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: \( 15.9608513054 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.596558203\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.128937132\) \(a_{7}=-0.356810639\) \(a_{8}=-0.353553391\) \(a_{9}=+1.548998095\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.667905973\) \(a_{12}=+0.798279101\) \(a_{13}=+1.528741452\) \(a_{14}=+0.252303222\) \(a_{15}=-0.714002534\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.142699094\) \(a_{18}=-1.095307057\) \(a_{19}=-1.874128336\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.569668952\) \(a_{22}=+0.472280843\) \(a_{23}=+0.204548519\) \(a_{24}=-0.564468566\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.080983447\) \(a_{27}=+0.876507412\) \(a_{28}=-0.178405319\) \(a_{29}=+0.658012053\) \(a_{30}=+0.504876034\)
\(a_{31}=-0.345910749\) \(a_{32}=-0.176776695\) \(a_{33}=-1.066350760\) \(a_{34}=+0.808010278\) \(a_{35}=+0.159570569\)
\(a_{36}=+0.774499047\) \(a_{37}=-0.390421513\) \(a_{38}=+1.325208855\) \(a_{39}=+2.440724705\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.567332636\) \(a_{42}=+0.402816779\) \(a_{43}=-1.687774357\) \(a_{44}=-0.333952987\) \(a_{45}=-0.692733007\)
\(a_{46}=-0.144637645\) \(a_{47}=+1.826967540\) \(a_{48}=+0.399139551\) \(a_{49}=-0.872686168\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.824385612\) \(a_{52}=+0.764370726\) \(a_{53}=-0.292426342\) \(a_{54}=-0.619784335\) \(a_{55}=+0.298696632\)
\(a_{56}=+0.126151611\) \(a_{57}=-2.992154968\) \(a_{58}=-0.465284785\) \(a_{59}=+1.063405902\) \(a_{60}=-0.357001267\)
\(a_{61}=-1.759090919\) \(a_{62}=+0.244595836\) \(a_{63}=-0.552699000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.683673961\)
\(a_{66}=+0.754023853\) \(a_{67}=-0.143035022\) \(a_{68}=-0.571349547\) \(a_{69}=+0.326573617\) \(a_{70}=-0.112833431\)
\(a_{71}=-0.736088934\) \(a_{72}=-0.547653528\) \(a_{73}=+0.742908993\) \(a_{74}=+0.276069699\) \(a_{75}=+0.319311641\)
\(a_{76}=-0.937064168\) \(a_{77}=+0.238315957\) \(a_{78}=-1.725852990\) \(a_{79}=-0.094679890\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.149602996\) \(a_{82}=+0.401164754\) \(a_{83}=-0.906634768\) \(a_{84}=-0.284834476\) \(a_{85}=+0.511030570\)
\(a_{86}=+1.193436693\) \(a_{87}=+1.050554542\) \(a_{88}=+0.236140421\) \(a_{89}=-0.813011291\) \(a_{90}=+0.489836207\)
\(a_{91}=-0.545471212\) \(a_{92}=+0.102274260\) \(a_{93}=-0.552266642\) \(a_{94}=-1.291861137\) \(a_{95}=+0.838135672\)
\(a_{96}=-0.282234283\) \(a_{97}=+0.927781867\) \(a_{98}=+0.617082307\) \(a_{99}=-1.034585111\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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