Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 24.6372905679 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.664122813\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.469605745\) \(a_{7}=+0.628202393\) \(a_{8}=+0.353553391\) \(a_{9}=-0.558940889\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.299138615\) \(a_{12}=+0.332061406\) \(a_{13}=-0.859296149\) \(a_{14}=+0.444206172\) \(a_{15}=-0.297004751\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.328004699\) \(a_{18}=-0.395230893\) \(a_{19}=+1.893285211\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.417203540\) \(a_{22}=+0.211522943\) \(a_{23}=+0.706602569\) \(a_{24}=+0.234802872\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.607614134\) \(a_{27}=-1.035328209\) \(a_{28}=+0.314101196\) \(a_{29}=+0.614189391\) \(a_{30}=-0.210014073\)
\(a_{31}=+0.709264766\) \(a_{32}=+0.176776695\) \(a_{33}=+0.198664778\) \(a_{34}=-0.939041128\) \(a_{35}=-0.280940651\)
\(a_{36}=-0.279470445\) \(a_{37}=-0.167197655\) \(a_{38}=+1.338754811\) \(a_{39}=-0.570678175\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.196959354\) \(a_{42}=+0.295007452\) \(a_{43}=+1.908244204\) \(a_{44}=+0.149569307\) \(a_{45}=+0.249965965\)
\(a_{46}=+0.499643468\) \(a_{47}=+0.873188804\) \(a_{48}=+0.166030703\) \(a_{49}=-0.605361753\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.881958216\) \(a_{52}=-0.429648074\) \(a_{53}=+0.186268927\) \(a_{54}=-0.732087597\) \(a_{55}=-0.133778856\)
\(a_{56}=+0.222103086\) \(a_{57}=+1.257373900\) \(a_{58}=+0.434297484\) \(a_{59}=-0.236102311\) \(a_{60}=-0.148502376\)
\(a_{61}=+1.143388712\) \(a_{62}=+0.501525926\) \(a_{63}=-0.351128004\) \(a_{64}=+0.125000000\) \(a_{65}=+0.384288920\)
\(a_{66}=+0.140477212\) \(a_{67}=+1.054103407\) \(a_{68}=-0.664002350\) \(a_{69}=+0.469270886\) \(a_{70}=-0.198655039\)
\(a_{71}=-1.617727120\) \(a_{72}=-0.197615447\) \(a_{73}=+1.705295549\) \(a_{74}=-0.118226595\) \(a_{75}=+0.132824563\)
\(a_{76}=+0.946642605\) \(a_{77}=+0.187919594\) \(a_{78}=-0.403530408\) \(a_{79}=+1.240996309\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.128644193\) \(a_{82}=-0.139271295\) \(a_{83}=-0.538119638\) \(a_{84}=+0.208601770\) \(a_{85}=+0.593901756\)
\(a_{86}=+1.349332417\) \(a_{87}=+0.407897186\) \(a_{88}=+0.105761472\) \(a_{89}=+0.640534610\) \(a_{90}=+0.176752629\)
\(a_{91}=-0.539811897\) \(a_{92}=+0.353301285\) \(a_{93}=+0.471038912\) \(a_{94}=+0.617437725\) \(a_{95}=-0.846702886\)
\(a_{96}=+0.117401436\) \(a_{97}=-0.804301457\) \(a_{98}=-0.428055401\) \(a_{99}=-0.167200803\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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