Properties

Level $22$
Weight $0$
Character 22.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 5.39459707358 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.515289347\) \(a_{4}=+0.500000000\) \(a_{5}=-1.903101661\)
\(a_{6}=-0.364364592\) \(a_{7}=+0.829579339\) \(a_{8}=-0.353553391\) \(a_{9}=-0.734476889\) \(a_{10}=+1.345696090\)
\(a_{11}=+0.301511345\) \(a_{12}=+0.257644674\) \(a_{13}=+1.589261697\) \(a_{14}=-0.586601176\) \(a_{15}=-0.980648012\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.409373928\) \(a_{18}=+0.519353589\) \(a_{19}=+1.452575567\) \(a_{20}=-0.951550831\)
\(a_{21}=+0.427473396\) \(a_{22}=-0.213200716\) \(a_{23}=-0.358749331\) \(a_{24}=-0.182182296\) \(a_{25}=+2.621795933\)
\(a_{26}=-1.123777723\) \(a_{27}=-0.893757463\) \(a_{28}=+0.414789669\) \(a_{29}=+0.503567746\) \(a_{30}=+0.693422859\)
\(a_{31}=+0.202833232\) \(a_{32}=-0.176776695\) \(a_{33}=+0.155365584\) \(a_{34}=-0.289471080\) \(a_{35}=-1.578773818\)
\(a_{36}=-0.367238444\) \(a_{37}=-0.559775628\) \(a_{38}=-1.027126033\) \(a_{39}=+0.818929622\) \(a_{40}=+0.672848045\)
\(a_{41}=+1.452800643\) \(a_{42}=-0.302269337\) \(a_{43}=-1.058699529\) \(a_{44}=+0.150755672\) \(a_{45}=+1.397784187\)
\(a_{46}=+0.253674084\) \(a_{47}=+0.926525182\) \(a_{48}=+0.128822337\) \(a_{49}=-0.311798120\) \(a_{50}=-1.853889683\)
\(a_{51}=+0.210946024\) \(a_{52}=+0.794630848\) \(a_{53}=+0.122616029\) \(a_{54}=+0.631981963\) \(a_{55}=-0.573806741\)
\(a_{56}=-0.293300588\) \(a_{57}=+0.748496715\) \(a_{58}=-0.356076168\) \(a_{59}=+0.171788204\) \(a_{60}=-0.490324006\)
\(a_{61}=+0.294121203\) \(a_{62}=-0.143424754\) \(a_{63}=-0.609306852\) \(a_{64}=+0.125000000\) \(a_{65}=-3.024526575\)
\(a_{66}=-0.109860058\) \(a_{67}=+0.230939972\) \(a_{68}=+0.204686964\) \(a_{69}=-0.184859708\) \(a_{70}=+1.116361673\)
\(a_{71}=-0.462940746\) \(a_{72}=+0.259676794\) \(a_{73}=+0.900620962\) \(a_{74}=+0.395821143\) \(a_{75}=+1.350983514\)
\(a_{76}=+0.726287783\) \(a_{77}=+0.250127582\) \(a_{78}=-0.579070689\) \(a_{79}=+0.201680678\) \(a_{80}=-0.475775415\)
\(a_{81}=+0.273933189\) \(a_{82}=-1.027285187\) \(a_{83}=+0.472339979\) \(a_{84}=+0.213736698\) \(a_{85}=-0.779080202\)
\(a_{86}=+0.748613616\) \(a_{87}=+0.259483095\) \(a_{88}=-0.106600358\) \(a_{89}=+0.819007038\) \(a_{90}=-0.988382677\)
\(a_{91}=+1.318418668\) \(a_{92}=-0.179374665\) \(a_{93}=+0.104517804\) \(a_{94}=-0.655152239\) \(a_{95}=-2.764398974\)
\(a_{96}=-0.091091148\) \(a_{97}=-0.774550074\) \(a_{98}=+0.220474565\) \(a_{99}=-0.221453114\) \(a_{100}=+1.310897966\)

Showing 100 of 280 available coefficients

Rows: Cols: