Properties

Level $1$
Weight $0$
Character 1.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 29.1375875578 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.085105239\) \(a_{3}=+0.820704067\) \(a_{4}=-0.992757098\) \(a_{5}=+1.031232115\)
\(a_{6}=-0.069846215\) \(a_{7}=-1.034399566\) \(a_{8}=+0.169594068\) \(a_{9}=-0.326444834\) \(a_{10}=-0.087763255\)
\(a_{11}=+1.014604187\) \(a_{12}=-0.814759788\) \(a_{13}=-0.331624885\) \(a_{14}=+0.088032822\) \(a_{15}=+0.846336391\)
\(a_{16}=+0.978323757\) \(a_{17}=-1.058823595\) \(a_{18}=+0.027782166\) \(a_{19}=-1.594435455\) \(a_{20}=-1.023763002\)
\(a_{21}=-0.848935931\) \(a_{22}=-0.086348131\) \(a_{23}=-1.263695538\) \(a_{24}=+0.139186542\) \(a_{25}=+0.063439675\)
\(a_{26}=+0.028223015\) \(a_{27}=-1.088618670\) \(a_{28}=+1.026907512\) \(a_{29}=-0.200010899\) \(a_{30}=-0.072027661\)
\(a_{31}=-0.255735720\) \(a_{32}=-0.252854545\) \(a_{33}=+0.832689783\) \(a_{34}=+0.090111435\) \(a_{35}=-1.066706052\)
\(a_{36}=+0.324080426\) \(a_{37}=+0.388397276\) \(a_{38}=+0.135694810\) \(a_{39}=-0.272165892\) \(a_{40}=+0.174890850\)
\(a_{41}=-0.752893456\) \(a_{42}=+0.072248895\) \(a_{43}=+1.561332522\) \(a_{44}=-1.007255509\) \(a_{45}=-0.336640397\)
\(a_{46}=+0.107547110\) \(a_{47}=-0.317394513\) \(a_{48}=+0.802914285\) \(a_{49}=+0.069982462\) \(a_{50}=-0.005399049\)
\(a_{51}=-0.868980831\) \(a_{52}=+0.329222958\) \(a_{53}=-0.153442722\) \(a_{54}=+0.092647152\) \(a_{55}=+1.046292421\)
\(a_{56}=-0.175428031\) \(a_{57}=-1.308559663\) \(a_{58}=+0.017021975\) \(a_{59}=+1.014766420\) \(a_{60}=-0.840206461\)
\(a_{61}=+0.773096721\) \(a_{62}=+0.021764451\) \(a_{63}=+0.337674390\) \(a_{64}=-0.956804494\) \(a_{65}=-0.341982231\)
\(a_{66}=-0.070866263\) \(a_{67}=+0.750278582\) \(a_{68}=+1.051154640\) \(a_{69}=-1.037120067\) \(a_{70}=+0.090782273\)
\(a_{71}=-0.381195154\) \(a_{72}=-0.055363108\) \(a_{73}=-0.020537188\) \(a_{74}=-0.033054643\) \(a_{75}=+0.052065199\)
\(a_{76}=+1.582887116\) \(a_{77}=-1.049506131\) \(a_{78}=+0.023162743\) \(a_{79}=-1.222828174\) \(a_{80}=+1.008878875\)
\(a_{81}=-0.566988936\) \(a_{82}=+0.064075177\) \(a_{83}=+0.764553230\) \(a_{84}=+0.842787172\) \(a_{85}=-1.091892895\)
\(a_{86}=-0.132877577\) \(a_{87}=-0.164149758\) \(a_{88}=+0.172070852\) \(a_{89}=-0.558839611\) \(a_{90}=+0.028649861\)
\(a_{91}=+0.343032637\) \(a_{92}=+1.254542715\) \(a_{93}=-0.209883345\) \(a_{94}=+0.027011936\) \(a_{95}=-1.644233046\)
\(a_{96}=-0.207518754\) \(a_{97}=+1.066294370\) \(a_{98}=-0.005955873\) \(a_{99}=-0.331212296\) \(a_{100}=-0.062980189\)

Showing 100 of 5000 available coefficients

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