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: \( 14.7336237927 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.128270163\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.797807483\) \(a_{7}=-1.916800763\) \(a_{8}=-0.353553391\) \(a_{9}=+0.272993561\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.498234422\) \(a_{12}=+0.564135082\) \(a_{13}=+0.599853100\) \(a_{14}=+1.355382817\) \(a_{15}=+0.504577756\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.690406967\) \(a_{18}=-0.193035598\) \(a_{19}=+1.150665790\) \(a_{20}=+0.223606798\)
\(a_{21}=-2.162669109\) \(a_{22}=+1.059411720\) \(a_{23}=+0.927870132\) \(a_{24}=-0.398903742\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.424160195\) \(a_{27}=-0.820259673\) \(a_{28}=-0.958400381\) \(a_{29}=+1.018132533\) \(a_{30}=-0.356790353\)
\(a_{31}=-0.063319551\) \(a_{32}=-0.176776695\) \(a_{33}=-1.690413196\) \(a_{34}=-0.488191448\) \(a_{35}=-0.857219361\)
\(a_{36}=+0.136496781\) \(a_{37}=+1.273687715\) \(a_{38}=-0.813643583\) \(a_{39}=+0.676796355\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.264895844\) \(a_{42}=+1.529237993\) \(a_{43}=+0.327899543\) \(a_{44}=-0.749117211\) \(a_{45}=+0.122086432\)
\(a_{46}=-0.656103262\) \(a_{47}=-0.478307988\) \(a_{48}=+0.282067541\) \(a_{49}=+2.674125164\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.778965581\) \(a_{52}=+0.299926550\) \(a_{53}=+0.846076506\) \(a_{54}=+0.580011177\) \(a_{55}=-0.670030803\)
\(a_{56}=+0.677691409\) \(a_{57}=+1.298261878\) \(a_{58}=-0.719928418\) \(a_{59}=+0.391411096\) \(a_{60}=+0.252288878\)
\(a_{61}=-0.961563708\) \(a_{62}=+0.044773684\) \(a_{63}=-0.523274266\) \(a_{64}=+0.125000000\) \(a_{65}=+0.268262462\)
\(a_{66}=+1.195302634\) \(a_{67}=-0.696690315\) \(a_{68}=+0.345203483\) \(a_{69}=+1.046888185\) \(a_{70}=+0.606145623\)
\(a_{71}=-0.488785484\) \(a_{72}=-0.096517799\) \(a_{73}=-0.392173774\) \(a_{74}=-0.900633220\) \(a_{75}=+0.225654033\)
\(a_{76}=+0.575332895\) \(a_{77}=+2.871816883\) \(a_{78}=-0.478567292\) \(a_{79}=-1.257810664\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.198468077\) \(a_{82}=-0.894416429\) \(a_{83}=+0.528765491\) \(a_{84}=-1.081334555\) \(a_{85}=+0.308759382\)
\(a_{86}=-0.231859990\) \(a_{87}=+1.148728558\) \(a_{88}=+0.529705860\) \(a_{89}=+0.705648467\) \(a_{90}=-0.086328144\)
\(a_{91}=-1.149798878\) \(a_{92}=+0.463935066\) \(a_{93}=-0.071441567\) \(a_{94}=+0.338214822\) \(a_{95}=+0.514593385\)
\(a_{96}=-0.199451871\) \(a_{97}=+1.494018109\) \(a_{98}=-1.890892037\) \(a_{99}=-0.409008362\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

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