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: \( 28.8500871556 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.677270751\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.478902741\) \(a_{7}=+1.562310273\) \(a_{8}=+0.353553391\) \(a_{9}=-0.541304330\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.546616242\) \(a_{12}=+0.338635375\) \(a_{13}=-1.344744128\) \(a_{14}=+1.104720189\) \(a_{15}=-0.302884688\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.163531128\) \(a_{18}=-0.382759962\) \(a_{19}=+1.532705856\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.058107052\) \(a_{22}=-0.386516051\) \(a_{23}=+0.518564035\) \(a_{24}=+0.239451370\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.950877692\) \(a_{27}=-1.043880341\) \(a_{28}=+0.781155137\) \(a_{29}=-1.508406790\) \(a_{30}=-0.214171817\)
\(a_{31}=-1.727417594\) \(a_{32}=+0.176776695\) \(a_{33}=-0.370207193\) \(a_{34}=-0.115633969\) \(a_{35}=-0.698686395\)
\(a_{36}=-0.270652165\) \(a_{37}=+1.681664150\) \(a_{38}=+1.083786704\) \(a_{39}=-0.910755866\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.137795771\) \(a_{42}=+0.748194672\) \(a_{43}=-1.762963777\) \(a_{44}=-0.273308121\) \(a_{45}=+0.242078656\)
\(a_{46}=+0.366680145\) \(a_{47}=-0.705844811\) \(a_{48}=+0.169317688\) \(a_{49}=+1.440813390\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.110754850\) \(a_{52}=-0.672372064\) \(a_{53}=-0.615992274\) \(a_{54}=-0.738134868\) \(a_{55}=+0.244454215\)
\(a_{56}=+0.552360094\) \(a_{57}=+1.038056846\) \(a_{58}=-1.066604670\) \(a_{59}=+0.438494731\) \(a_{60}=-0.151442344\)
\(a_{61}=-0.729003187\) \(a_{62}=-1.221468695\) \(a_{63}=-0.845685316\) \(a_{64}=+0.125000000\) \(a_{65}=+0.601387857\)
\(a_{66}=-0.261776016\) \(a_{67}=-1.299515142\) \(a_{68}=-0.081765564\) \(a_{69}=+0.351208253\) \(a_{70}=-0.494045888\)
\(a_{71}=-0.264681640\) \(a_{72}=-0.191379981\) \(a_{73}=-0.409833662\) \(a_{74}=+1.189116124\) \(a_{75}=+0.135454150\)
\(a_{76}=+0.766352928\) \(a_{77}=-0.853984170\) \(a_{78}=-0.644001649\) \(a_{79}=+1.127772533\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.165685292\) \(a_{82}=+0.097436324\) \(a_{83}=+1.440065218\) \(a_{84}=+0.529053526\) \(a_{85}=+0.073133344\)
\(a_{86}=-1.246603642\) \(a_{87}=-1.021599800\) \(a_{88}=-0.193258026\) \(a_{89}=-0.038559465\) \(a_{90}=+0.171175459\)
\(a_{91}=-2.100907567\) \(a_{92}=+0.259282017\) \(a_{93}=-1.169929411\) \(a_{94}=-0.499107652\) \(a_{95}=-0.685446896\)
\(a_{96}=+0.119725685\) \(a_{97}=-1.087833555\) \(a_{98}=+1.018808919\) \(a_{99}=+0.295885739\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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