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: \( 28.0335697639 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.777023073\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.549438284\) \(a_{7}=-1.000331021\) \(a_{8}=+0.353553391\) \(a_{9}=-0.396235144\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.087114704\) \(a_{12}=-0.388511536\) \(a_{13}=+0.187252102\) \(a_{14}=-0.707340848\) \(a_{15}=+0.347495282\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.832980088\) \(a_{18}=-0.280180557\) \(a_{19}=+0.420332314\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.777280284\) \(a_{22}=-0.768706179\) \(a_{23}=+0.704277877\) \(a_{24}=-0.274719142\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.132407231\) \(a_{27}=+1.084906922\) \(a_{28}=-0.500165510\) \(a_{29}=+1.631727849\) \(a_{30}=+0.245716271\)
\(a_{31}=-1.753689602\) \(a_{32}=+0.176776695\) \(a_{33}=+0.844713208\) \(a_{34}=+1.296112650\) \(a_{35}=+0.447361632\)
\(a_{36}=-0.198117572\) \(a_{37}=+0.620238915\) \(a_{38}=+0.297219829\) \(a_{39}=-0.145499204\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.828197544\) \(a_{42}=+0.549620159\) \(a_{43}=-1.343528169\) \(a_{44}=-0.543557352\) \(a_{45}=+0.177201743\)
\(a_{46}=+0.497999663\) \(a_{47}=-1.304733916\) \(a_{48}=-0.194255768\) \(a_{49}=+0.000662151\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.424267821\) \(a_{52}=+0.093626051\) \(a_{53}=+0.822647473\) \(a_{54}=+0.767145042\) \(a_{55}=+0.486172475\)
\(a_{56}=-0.353670424\) \(a_{57}=-0.326607906\) \(a_{58}=+1.153805827\) \(a_{59}=-0.725520757\) \(a_{60}=+0.173747641\)
\(a_{61}=+0.601043028\) \(a_{62}=-1.240045810\) \(a_{63}=+0.396366306\) \(a_{64}=+0.125000000\) \(a_{65}=-0.083741686\)
\(a_{66}=+0.597302437\) \(a_{67}=+1.379909777\) \(a_{68}=+0.916490044\) \(a_{69}=-0.547240161\) \(a_{70}=+0.316332444\)
\(a_{71}=+0.046103681\) \(a_{72}=-0.140090279\) \(a_{73}=+0.772681597\) \(a_{74}=+0.438575143\) \(a_{75}=-0.155404615\)
\(a_{76}=+0.210166157\) \(a_{77}=+1.087474561\) \(a_{78}=-0.102883474\) \(a_{79}=+0.109798435\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.446762566\) \(a_{82}=+0.585624099\) \(a_{83}=-1.699950799\) \(a_{84}=+0.388640142\) \(a_{85}=-0.819733616\)
\(a_{86}=-0.950017879\) \(a_{87}=-1.267890188\) \(a_{88}=-0.384353090\) \(a_{89}=-0.580991570\) \(a_{90}=+0.125300554\)
\(a_{91}=-0.187314086\) \(a_{92}=+0.352138939\) \(a_{93}=+1.362657284\) \(a_{94}=-0.922586199\) \(a_{95}=-0.187978325\)
\(a_{96}=-0.137359571\) \(a_{97}=+1.508826855\) \(a_{98}=+0.000468212\) \(a_{99}=+0.430753051\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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