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: \( 28.9384997445 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.245179729\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.173368249\) \(a_{7}=+1.621165916\) \(a_{8}=+0.353553391\) \(a_{9}=-0.939886900\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.524664975\) \(a_{12}=-0.122589865\) \(a_{13}=+1.385833868\) \(a_{14}=+1.146337413\) \(a_{15}=+0.109647708\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.293952423\) \(a_{18}=-0.664600401\) \(a_{19}=-1.448697307\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.397477020\) \(a_{22}=-1.078100943\) \(a_{23}=-0.599475561\) \(a_{24}=-0.086684125\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.979932526\) \(a_{27}=+0.475620945\) \(a_{28}=+0.810582958\) \(a_{29}=+0.081269180\) \(a_{30}=+0.077532638\)
\(a_{31}=+0.792761654\) \(a_{32}=+0.176776695\) \(a_{33}=+0.373816946\) \(a_{34}=+0.914962533\) \(a_{35}=-0.725007438\)
\(a_{36}=-0.469943450\) \(a_{37}=+0.467485815\) \(a_{38}=-1.024383690\) \(a_{39}=-0.339778373\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.628116275\) \(a_{42}=-0.281058696\) \(a_{43}=+1.681183953\) \(a_{44}=-0.762332488\) \(a_{45}=+0.420330200\)
\(a_{46}=-0.423893235\) \(a_{47}=-0.177228041\) \(a_{48}=-0.061294932\) \(a_{49}=+1.628178927\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.317250905\) \(a_{52}=+0.692916934\) \(a_{53}=-1.879094649\) \(a_{54}=+0.336314796\) \(a_{55}=+0.681850905\)
\(a_{56}=+0.573168706\) \(a_{57}=+0.355191214\) \(a_{58}=+0.057465989\) \(a_{59}=-0.606457894\) \(a_{60}=+0.054823854\)
\(a_{61}=+0.196092033\) \(a_{62}=+0.560567142\) \(a_{63}=-1.523712608\) \(a_{64}=+0.125000000\) \(a_{65}=-0.619763747\)
\(a_{66}=+0.264328497\) \(a_{67}=+0.972653056\) \(a_{68}=+0.646976212\) \(a_{69}=+0.146979256\) \(a_{70}=-0.512657676\)
\(a_{71}=-0.319938788\) \(a_{72}=-0.332300200\) \(a_{73}=+0.815677077\) \(a_{74}=+0.330562390\) \(a_{75}=-0.049035946\)
\(a_{76}=-0.724348654\) \(a_{77}=-2.471734891\) \(a_{78}=-0.240259591\) \(a_{79}=-0.802895561\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.823274286\) \(a_{82}=-0.444145278\) \(a_{83}=+1.409704964\) \(a_{84}=-0.198738510\) \(a_{85}=-0.578673116\)
\(a_{86}=+1.188776573\) \(a_{87}=-0.019925556\) \(a_{88}=-0.539050471\) \(a_{89}=-0.171287656\) \(a_{90}=+0.297218335\)
\(a_{91}=+2.246666632\) \(a_{92}=-0.299737781\) \(a_{93}=-0.194369088\) \(a_{94}=-0.125319150\) \(a_{95}=+0.647877132\)
\(a_{96}=-0.043342062\) \(a_{97}=-0.210178851\) \(a_{98}=+1.151296360\) \(a_{99}=+1.433012638\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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