Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 26.1494656272 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.800155620\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.565795465\) \(a_{7}=-1.070586959\) \(a_{8}=-0.353553391\) \(a_{9}=-0.359750985\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.517556797\) \(a_{12}=+0.400077810\) \(a_{13}=+1.403364847\) \(a_{14}=+0.757019299\) \(a_{15}=-0.357840472\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.261921101\) \(a_{18}=+0.254382361\) \(a_{19}=-0.895843245\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.856636172\) \(a_{22}=-0.365967921\) \(a_{23}=+0.277894787\) \(a_{24}=-0.282897732\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.992328800\) \(a_{27}=-1.088012391\) \(a_{28}=-0.535293480\) \(a_{29}=-0.326531156\) \(a_{30}=+0.253031424\)
\(a_{31}=-0.248891676\) \(a_{32}=-0.176776695\) \(a_{33}=+0.414125979\) \(a_{34}=-0.892312968\) \(a_{35}=+0.478781043\)
\(a_{36}=-0.179875492\) \(a_{37}=-1.849475939\) \(a_{38}=+0.633456833\) \(a_{39}=+1.122910268\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.844380266\) \(a_{42}=+0.605733246\) \(a_{43}=-1.899640658\) \(a_{44}=+0.258778398\) \(a_{45}=+0.160885531\)
\(a_{46}=-0.196501288\) \(a_{47}=+0.202097796\) \(a_{48}=+0.200038905\) \(a_{49}=+0.146156437\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.009733260\) \(a_{52}=+0.701682423\) \(a_{53}=+0.398297646\) \(a_{54}=+0.769340940\) \(a_{55}=-0.231458436\)
\(a_{56}=+0.378509649\) \(a_{57}=-0.716814006\) \(a_{58}=+0.230892395\) \(a_{59}=+0.559686028\) \(a_{60}=-0.178920236\)
\(a_{61}=+1.519755107\) \(a_{62}=+0.175992992\) \(a_{63}=+0.385144713\) \(a_{64}=+0.125000000\) \(a_{65}=-0.627603839\)
\(a_{66}=-0.292831288\) \(a_{67}=-0.294072653\) \(a_{68}=+0.630960551\) \(a_{69}=+0.222359075\) \(a_{70}=-0.338549322\)
\(a_{71}=-0.508633556\) \(a_{72}=+0.127191180\) \(a_{73}=+0.497761334\) \(a_{74}=+1.307776978\) \(a_{75}=+0.160031124\)
\(a_{76}=-0.447921622\) \(a_{77}=-0.554089557\) \(a_{78}=-0.794017465\) \(a_{79}=-1.440143255\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.510828245\) \(a_{82}=-0.597067012\) \(a_{83}=-1.551257986\) \(a_{84}=-0.428318086\) \(a_{85}=-0.564348273\)
\(a_{86}=+1.343248791\) \(a_{87}=-0.261275740\) \(a_{88}=-0.182983960\) \(a_{89}=+1.174556654\) \(a_{90}=-0.113763250\)
\(a_{91}=-1.502424104\) \(a_{92}=+0.138947393\) \(a_{93}=-0.199152073\) \(a_{94}=-0.142904722\) \(a_{95}=+0.400633278\)
\(a_{96}=-0.141448866\) \(a_{97}=+1.661223776\) \(a_{98}=-0.103348208\) \(a_{99}=-0.186191567\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

Rows: Cols: