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: \( 21.617168802 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.078255100\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.055334712\) \(a_{7}=-1.124354170\) \(a_{8}=+0.353553391\) \(a_{9}=-0.993876139\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.158336619\) \(a_{12}=-0.039127550\) \(a_{13}=-0.326090604\) \(a_{14}=-0.795038458\) \(a_{15}=-0.034996745\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.100568811\) \(a_{18}=-0.702776558\) \(a_{19}=+0.227943488\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.087986448\) \(a_{22}=+0.111960897\) \(a_{23}=+0.565297718\) \(a_{24}=-0.027667356\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.230580877\) \(a_{27}=+0.156030977\) \(a_{28}=-0.562177085\) \(a_{29}=+1.343084765\) \(a_{30}=-0.024746435\)
\(a_{31}=+1.492547523\) \(a_{32}=+0.176776695\) \(a_{33}=-0.012390648\) \(a_{34}=-0.778219669\) \(a_{35}=-0.502826471\)
\(a_{36}=-0.496938070\) \(a_{37}=-0.564824058\) \(a_{38}=+0.161180386\) \(a_{39}=+0.025518253\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.804056398\) \(a_{42}=+0.062215814\) \(a_{43}=-0.395025121\) \(a_{44}=+0.079168310\) \(a_{45}=-0.444474922\)
\(a_{46}=+0.399725849\) \(a_{47}=-0.063656154\) \(a_{48}=-0.019563775\) \(a_{49}=+0.264172300\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.086125122\) \(a_{52}=-0.163045302\) \(a_{53}=+1.137427011\) \(a_{54}=+0.110330562\) \(a_{55}=+0.070810289\)
\(a_{56}=-0.397519229\) \(a_{57}=-0.017837740\) \(a_{58}=+0.949704345\) \(a_{59}=-1.120426282\) \(a_{60}=-0.017498372\)
\(a_{61}=+1.847099876\) \(a_{62}=+1.055390474\) \(a_{63}=+1.117468782\) \(a_{64}=+0.125000000\) \(a_{65}=-0.145832151\)
\(a_{66}=-0.008761511\) \(a_{67}=+0.833163198\) \(a_{68}=-0.550284405\) \(a_{69}=-0.044237429\) \(a_{70}=-0.355552007\)
\(a_{71}=+0.137626237\) \(a_{72}=-0.351388279\) \(a_{73}=-1.068204382\) \(a_{74}=-0.399390922\) \(a_{75}=-0.015651020\)
\(a_{76}=+0.113971744\) \(a_{77}=-0.178026438\) \(a_{78}=+0.018044130\) \(a_{79}=-1.012301708\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.981665920\) \(a_{82}=+0.568553731\) \(a_{83}=-1.668802400\) \(a_{84}=+0.043993224\) \(a_{85}=-0.492189335\)
\(a_{86}=-0.279324942\) \(a_{87}=-0.105103233\) \(a_{88}=+0.055980449\) \(a_{89}=+0.919842351\) \(a_{90}=-0.314291231\)
\(a_{91}=+0.366641330\) \(a_{92}=+0.282648859\) \(a_{93}=-0.116799456\) \(a_{94}=-0.045011698\) \(a_{95}=+0.101939427\)
\(a_{96}=-0.013833678\) \(a_{97}=+1.455536052\) \(a_{98}=+0.186798025\) \(a_{99}=-0.157366988\) \(a_{100}=+0.099975586\)

Showing 100 of 208 available coefficients

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