Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 28.3326105901 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.975547685\) \(a_{4}=+0.500000000\) \(a_{5}=-0.531713379\)
\(a_{6}=+0.689816383\) \(a_{7}=-0.691334602\) \(a_{8}=+0.353553391\) \(a_{9}=-0.048306715\) \(a_{10}=-0.375978136\)
\(a_{11}=+0.778534998\) \(a_{12}=+0.487773842\) \(a_{13}=+1.636139521\) \(a_{14}=-0.488847385\) \(a_{15}=-0.518711755\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.302356333\) \(a_{18}=-0.034158006\) \(a_{19}=+1.216784891\) \(a_{20}=-0.265856689\)
\(a_{21}=-0.674429870\) \(a_{22}=+0.550507377\) \(a_{23}=+1.343847312\) \(a_{24}=+0.344908192\) \(a_{25}=-0.717280883\)
\(a_{26}=+1.156925350\) \(a_{27}=-1.022673189\) \(a_{28}=-0.345667301\) \(a_{29}=-0.776884634\) \(a_{30}=-0.366784600\)
\(a_{31}=-0.303142248\) \(a_{32}=+0.176776695\) \(a_{33}=+0.759498015\) \(a_{34}=+0.920904995\) \(a_{35}=+0.367591857\)
\(a_{36}=-0.024153358\) \(a_{37}=+1.308189051\) \(a_{38}=+0.860396847\) \(a_{39}=+1.596132121\) \(a_{40}=-0.187989068\)
\(a_{41}=+0.326196613\) \(a_{42}=-0.476893935\) \(a_{43}=+1.296390228\) \(a_{44}=+0.389267499\) \(a_{45}=+0.025685327\)
\(a_{46}=+0.950243547\) \(a_{47}=-0.713320073\) \(a_{48}=+0.243886921\) \(a_{49}=-0.522056468\) \(a_{50}=-0.507194176\)
\(a_{51}=+1.270510705\) \(a_{52}=+0.818069760\) \(a_{53}=-0.257873423\) \(a_{54}=-0.723139147\) \(a_{55}=-0.413957474\)
\(a_{56}=-0.244423693\) \(a_{57}=+1.187031683\) \(a_{58}=-0.549340393\) \(a_{59}=+0.099083064\) \(a_{60}=-0.259355878\)
\(a_{61}=+0.712889907\) \(a_{62}=-0.214353940\) \(a_{63}=+0.033396104\) \(a_{64}=+0.125000000\) \(a_{65}=-0.869957273\)
\(a_{66}=+0.537046197\) \(a_{67}=-1.306151778\) \(a_{68}=+0.651178167\) \(a_{69}=+1.310987133\) \(a_{70}=+0.259926695\)
\(a_{71}=-0.216544782\) \(a_{72}=-0.017079003\) \(a_{73}=-1.786131265\) \(a_{74}=+0.925029349\) \(a_{75}=-0.699741704\)
\(a_{76}=+0.608392445\) \(a_{77}=-0.538228183\) \(a_{78}=+1.128635846\) \(a_{79}=+0.621049836\) \(a_{80}=-0.132928345\)
\(a_{81}=-0.949359746\) \(a_{82}=+0.230655837\) \(a_{83}=-0.047671250\) \(a_{84}=-0.337214935\) \(a_{85}=-0.692480286\)
\(a_{86}=+0.916686321\) \(a_{87}=-0.757888005\) \(a_{88}=+0.275253688\) \(a_{89}=+1.528012147\) \(a_{90}=+0.018162269\)
\(a_{91}=-1.131119865\) \(a_{92}=+0.671923656\) \(a_{93}=-0.295729719\) \(a_{94}=-0.504393461\) \(a_{95}=-0.646980805\)
\(a_{96}=+0.172454096\) \(a_{97}=+1.091534803\) \(a_{98}=-0.369149669\) \(a_{99}=-0.037608468\) \(a_{100}=-0.358640441\)

Showing 100 of 1228 available coefficients

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