Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.87100130387 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.915740573\) \(a_{3}=-0.577350269\) \(a_{4}=-0.161419204\) \(a_{5}=-0.934198894\)
\(a_{6}=-0.528703066\) \(a_{7}=-0.377964473\) \(a_{8}=-1.063558687\) \(a_{9}=+0.333333333\) \(a_{10}=-0.855483830\)
\(a_{11}=+0.705777329\) \(a_{12}=+0.093195421\) \(a_{13}=+0.759172761\) \(a_{14}=-0.346117403\) \(a_{15}=+0.539359983\)
\(a_{16}=-0.812524637\) \(a_{17}=-1.342277175\) \(a_{18}=+0.305246858\) \(a_{19}=-1.503696064\) \(a_{20}=+0.150797641\)
\(a_{21}=+0.218217890\) \(a_{22}=+0.646308935\) \(a_{23}=+0.263545946\) \(a_{24}=+0.614045894\) \(a_{25}=-0.127272426\)
\(a_{26}=+0.695205299\) \(a_{27}=-0.192450091\) \(a_{28}=+0.061010724\) \(a_{29}=+1.176092256\) \(a_{30}=+0.493913821\)
\(a_{31}=-1.492265711\) \(a_{32}=+0.319496908\) \(a_{33}=-0.407480733\) \(a_{34}=-1.229177663\) \(a_{35}=+0.353093999\)
\(a_{36}=-0.053806403\) \(a_{37}=+0.589031034\) \(a_{38}=-1.376995503\) \(a_{39}=-0.438308593\) \(a_{40}=+0.993575352\)
\(a_{41}=-0.601425537\) \(a_{42}=+0.199830970\) \(a_{43}=-0.189551306\) \(a_{44}=-0.113926036\) \(a_{45}=-0.311399616\)
\(a_{46}=+0.241339707\) \(a_{47}=+1.380245546\) \(a_{48}=+0.469111301\) \(a_{49}=+0.142857061\) \(a_{50}=-0.116548411\)
\(a_{51}=+0.774964195\) \(a_{52}=-0.122544748\) \(a_{53}=-1.319392895\) \(a_{54}=-0.176234348\) \(a_{55}=-0.659336412\)
\(a_{56}=+0.401987392\) \(a_{57}=+0.868159312\) \(a_{58}=+1.076995415\) \(a_{59}=+1.334127483\) \(a_{60}=-0.087063119\)
\(a_{61}=-1.602115712\) \(a_{62}=-1.366528132\) \(a_{63}=-0.125988059\) \(a_{64}=+1.105100743\) \(a_{65}=-0.709218640\)
\(a_{66}=-0.373146588\) \(a_{67}=-0.388521582\) \(a_{68}=+0.216669375\) \(a_{69}=-0.152158471\) \(a_{70}=+0.323342412\)
\(a_{71}=+0.580068961\) \(a_{72}=-0.354519448\) \(a_{73}=-1.062980137\) \(a_{74}=+0.539399563\) \(a_{75}=+0.073480669\)
\(a_{76}=+0.242725511\) \(a_{77}=-0.266758768\) \(a_{78}=-0.401377001\) \(a_{79}=+0.146303846\) \(a_{80}=+0.759059596\)
\(a_{81}=+0.111111185\) \(a_{82}=-0.550749762\) \(a_{83}=-0.796578666\) \(a_{84}=-0.035224582\) \(a_{85}=+1.253953793\)
\(a_{86}=-0.173579790\) \(a_{87}=-0.679017105\) \(a_{88}=-0.750635651\) \(a_{89}=+1.425140751\) \(a_{90}=-0.285161278\)
\(a_{91}=-0.286940358\) \(a_{92}=-0.042541382\) \(a_{93}=+0.861559958\) \(a_{94}=+1.263946996\) \(a_{95}=+1.404751174\)
\(a_{96}=-0.184461787\) \(a_{97}=-0.140692478\) \(a_{98}=+0.130820300\) \(a_{99}=+0.235259463\) \(a_{100}=+0.020544004\)

Showing 100 of 1500 available coefficients

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