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: \( 22.5860946319 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.366805618\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.966477521\) \(a_{7}=-0.559621680\) \(a_{8}=+0.353553391\) \(a_{9}=+0.868157599\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.175296894\) \(a_{12}=-0.683402809\) \(a_{13}=-1.266671271\) \(a_{14}=-0.395712285\) \(a_{15}=+0.611254055\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.262494063\) \(a_{18}=+0.613880125\) \(a_{19}=+0.830491494\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.764894057\) \(a_{22}=+0.831060404\) \(a_{23}=+1.716489460\) \(a_{24}=-0.483238761\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.895671845\) \(a_{27}=+0.180202935\) \(a_{28}=-0.279810840\) \(a_{29}=-0.628890628\) \(a_{30}=+0.432221887\)
\(a_{31}=+0.330621864\) \(a_{32}=+0.176776695\) \(a_{33}=-1.606402398\) \(a_{34}=-0.892718113\) \(a_{35}=+0.250270424\)
\(a_{36}=+0.434078799\) \(a_{37}=+1.089838601\) \(a_{38}=+0.587246167\) \(a_{39}=+1.731293410\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.715033976\) \(a_{42}=+0.540861774\) \(a_{43}=+0.757488993\) \(a_{44}=+0.587648447\) \(a_{45}=-0.388251881\)
\(a_{46}=+1.213741337\) \(a_{47}=-0.827488998\) \(a_{48}=-0.341701405\) \(a_{49}=-0.686823575\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.725583979\) \(a_{52}=-0.633335636\) \(a_{53}=-0.025845637\) \(a_{54}=+0.127422717\) \(a_{55}=-0.525608750\)
\(a_{56}=-0.197856142\) \(a_{57}=-1.135120440\) \(a_{58}=-0.444692827\) \(a_{59}=+1.066557249\) \(a_{60}=+0.305627027\)
\(a_{61}=-0.132090434\) \(a_{62}=+0.233784962\) \(a_{63}=-0.485839814\) \(a_{64}=+0.125000000\) \(a_{65}=+0.566472614\)
\(a_{66}=-1.135898029\) \(a_{67}=-1.265726427\) \(a_{68}=-0.631247032\) \(a_{69}=-2.346107438\) \(a_{70}=+0.176967914\)
\(a_{71}=+1.452482836\) \(a_{72}=+0.306940063\) \(a_{73}=-1.978102650\) \(a_{74}=+0.770632265\) \(a_{75}=-0.273361124\)
\(a_{76}=+0.415245747\) \(a_{77}=-0.657721622\) \(a_{78}=+1.224209311\) \(a_{79}=+1.300095744\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.114459983\) \(a_{82}=+0.505605374\) \(a_{83}=-0.952709934\) \(a_{84}=+0.382447028\) \(a_{85}=+0.564604509\)
\(a_{86}=+0.535625604\) \(a_{87}=+0.859571243\) \(a_{88}=+0.415530202\) \(a_{89}=-0.126716283\) \(a_{90}=-0.274535538\)
\(a_{91}=+0.708856705\) \(a_{92}=+0.858244730\) \(a_{93}=-0.451895822\) \(a_{94}=-0.585123082\) \(a_{95}=-0.371407087\)
\(a_{96}=-0.241619380\) \(a_{97}=+0.770287021\) \(a_{98}=-0.485657607\) \(a_{99}=+1.020342929\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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