Properties

Level $22$
Weight $0$
Character 22.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.72969651767 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.252211233\) \(a_{4}=+0.500000000\) \(a_{5}=+0.306452760\)
\(a_{6}=+0.178340273\) \(a_{7}=+1.575696052\) \(a_{8}=-0.353553391\) \(a_{9}=-0.936389494\) \(a_{10}=-0.216694825\)
\(a_{11}=-0.301511344\) \(a_{12}=-0.126105616\) \(a_{13}=+0.463857834\) \(a_{14}=-1.114185363\) \(a_{15}=-0.077290828\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.759808407\) \(a_{18}=+0.662127361\) \(a_{19}=+1.620847320\) \(a_{20}=+0.153226380\)
\(a_{21}=-0.397408244\) \(a_{22}=+0.213200717\) \(a_{23}=+0.419091803\) \(a_{24}=+0.089170137\) \(a_{25}=-0.906086707\)
\(a_{26}=-0.327997022\) \(a_{27}=+0.488379181\) \(a_{28}=+0.787848029\) \(a_{29}=-0.170498391\) \(a_{30}=+0.054652867\)
\(a_{31}=-1.805317242\) \(a_{32}=-0.176776697\) \(a_{33}=+0.076044554\) \(a_{34}=+0.537265686\) \(a_{35}=+0.482876404\)
\(a_{36}=-0.468194767\) \(a_{37}=+0.717715727\) \(a_{38}=-1.146112108\) \(a_{39}=-0.116990125\) \(a_{40}=-0.108347420\)
\(a_{41}=+0.173491064\) \(a_{42}=+0.281010028\) \(a_{43}=-0.403871175\) \(a_{44}=-0.150755678\) \(a_{45}=-0.286959147\)
\(a_{46}=-0.296342666\) \(a_{47}=+0.556380944\) \(a_{48}=-0.063052806\) \(a_{49}=+1.482818091\) \(a_{50}=+0.640700044\)
\(a_{51}=+0.191632213\) \(a_{52}=+0.231928956\) \(a_{53}=+0.899849554\) \(a_{54}=-0.345336945\) \(a_{55}=-0.092398405\)
\(a_{56}=-0.557091292\) \(a_{57}=-0.408795835\) \(a_{58}=+0.120560629\) \(a_{59}=+0.558027386\) \(a_{60}=-0.038645304\)
\(a_{61}=-1.445073968\) \(a_{62}=+1.276551382\) \(a_{63}=-1.475465021\) \(a_{64}=+0.124999497\) \(a_{65}=+0.142150865\)
\(a_{66}=-0.053771910\) \(a_{67}=-0.856981905\) \(a_{68}=-0.379903293\) \(a_{69}=-0.105702837\) \(a_{70}=-0.341444690\)
\(a_{71}=-0.973058033\) \(a_{72}=+0.331061681\) \(a_{73}=+0.291321378\) \(a_{74}=-0.507500470\) \(a_{75}=+0.228523299\)
\(a_{76}=+0.810423953\) \(a_{77}=-0.475089001\) \(a_{78}=+0.082730823\) \(a_{79}=+1.249037210\) \(a_{80}=+0.076613131\)
\(a_{81}=+0.813214766\) \(a_{82}=-0.122676762\) \(a_{83}=+0.690833867\) \(a_{84}=-0.198704123\) \(a_{85}=-0.232845332\)
\(a_{86}=+0.285580076\) \(a_{87}=+0.043001707\) \(a_{88}=+0.106600205\) \(a_{89}=-0.212163119\) \(a_{90}=+0.202910711\)
\(a_{91}=+0.730898956\) \(a_{92}=+0.209546372\) \(a_{93}=+0.455321113\) \(a_{94}=-0.393421131\) \(a_{95}=+0.496713126\)
\(a_{96}=+0.044585145\) \(a_{97}=-0.304029827\) \(a_{98}=-1.048510738\) \(a_{99}=+0.282332052\) \(a_{100}=-0.453043497\)

Showing 100 of 1500 available coefficients

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