Properties

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

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 26.5612552725 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.184402049\) \(a_{4}=+0.500000000\) \(a_{5}=-1.677939800\)
\(a_{6}=+0.837498720\) \(a_{7}=+0.497576048\) \(a_{8}=+0.353553391\) \(a_{9}=+0.402808213\) \(a_{10}=-1.186482611\)
\(a_{11}=-1.619494673\) \(a_{12}=+0.592201024\) \(a_{13}=-0.421491141\) \(a_{14}=+0.351839397\) \(a_{15}=-1.987355337\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.200766213\) \(a_{18}=+0.284828419\) \(a_{19}=-1.048454775\) \(a_{20}=-0.838969900\)
\(a_{21}=+0.589330090\) \(a_{22}=-1.145155665\) \(a_{23}=+0.446268374\) \(a_{24}=+0.418749360\) \(a_{25}=+1.815481973\)
\(a_{26}=-0.298039244\) \(a_{27}=-0.707315176\) \(a_{28}=+0.248788024\) \(a_{29}=+0.391513782\) \(a_{30}=-1.405272435\)
\(a_{31}=-1.131123856\) \(a_{32}=+0.176776695\) \(a_{33}=-1.918132808\) \(a_{34}=-0.141963150\) \(a_{35}=-0.834902654\)
\(a_{36}=+0.201404106\) \(a_{37}=-0.536269167\) \(a_{38}=-0.741369481\) \(a_{39}=-0.499214971\) \(a_{40}=-0.593241306\)
\(a_{41}=+0.641223143\) \(a_{42}=+0.416719303\) \(a_{43}=-0.006038775\) \(a_{44}=-0.809747336\) \(a_{45}=-0.675887932\)
\(a_{46}=+0.315559393\) \(a_{47}=+0.307707004\) \(a_{48}=+0.296100512\) \(a_{49}=-0.752418077\) \(a_{50}=+1.283739614\)
\(a_{51}=-0.237787914\) \(a_{52}=-0.210745571\) \(a_{53}=-1.667127486\) \(a_{54}=-0.500147357\) \(a_{55}=+2.717414568\)
\(a_{56}=+0.175919699\) \(a_{57}=-1.241791983\) \(a_{58}=+0.276842050\) \(a_{59}=+0.091023873\) \(a_{60}=-0.993677668\)
\(a_{61}=+1.086486334\) \(a_{62}=-0.799825349\) \(a_{63}=+0.200427719\) \(a_{64}=+0.125000000\) \(a_{65}=+0.707236762\)
\(a_{66}=-1.356324716\) \(a_{67}=+1.298018900\) \(a_{68}=-0.100383106\) \(a_{69}=+0.528561176\) \(a_{70}=-0.590365328\)
\(a_{71}=-1.703984344\) \(a_{72}=+0.142414209\) \(a_{73}=+0.932511958\) \(a_{74}=-0.379199564\) \(a_{75}=+2.150260568\)
\(a_{76}=-0.524227387\) \(a_{77}=-0.805821759\) \(a_{78}=-0.352998292\) \(a_{79}=+0.605379991\) \(a_{80}=-0.419484950\)
\(a_{81}=-1.240553757\) \(a_{82}=+0.453413232\) \(a_{83}=+0.524687414\) \(a_{84}=+0.294665045\) \(a_{85}=+0.336873619\)
\(a_{86}=-0.004270059\) \(a_{87}=+0.463709725\) \(a_{88}=-0.572577833\) \(a_{89}=+0.110348938\) \(a_{90}=-0.477924940\)
\(a_{91}=-0.209723896\) \(a_{92}=+0.223134187\) \(a_{93}=-1.339705413\) \(a_{94}=+0.217581709\) \(a_{95}=+1.759243995\)
\(a_{96}=+0.209374680\) \(a_{97}=+0.116987035\) \(a_{98}=-0.532039924\) \(a_{99}=-0.652345755\) \(a_{100}=+0.907740987\)

Showing 100 of 1228 available coefficients

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