Properties

Level 10
Weight 0
Character 10.1
Symmetry even
Fricke sign -1

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: \(-1\)
Spectral parameter: \( 12.9582818801 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.885765320\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.626330664\) \(a_{7}=-0.890160209\) \(a_{8}=-0.353553391\) \(a_{9}=-0.215419798\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.025401580\) \(a_{12}=-0.442882660\) \(a_{13}=+1.364018810\) \(a_{14}=+0.629438320\) \(a_{15}=-0.396126294\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.169867128\) \(a_{18}=+0.152324800\) \(a_{19}=+0.550229075\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.788473042\) \(a_{22}=-0.017961629\) \(a_{23}=+1.633451941\) \(a_{24}=+0.313165332\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.964506950\) \(a_{27}=+1.076576706\) \(a_{28}=-0.445080104\) \(a_{29}=-0.112110883\) \(a_{30}=+0.280103588\)
\(a_{31}=-1.206332684\) \(a_{32}=-0.176776695\) \(a_{33}=-0.022499839\) \(a_{34}=+0.120114198\) \(a_{35}=-0.398091748\)
\(a_{36}=-0.107709899\) \(a_{37}=-1.361417949\) \(a_{38}=-0.389070710\) \(a_{39}=-1.208200558\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.843747464\) \(a_{42}=-0.557534635\) \(a_{43}=+1.098334587\) \(a_{44}=+0.012700790\) \(a_{45}=-0.096338662\)
\(a_{46}=-1.155024944\) \(a_{47}=+0.585830340\) \(a_{48}=-0.221441330\) \(a_{49}=-0.207614803\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.150462411\) \(a_{52}=+0.682009405\) \(a_{53}=-1.189873059\) \(a_{54}=-0.761254689\) \(a_{55}=+0.011359932\)
\(a_{56}=+0.314719160\) \(a_{57}=-0.487373833\) \(a_{58}=+0.079274366\) \(a_{59}=-1.546185774\) \(a_{60}=-0.198063147\)
\(a_{61}=+1.372244328\) \(a_{62}=+0.853006021\) \(a_{63}=+0.191758132\) \(a_{64}=+0.125000000\) \(a_{65}=+0.610007756\)
\(a_{66}=+0.015909788\) \(a_{67}=+0.806931781\) \(a_{68}=-0.084933564\) \(a_{69}=-1.446855081\) \(a_{70}=+0.281493374\)
\(a_{71}=-1.182509947\) \(a_{72}=+0.076162400\) \(a_{73}=-1.791934077\) \(a_{74}=+0.962667864\) \(a_{75}=-0.177153064\)
\(a_{76}=+0.275114537\) \(a_{77}=-0.022611476\) \(a_{78}=+0.854326807\) \(a_{79}=-0.207074055\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.738174511\) \(a_{82}=+0.596619553\) \(a_{83}=+1.576722176\) \(a_{84}=+0.394236521\) \(a_{85}=-0.075966889\)
\(a_{86}=-0.776639834\) \(a_{87}=+0.099303931\) \(a_{88}=-0.008980815\) \(a_{89}=-0.949192115\) \(a_{90}=+0.068121721\)
\(a_{91}=-1.214195280\) \(a_{92}=+0.816725970\) \(a_{93}=+1.068527661\) \(a_{94}=-0.414244606\) \(a_{95}=+0.246069923\)
\(a_{96}=+0.156582666\) \(a_{97}=-0.572152539\) \(a_{98}=+0.146805835\) \(a_{99}=-0.005472048\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

Rows: Cols: