Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 28.5712269238 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.412725756\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.998947962\) \(a_{7}=+0.075126043\) \(a_{8}=-0.353553391\) \(a_{9}=+0.995794062\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.060285880\) \(a_{12}=-0.706362878\) \(a_{13}=+0.695278662\) \(a_{14}=-0.053122135\) \(a_{15}=-0.631790165\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.864687450\) \(a_{18}=-0.704132734\) \(a_{19}=-1.206199271\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.106132497\) \(a_{22}=-0.749735336\) \(a_{23}=+0.100604942\) \(a_{24}=+0.499473981\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.491636257\) \(a_{27}=+0.005941836\) \(a_{28}=+0.037563022\) \(a_{29}=-0.055291043\) \(a_{30}=+0.446743110\)
\(a_{31}=-0.668666939\) \(a_{32}=-0.176776695\) \(a_{33}=-1.497893172\) \(a_{34}=-0.611426360\) \(a_{35}=+0.033597388\)
\(a_{36}=+0.497897031\) \(a_{37}=-0.637786482\) \(a_{38}=+0.852911684\) \(a_{39}=-0.982238073\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.515349900\) \(a_{42}=+0.075047008\) \(a_{43}=+0.189454510\) \(a_{44}=+0.530142940\) \(a_{45}=+0.445332643\)
\(a_{46}=-0.071138437\) \(a_{47}=-1.698456818\) \(a_{48}=-0.353181439\) \(a_{49}=-0.994356078\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.221566232\) \(a_{52}=+0.347639331\) \(a_{53}=-1.708315142\) \(a_{54}=-0.004201513\) \(a_{55}=+0.474174261\)
\(a_{56}=-0.026561067\) \(a_{57}=+1.704028777\) \(a_{58}=+0.039096671\) \(a_{59}=+1.552533634\) \(a_{60}=-0.315895082\)
\(a_{61}=+1.337259222\) \(a_{62}=+0.472818927\) \(a_{63}=+0.074810068\) \(a_{64}=+0.125000000\) \(a_{65}=+0.310938070\)
\(a_{66}=+1.059170419\) \(a_{67}=+0.009299405\) \(a_{68}=+0.432343725\) \(a_{69}=-0.142127192\) \(a_{70}=-0.023756941\)
\(a_{71}=+0.032939157\) \(a_{72}=-0.352066367\) \(a_{73}=+0.259471930\) \(a_{74}=+0.450983147\) \(a_{75}=-0.282545151\)
\(a_{76}=-0.603099635\) \(a_{77}=+0.079655083\) \(a_{78}=+0.694547202\) \(a_{79}=+1.852443066\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.004188248\) \(a_{82}=+0.364407409\) \(a_{83}=+0.441677507\) \(a_{84}=-0.053066248\) \(a_{85}=+0.386699984\)
\(a_{86}=-0.133964569\) \(a_{87}=+0.078111081\) \(a_{88}=-0.374867668\) \(a_{89}=-0.673964543\) \(a_{90}=-0.314897732\)
\(a_{91}=+0.052233535\) \(a_{92}=+0.050302471\) \(a_{93}=+0.944643008\) \(a_{94}=+1.200990333\) \(a_{95}=-0.539428713\)
\(a_{96}=+0.249736991\) \(a_{97}=+0.606065555\) \(a_{98}=+0.703115925\) \(a_{99}=+1.055826384\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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