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: \( 27.3228024652 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.802893721\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.274838376\) \(a_{7}=+0.004183711\) \(a_{8}=-0.353553391\) \(a_{9}=+2.250425769\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.321328507\) \(a_{12}=-0.901446860\) \(a_{13}=+0.374053935\) \(a_{14}=-0.002958331\) \(a_{15}=+0.806278583\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.697104709\) \(a_{18}=-1.591291321\) \(a_{19}=-0.761862513\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.007542787\) \(a_{22}=-0.934320347\) \(a_{23}=+0.201761215\) \(a_{24}=+0.637419188\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.264496074\) \(a_{27}=-2.254384766\) \(a_{28}=+0.002091856\) \(a_{29}=+0.085545892\) \(a_{30}=-0.570125054\)
\(a_{31}=+0.407913248\) \(a_{32}=-0.176776695\) \(a_{33}=-2.382214868\) \(a_{34}=+1.200034248\) \(a_{35}=-0.001871013\)
\(a_{36}=+1.125212884\) \(a_{37}=+0.988836997\) \(a_{38}=+0.538718149\) \(a_{39}=-0.674379490\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.655828582\) \(a_{42}=+0.005333556\) \(a_{43}=-1.817289013\) \(a_{44}=+0.660664253\) \(a_{45}=-1.006420999\)
\(a_{46}=-0.142666723\) \(a_{47}=-1.684077979\) \(a_{48}=-0.450723430\) \(a_{49}=-0.999982497\) \(a_{50}=-0.141421356\)
\(a_{51}=+3.059699424\) \(a_{52}=+0.187026967\) \(a_{53}=+1.073860647\) \(a_{54}=+1.594090756\) \(a_{55}=-0.590916072\)
\(a_{56}=-0.001479165\) \(a_{57}=+1.373557141\) \(a_{58}=-0.060490080\) \(a_{59}=+1.516538590\) \(a_{60}=+0.403139292\)
\(a_{61}=-0.296697005\) \(a_{62}=-0.288438224\) \(a_{63}=+0.009415132\) \(a_{64}=+0.125000000\) \(a_{65}=-0.167282005\)
\(a_{66}=+1.684480287\) \(a_{67}=+1.627800235\) \(a_{68}=-0.848552355\) \(a_{69}=-0.363754027\) \(a_{70}=+0.001323006\)
\(a_{71}=+1.537224333\) \(a_{72}=-0.795645661\) \(a_{73}=+0.886330136\) \(a_{74}=-0.699213346\) \(a_{75}=-0.360578744\)
\(a_{76}=-0.380931257\) \(a_{77}=+0.005528057\) \(a_{78}=+0.476858311\) \(a_{79}=-0.358982466\) \(a_{80}=-0.111803399\)
\(a_{81}=+1.813990371\) \(a_{82}=+0.463740838\) \(a_{83}=-1.262356293\) \(a_{84}=-0.003771393\) \(a_{85}=+0.758968299\)
\(a_{86}=+1.285017384\) \(a_{87}=-0.154230152\) \(a_{88}=-0.467160174\) \(a_{89}=+1.008575932\) \(a_{90}=+0.711647113\)
\(a_{91}=+0.001564934\) \(a_{92}=+0.100880607\) \(a_{93}=-0.735424233\) \(a_{94}=+1.190822959\) \(a_{95}=+0.340715274\)
\(a_{96}=+0.318709594\) \(a_{97}=+0.053533952\) \(a_{98}=+0.707094404\) \(a_{99}=+2.973551720\) \(a_{100}=+0.099975586\)

Showing 100 of 237 available coefficients

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