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: \( 20.7236246695 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.002631899\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.001861034\) \(a_{7}=-1.663091065\) \(a_{8}=-0.353553391\) \(a_{9}=-0.999993073\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.707061422\) \(a_{12}=-0.001315950\) \(a_{13}=+1.383807718\) \(a_{14}=+1.175982970\) \(a_{15}=-0.001177021\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.723251458\) \(a_{18}=+0.707101883\) \(a_{19}=-1.003332043\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.004377088\) \(a_{22}=-0.499967926\) \(a_{23}=-0.457177476\) \(a_{24}=+0.000930517\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.978499821\) \(a_{27}=+0.005263780\) \(a_{28}=-0.831545532\) \(a_{29}=+0.789664602\) \(a_{30}=+0.000832280\)
\(a_{31}=+1.085338092\) \(a_{32}=-0.176776695\) \(a_{33}=-0.001860914\) \(a_{34}=-0.511416010\) \(a_{35}=-0.743756935\)
\(a_{36}=-0.499996537\) \(a_{37}=-1.200269098\) \(a_{38}=+0.709462891\) \(a_{39}=-0.003642042\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.073409150\) \(a_{42}=-0.003095069\) \(a_{43}=+1.434303773\) \(a_{44}=+0.353530711\) \(a_{45}=-0.447210498\)
\(a_{46}=+0.323273294\) \(a_{47}=+0.543737547\) \(a_{48}=-0.000657975\) \(a_{49}=+1.765871890\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.001903525\) \(a_{52}=+0.691903859\) \(a_{53}=-1.548804805\) \(a_{54}=-0.003722055\) \(a_{55}=+0.316207481\)
\(a_{56}=+0.587991485\) \(a_{57}=+0.002640669\) \(a_{58}=-0.558377195\) \(a_{59}=+0.585510996\) \(a_{60}=-0.000588511\)
\(a_{61}=-1.645096876\) \(a_{62}=-0.767449925\) \(a_{63}=+1.663079545\) \(a_{64}=+0.125000000\) \(a_{65}=+0.618857625\)
\(a_{66}=+0.001315865\) \(a_{67}=+1.116844731\) \(a_{68}=+0.361625729\) \(a_{69}=+0.001203245\) \(a_{70}=+0.525915572\)
\(a_{71}=-0.851625246\) \(a_{72}=+0.353550942\) \(a_{73}=+1.849780688\) \(a_{74}=+0.848718418\) \(a_{75}=-0.000526380\)
\(a_{76}=-0.501666022\) \(a_{77}=-1.175907533\) \(a_{78}=+0.002575313\) \(a_{79}=-1.042300409\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.999979219\) \(a_{82}=-0.051908108\) \(a_{83}=+0.119178349\) \(a_{84}=+0.002188544\) \(a_{85}=+0.323447885\)
\(a_{86}=-1.014205924\) \(a_{87}=-0.002078318\) \(a_{88}=-0.249983963\) \(a_{89}=+0.432310590\) \(a_{90}=+0.316225576\)
\(a_{91}=-2.301398252\) \(a_{92}=-0.228588738\) \(a_{93}=-0.002856500\) \(a_{94}=-0.384480507\) \(a_{95}=-0.448703730\)
\(a_{96}=+0.000465258\) \(a_{97}=-1.393581967\) \(a_{98}=-1.248659988\) \(a_{99}=-0.707056524\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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