\) \(a_{14}=+1.835634333\) \(a_{15}=-0.642419246\)
\(a_{16}=-1.247821582\) \(a_{17}=+0.055616778\) \(a_{18}=-0.401846637\) \(a_{19}=-0.481393640\) \(a_{20}=+0.504417628\)
\(a_{21}=+0.879111481\) \(a_{22}=+1.871005966\) \(a_{23}=+0.909109526\) \(a_{24}=-0.380495045\) \(a_{25}=+0.238107464\)
\(a_{26}=-0.334356613\) \(a_{27}=-0.192450090\) \(a_{28}=-0.690264700\) \(a_{29}=-0.789863494\) \(a_{30}=+0.774462041\)
\(a_{31}=-0.966153493\) \(a_{32}=+0.845261969\) \(a_{33}=+0.896051461\) \(a_{34}=-0.067048245\) \(a_{35}=-1.694274405\)
\(a_{36}=+0.151108826\) \(a_{37}=-0.885819754\) \(a_{38}=+0.580339246\) \(a_{39}=-0.160128154\) \(a_{40}=+0.733312021\)
\(a_{41}=-0.804258945\) \(a_{42}=-1.059803976\) \(a_{43}=+0.320318760\) \(a_{44}=-0.703565709\) \(a_{45}=+0.370900925\)
\(a_{46}=-1.095967817\) \(a_{47}=+1.415905067\) \(a_{48}=+0.720430126\) \(a_{49}=+1.318510987\) \(a_{50}=-0.287048051\)
\(a_{51}=-0.032110361\) \(a_{52}=+0.125730143\) \(a_{53}=+0.919039026\) \(a_{54}=+0.232006264\) \(a_{55}=-1.726922112\)
\(a_{56}=-1.003492688\) \(a_{57}=+0.277932748\) \(a_{58}=+0.952211966\) \(a_{59}=-1.019927350\) \(a_{60}=-0.291225654\)
\(a_{61}=+0.455187248\) \(a_{62}=+1.164736596\) \(a_{63}=-0.507555250\) \(a_{64}=+0.228824544\) \(a_{65}=+0.308608224\)
\(a_{66}=-1.080225798\) \(a_{67}=+0.412988541\) \(a_{68}=+0.025212558\) \(a_{69}=-0.524874630\) \(a_{70}=+2.042515415\)
\(a_{71}=-0.015339774\) \(a_{72}=+0.219678917\) \(a_{73}=-1.876994800\) \(a_{74}=+1.067891067\) \(a_{75}=-0.137471408\)
\(a_{76}=-0.218228483\) \(a_{77}=+2.363187379\) \(a_{78}=+0.193040880\) \(a_{79}=-0.685133860\) \(a_{80}=-1.388454536\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.969566257\) \(a_{83}=-1.249920382\) \(a_{84}=+0.398524510\) \(a_{85}=+0.061884943\)
\(a_{86}=-0.386157049\) \(a_{87}=+0.456027901\) \(a_{88}=-1.022829423\) \(a_{89}=+1.304707990\) \(a_{90}=-0.447135868\)
\(a_{91}=-0.422311495\) \(a_{92}=+0.412123419\) \(a_{93}=+0.557808979\) \(a_{94}=-1.706930068\) \(a_{95}=-0.535648039\)
\(a_{96}=-0.488012225\) \(a_{97}=-1.640417400\) \(a_{98}=-1.589517618\) \(a_{99}=-0.517335552\) \(a_{100}=+0.107940418\)

Showing 100 of 310 available coefficients

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