Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 43.2671820388 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.439681699\) \(a_{3}=+0.476956413\) \(a_{4}=+1.072683394\) \(a_{5}=-0.080803978\)
\(a_{6}=-0.686665420\) \(a_{7}=-1.321960303\) \(a_{8}=-0.104640952\) \(a_{9}=-0.772512580\) \(a_{10}=+0.116332009\)
\(a_{11}=+1.331967459\) \(a_{12}=+0.511623224\) \(a_{13}=-0.808836451\) \(a_{14}=+1.903202055\) \(a_{15}=-0.038539976\)
\(a_{16}=-0.922033730\) \(a_{17}=+0.834255069\) \(a_{18}=+1.112172223\) \(a_{19}=-0.012706860\) \(a_{20}=-0.086677084\)
\(a_{21}=-0.630517462\) \(a_{22}=-1.917609174\) \(a_{23}=-1.821881568\) \(a_{24}=-0.049909173\) \(a_{25}=-0.993470717\)
\(a_{26}=+1.164467037\) \(a_{27}=-0.845411243\) \(a_{28}=-1.418044865\) \(a_{29}=+0.511832151\) \(a_{30}=+0.055485298\)
\(a_{31}=-0.237007819\) \(a_{32}=+1.432076039\) \(a_{33}=+0.635290422\) \(a_{34}=-1.201061755\) \(a_{35}=+0.106819652\)
\(a_{36}=-0.828661416\) \(a_{37}=-0.925032107\) \(a_{38}=+0.018293833\) \(a_{39}=-0.385779733\) \(a_{40}=+0.008455405\)
\(a_{41}=+1.371828129\) \(a_{42}=+0.907744426\) \(a_{43}=+0.213777669\) \(a_{44}=+1.428779375\) \(a_{45}=+0.062422090\)
\(a_{46}=+2.622929552\) \(a_{47}=-0.160279124\) \(a_{48}=-0.439769901\) \(a_{49}=+0.747579043\) \(a_{50}=+1.430281610\)
\(a_{51}=+0.397903305\) \(a_{52}=-0.867625430\) \(a_{53}=-0.294864090\) \(a_{54}=+1.217123094\) \(a_{55}=-0.107628270\)
\(a_{56}=+0.138331185\) \(a_{57}=-0.006060618\) \(a_{58}=-0.736875381\) \(a_{59}=+0.810032875\) \(a_{60}=-0.041341192\)
\(a_{61}=-0.553434565\) \(a_{62}=+0.341215819\) \(a_{63}=+1.021230964\) \(a_{64}=-1.139699936\) \(a_{65}=+0.065357204\)
\(a_{66}=-0.914615998\) \(a_{67}=+1.200006738\) \(a_{68}=+0.894891569\) \(a_{69}=-0.868958106\) \(a_{70}=-0.153786298\)
\(a_{71}=-0.636305723\) \(a_{72}=+0.080836452\) \(a_{73}=+0.201337437\) \(a_{74}=+1.331751796\) \(a_{75}=-0.473842230\)
\(a_{76}=-0.013630437\) \(a_{77}=-1.760808106\) \(a_{78}=+0.555400021\) \(a_{79}=+1.054035988\) \(a_{80}=+0.074503994\)
\(a_{81}=+0.369288266\) \(a_{82}=-1.974995851\) \(a_{83}=+1.853511745\) \(a_{84}=-0.676345593\) \(a_{85}=-0.067411129\)
\(a_{86}=-0.307771797\) \(a_{87}=+0.244121627\) \(a_{88}=-0.139378344\) \(a_{89}=+0.592554397\) \(a_{90}=-0.089867940\)
\(a_{91}=+1.069249680\) \(a_{92}=-1.954302105\) \(a_{93}=-0.113042399\) \(a_{94}=+0.230750922\) \(a_{95}=+0.001026765\)
\(a_{96}=+0.683037851\) \(a_{97}=+1.601140951\) \(a_{98}=-1.076275866\) \(a_{99}=-1.028961618\) \(a_{100}=-1.065679541\)

Showing 100 of 5000 available coefficients

Rows: Cols: