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: \( 26.0094853283 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.715259479\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.212871609\) \(a_{7}=+0.324787324\) \(a_{8}=-0.353553391\) \(a_{9}=+1.942115080\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.081300089\) \(a_{12}=-0.857629739\) \(a_{13}=+1.750081965\) \(a_{14}=-0.229659319\) \(a_{15}=-0.767087359\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.548424403\) \(a_{18}=-1.373282743\) \(a_{19}=+0.653595704\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.557094536\) \(a_{22}=+0.057487844\) \(a_{23}=-0.928445128\) \(a_{24}=+0.606435805\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.237494825\) \(a_{27}=-1.615971821\) \(a_{28}=+0.162393662\) \(a_{29}=-0.929085148\) \(a_{30}=+0.542412673\)
\(a_{31}=-0.416231062\) \(a_{32}=-0.176776695\) \(a_{33}=+0.139450748\) \(a_{34}=+0.387794614\) \(a_{35}=+0.145249307\)
\(a_{36}=+0.971057540\) \(a_{37}=-1.211619180\) \(a_{38}=-0.462161955\) \(a_{39}=-3.001844680\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.527570507\) \(a_{42}=+0.393925324\) \(a_{43}=+0.168286645\) \(a_{44}=-0.040650045\) \(a_{45}=+0.868540268\)
\(a_{46}=+0.656509846\) \(a_{47}=+1.819820865\) \(a_{48}=-0.428814870\) \(a_{49}=-0.894513194\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.940690155\) \(a_{52}=+0.875040983\) \(a_{53}=+1.845562101\) \(a_{54}=+1.142664633\) \(a_{55}=-0.036358505\)
\(a_{56}=-0.114829660\) \(a_{57}=-1.121086227\) \(a_{58}=+0.656962409\) \(a_{59}=+1.464439645\) \(a_{60}=-0.383543679\)
\(a_{61}=-0.159519598\) \(a_{62}=+0.294319806\) \(a_{63}=+0.630774359\) \(a_{64}=+0.125000000\) \(a_{65}=+0.782660448\)
\(a_{66}=-0.098606570\) \(a_{67}=-1.351537036\) \(a_{68}=-0.274212201\) \(a_{69}=+1.592524306\) \(a_{70}=-0.102706770\)
\(a_{71}=-0.172686496\) \(a_{72}=-0.686641371\) \(a_{73}=+0.213469198\) \(a_{74}=+0.856744138\) \(a_{75}=-0.343051896\)
\(a_{76}=+0.326797852\) \(a_{77}=-0.026405238\) \(a_{78}=+2.122624729\) \(a_{79}=-0.750946392\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.829695904\) \(a_{82}=+1.080155464\) \(a_{83}=+1.667838707\) \(a_{84}=-0.278547268\) \(a_{85}=-0.245262849\)
\(a_{86}=-0.118996628\) \(a_{87}=+1.593622107\) \(a_{88}=+0.028743922\) \(a_{89}=-1.383913414\) \(a_{90}=-0.614150713\)
\(a_{91}=+0.568404438\) \(a_{92}=-0.464222564\) \(a_{93}=+0.713944274\) \(a_{94}=-1.286807674\) \(a_{95}=+0.292296885\)
\(a_{96}=+0.303217902\) \(a_{97}=-1.305764211\) \(a_{98}=+0.632516346\) \(a_{99}=-0.157894129\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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