Properties

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

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 6.5296082276 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.452732057\) \(a_{4}=+0.500000000\) \(a_{5}=+0.873628540\)
\(a_{6}=-1.027236689\) \(a_{7}=+0.057807842\) \(a_{8}=+0.353553391\) \(a_{9}=+1.110430429\) \(a_{10}=+0.617748665\)
\(a_{11}=+0.301511345\) \(a_{12}=-0.726366028\) \(a_{13}=-1.312122494\) \(a_{14}=+0.040876317\) \(a_{15}=-1.269148186\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.181995490\) \(a_{18}=+0.785192886\) \(a_{19}=-0.677449745\) \(a_{20}=+0.436814270\)
\(a_{21}=-0.083979305\) \(a_{22}=+0.213200716\) \(a_{23}=-1.220075039\) \(a_{24}=-0.513618344\) \(a_{25}=-0.236773173\)
\(a_{26}=-0.927810713\) \(a_{27}=-0.160425824\) \(a_{28}=+0.028903921\) \(a_{29}=-0.179995639\) \(a_{30}=-0.897423289\)
\(a_{31}=+1.336093664\) \(a_{32}=+0.176776695\) \(a_{33}=-0.438015196\) \(a_{34}=-0.835797026\) \(a_{35}=+0.050502580\)
\(a_{36}=+0.555215214\) \(a_{37}=-1.739536279\) \(a_{38}=-0.479029309\) \(a_{39}=+1.906162410\) \(a_{40}=+0.308874333\)
\(a_{41}=+0.689037143\) \(a_{42}=-0.059382336\) \(a_{43}=+0.412256885\) \(a_{44}=+0.150755672\) \(a_{45}=+0.970103715\)
\(a_{46}=-0.862723334\) \(a_{47}=-1.266102085\) \(a_{48}=-0.363183014\) \(a_{49}=-0.996658253\) \(a_{50}=-0.167423917\)
\(a_{51}=+1.717122739\) \(a_{52}=-0.656061247\) \(a_{53}=-1.468512713\) \(a_{54}=-0.113438188\) \(a_{55}=+0.263408916\)
\(a_{56}=+0.020438158\) \(a_{57}=+0.984152961\) \(a_{58}=-0.127276137\) \(a_{59}=+1.095759459\) \(a_{60}=-0.634574093\)
\(a_{61}=-0.891620500\) \(a_{62}=+0.944760890\) \(a_{63}=+0.064191586\) \(a_{64}=+0.125000000\) \(a_{65}=-1.146307659\)
\(a_{66}=-0.309723515\) \(a_{67}=+1.287498641\) \(a_{68}=-0.590997745\) \(a_{69}=+1.772442121\) \(a_{70}=+0.035710717\)
\(a_{71}=-1.321774409\) \(a_{72}=+0.392596443\) \(a_{73}=+0.962934685\) \(a_{74}=-1.230037899\) \(a_{75}=+0.343967979\)
\(a_{76}=-0.338724872\) \(a_{77}=+0.017429720\) \(a_{78}=+1.347860366\) \(a_{79}=-0.202479200\) \(a_{80}=+0.218407135\)
\(a_{81}=-0.877374692\) \(a_{82}=+0.487222836\) \(a_{83}=-0.912525429\) \(a_{84}=-0.041989652\) \(a_{85}=-1.032624995\)
\(a_{86}=+0.291509639\) \(a_{87}=+0.261485435\) \(a_{88}=+0.106600358\) \(a_{89}=+0.893253930\) \(a_{90}=+0.685966915\)
\(a_{91}=-0.075850969\) \(a_{92}=-0.610037519\) \(a_{93}=-1.940986097\) \(a_{94}=-0.895269370\) \(a_{95}=-0.591839432\)
\(a_{96}=-0.256809172\) \(a_{97}=+0.878784930\) \(a_{98}=-0.704743810\) \(a_{99}=+0.334807372\) \(a_{100}=-0.118386587\)

Showing 100 of 226 available coefficients

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