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: \( 5.45975729468 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.801440803\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=+1.273811007\) \(a_{7}=-0.939838994\) \(a_{8}=-0.353553391\) \(a_{9}=+2.245188965\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.164122618\) \(a_{12}=-0.900720401\) \(a_{13}=+0.844818178\) \(a_{14}=+0.664566526\) \(a_{15}=-0.805628818\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.193064122\) \(a_{18}=-1.587588342\) \(a_{19}=-0.098107279\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.693064312\) \(a_{22}=-0.116052216\) \(a_{23}=+0.482532281\) \(a_{24}=+0.636905504\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.597376663\) \(a_{27}=-2.243134209\) \(a_{28}=-0.469919497\) \(a_{29}=-0.508577219\) \(a_{30}=+0.569665601\)
\(a_{31}=+1.844803436\) \(a_{32}=-0.176776695\) \(a_{33}=-0.295657180\) \(a_{34}=-0.136516950\) \(a_{35}=-0.420308776\)
\(a_{36}=+1.122594483\) \(a_{37}=+1.086660453\) \(a_{38}=+0.069372322\) \(a_{39}=-1.521889937\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.606225998\) \(a_{42}=-1.197177256\) \(a_{43}=+0.607905952\) \(a_{44}=+0.082061309\) \(a_{45}=+1.004079030\)
\(a_{46}=-0.341201848\) \(a_{47}=-1.192300487\) \(a_{48}=-0.450360201\) \(a_{49}=-0.116702665\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.347793586\) \(a_{52}=+0.422409089\) \(a_{53}=-0.076491306\) \(a_{54}=+1.586135410\) \(a_{55}=+0.073397866\)
\(a_{56}=+0.332283263\) \(a_{57}=+0.176734455\) \(a_{58}=+0.359618400\) \(a_{59}=-0.055132340\) \(a_{60}=-0.402814409\)
\(a_{61}=+1.187307021\) \(a_{62}=-1.304473019\) \(a_{63}=-2.110116139\) \(a_{64}=+0.125000000\) \(a_{65}=+0.377814175\)
\(a_{66}=+0.209061197\) \(a_{67}=+1.851355599\) \(a_{68}=+0.096532061\) \(a_{69}=-0.869253339\) \(a_{70}=+0.297203186\)
\(a_{71}=-1.510516600\) \(a_{72}=-0.793794171\) \(a_{73}=+1.277995440\) \(a_{74}=-0.768384975\) \(a_{75}=-0.360288161\)
\(a_{76}=-0.049053640\) \(a_{77}=-0.154248836\) \(a_{78}=+1.076138695\) \(a_{79}=-0.895211000\) \(a_{80}=+0.111803399\)
\(a_{81}=+1.795684525\) \(a_{82}=-0.428666514\) \(a_{83}=+1.195138801\) \(a_{84}=+0.846532156\) \(a_{85}=+0.086340900\)
\(a_{86}=-0.429854421\) \(a_{87}=+0.916171754\) \(a_{88}=-0.058026108\) \(a_{89}=-0.356257000\) \(a_{90}=-0.709991091\)
\(a_{91}=-0.793993067\) \(a_{92}=+0.241266140\) \(a_{93}=-3.323304182\) \(a_{94}=+0.843083759\) \(a_{95}=-0.043874909\)
\(a_{96}=+0.318452752\) \(a_{97}=-1.509686001\) \(a_{98}=+0.082521246\) \(a_{99}=+0.368486290\) \(a_{100}=+0.099975586\)

Showing 100 of 130 available coefficients

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