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: \( 25.1193355839 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.604185696\) \(a_{4}=+0.500000000\) \(a_{5}=-0.567463449\)
\(a_{6}=+1.134330584\) \(a_{7}=-1.388160128\) \(a_{8}=-0.353553391\) \(a_{9}=+1.573411747\) \(a_{10}=+0.401257253\)
\(a_{11}=+1.442947376\) \(a_{12}=-0.802092848\) \(a_{13}=+0.503840981\) \(a_{14}=+0.981577440\) \(a_{15}=+0.910316749\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.439243738\) \(a_{18}=-1.112570116\) \(a_{19}=+0.185908180\) \(a_{20}=-0.283731725\)
\(a_{21}=+2.226866621\) \(a_{22}=-1.020317875\) \(a_{23}=+0.816821391\) \(a_{24}=+0.567165292\) \(a_{25}=-0.677985234\)
\(a_{26}=-0.356269374\) \(a_{27}=-0.919858923\) \(a_{28}=-0.694080064\) \(a_{29}=-1.281860284\) \(a_{30}=-0.643691146\)
\(a_{31}=+0.236656445\) \(a_{32}=-0.176776695\) \(a_{33}=-2.314755541\) \(a_{34}=-0.310592226\) \(a_{35}=+0.787730135\)
\(a_{36}=+0.786705874\) \(a_{37}=-1.217179010\) \(a_{38}=-0.131456934\) \(a_{39}=-0.808254494\) \(a_{40}=+0.200628627\)
\(a_{41}=+1.302249077\) \(a_{42}=-1.574632489\) \(a_{43}=+0.807884963\) \(a_{44}=+0.721473688\) \(a_{45}=-0.892853658\)
\(a_{46}=-0.577579945\) \(a_{47}=+0.295307067\) \(a_{48}=-0.401046424\) \(a_{49}=+0.926988541\) \(a_{50}=+0.479407956\)
\(a_{51}=-0.704628522\) \(a_{52}=+0.251920490\) \(a_{53}=-0.725932202\) \(a_{54}=+0.650438482\) \(a_{55}=-0.818819895\)
\(a_{56}=+0.490788720\) \(a_{57}=-0.298231243\) \(a_{58}=+0.906412100\) \(a_{59}=-0.730548633\) \(a_{60}=+0.455158374\)
\(a_{61}=+0.872301666\) \(a_{62}=-0.167341377\) \(a_{63}=-2.184147453\) \(a_{64}=+0.125000000\) \(a_{65}=-0.285911341\)
\(a_{66}=+1.636779340\) \(a_{67}=+1.003557371\) \(a_{68}=+0.219621869\) \(a_{69}=-1.310333192\) \(a_{70}=-0.557009320\)
\(a_{71}=+0.463268246\) \(a_{72}=-0.556285058\) \(a_{73}=-0.642974595\) \(a_{74}=+0.860675532\) \(a_{75}=+1.087614214\)
\(a_{76}=+0.092954090\) \(a_{77}=-2.003042014\) \(a_{78}=+0.571522234\) \(a_{79}=+1.549593468\) \(a_{80}=-0.141865862\)
\(a_{81}=-0.097787220\) \(a_{82}=-0.920829153\) \(a_{83}=-1.212154004\) \(a_{84}=+1.113433311\) \(a_{85}=-0.249254767\)
\(a_{86}=-0.571260936\) \(a_{87}=+2.056341932\) \(a_{88}=-0.510158937\) \(a_{89}=-0.392524548\) \(a_{90}=+0.631342876\)
\(a_{91}=-0.699411960\) \(a_{92}=+0.408410696\) \(a_{93}=-0.379640884\) \(a_{94}=-0.208813629\) \(a_{95}=-0.105496097\)
\(a_{96}=+0.283582646\) \(a_{97}=-1.152546251\) \(a_{98}=-0.655479883\) \(a_{99}=+2.270350352\) \(a_{100}=-0.338992617\)

Showing 100 of 1228 available coefficients

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