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: \( 18.9864206642 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.789904028\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.558546494\) \(a_{7}=-1.077845435\) \(a_{8}=-0.353553391\) \(a_{9}=-0.376051627\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.619405359\) \(a_{12}=+0.394952014\) \(a_{13}=+0.169246628\) \(a_{14}=+0.762151816\) \(a_{15}=+0.353255820\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.233250429\) \(a_{18}=+0.265908656\) \(a_{19}=+0.385238573\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.851394450\) \(a_{22}=-1.145092511\) \(a_{23}=+1.300211262\) \(a_{24}=-0.279273247\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.119675438\) \(a_{27}=-1.086948723\) \(a_{28}=-0.538922717\) \(a_{29}=-1.661101237\) \(a_{30}=-0.249789586\)
\(a_{31}=-1.115443262\) \(a_{32}=-0.176776695\) \(a_{33}=+1.279174815\) \(a_{34}=+0.872039741\) \(a_{35}=-0.482027132\)
\(a_{36}=-0.188025814\) \(a_{37}=+1.339009980\) \(a_{38}=-0.272404807\) \(a_{39}=+0.133688593\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.374527124\) \(a_{42}=+0.602026789\) \(a_{43}=-0.589843509\) \(a_{44}=+0.809702679\) \(a_{45}=-0.168175400\)
\(a_{46}=-0.919388200\) \(a_{47}=+0.661371897\) \(a_{48}=+0.197476007\) \(a_{49}=+0.161750781\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.974149481\) \(a_{52}=+0.084623314\) \(a_{53}=+0.633196603\) \(a_{54}=+0.768588812\) \(a_{55}=+0.724220093\)
\(a_{56}=+0.381075908\) \(a_{57}=+0.304301500\) \(a_{58}=+1.174575949\) \(a_{59}=-1.266053933\) \(a_{60}=+0.176627910\)
\(a_{61}=+0.897900664\) \(a_{62}=+0.788737495\) \(a_{63}=+0.405325529\) \(a_{64}=+0.125000000\) \(a_{65}=+0.075689393\)
\(a_{66}=-0.904513186\) \(a_{67}=-1.532770018\) \(a_{68}=-0.616625214\) \(a_{69}=+1.027042112\) \(a_{70}=+0.340844654\)
\(a_{71}=-1.002137609\) \(a_{72}=+0.132954328\) \(a_{73}=+0.420331624\) \(a_{74}=-0.946823037\) \(a_{75}=+0.157980806\)
\(a_{76}=+0.192619286\) \(a_{77}=-1.745468673\) \(a_{78}=-0.094532111\) \(a_{79}=-0.515833413\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.482533547\) \(a_{82}=-0.264830669\) \(a_{83}=-0.642679759\) \(a_{84}=-0.425697225\) \(a_{85}=-0.551526358\)
\(a_{86}=+0.417082345\) \(a_{87}=-1.312110558\) \(a_{88}=-0.572546255\) \(a_{89}=-1.007005286\) \(a_{90}=+0.118917966\)
\(a_{91}=-0.182421705\) \(a_{92}=+0.650105631\) \(a_{93}=-0.881093126\) \(a_{94}=-0.467660553\) \(a_{95}=+0.172283927\)
\(a_{96}=-0.139636624\) \(a_{97}=+0.896277291\) \(a_{98}=-0.114375074\) \(a_{99}=-0.608980020\) \(a_{100}=+0.099975586\)

Showing 100 of 192 available coefficients

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