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: \( 7.22087197596 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.949350722\) \(a_{4}=+0.500000000\) \(a_{5}=-0.869713048\)
\(a_{6}=+0.671292334\) \(a_{7}=-0.061359867\) \(a_{8}=-0.353553392\) \(a_{9}=-0.098733187\) \(a_{10}=+0.614979994\)
\(a_{11}=-0.074141170\) \(a_{12}=-0.474675361\) \(a_{13}=-0.086312798\) \(a_{14}=+0.043387978\) \(a_{15}=+0.825662710\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.694902860\) \(a_{18}=+0.069814919\) \(a_{19}=+1.423495172\) \(a_{20}=-0.434856524\)
\(a_{21}=+0.058252034\) \(a_{22}=+0.052425724\) \(a_{23}=-0.759012926\) \(a_{24}=+0.335646167\) \(a_{25}=-0.243599214\)
\(a_{26}=+0.061032365\) \(a_{27}=+1.043083163\) \(a_{28}=-0.030679933\) \(a_{29}=-0.587866112\) \(a_{30}=-0.583831702\)
\(a_{31}=+0.095411447\) \(a_{32}=-0.176776695\) \(a_{33}=+0.070385973\) \(a_{34}=+1.198477306\) \(a_{35}=+0.053365477\)
\(a_{36}=-0.049366603\) \(a_{37}=-0.630971288\) \(a_{38}=-1.006563089\) \(a_{39}=+0.081941117\) \(a_{40}=+0.307489997\)
\(a_{41}=+1.103805026\) \(a_{42}=-0.041190408\) \(a_{43}=-0.439796406\) \(a_{44}=-0.037070585\) \(a_{45}=+0.085869559\)
\(a_{46}=+0.536703186\) \(a_{47}=-0.700857712\) \(a_{48}=-0.237337681\) \(a_{49}=-0.996234963\) \(a_{50}=+0.172250666\)
\(a_{51}=+1.609057242\) \(a_{52}=-0.043156429\) \(a_{53}=+0.600297011\) \(a_{54}=-0.737571145\) \(a_{55}=+0.064481451\)
\(a_{56}=+0.021693989\) \(a_{57}=-1.351396170\) \(a_{58}=+0.415684114\) \(a_{59}=-0.622549366\) \(a_{60}=+0.412831355\)
\(a_{61}=+1.265486938\) \(a_{62}=-0.067466081\) \(a_{63}=+0.006058256\) \(a_{64}=+0.125000000\) \(a_{65}=+0.075067367\)
\(a_{66}=-0.049770399\) \(a_{67}=-1.041071090\) \(a_{68}=-0.847451430\) \(a_{69}=+0.720569470\) \(a_{70}=-0.037735090\)
\(a_{71}=+0.895554918\) \(a_{72}=+0.034907460\) \(a_{73}=-0.912310485\) \(a_{74}=+0.446164077\) \(a_{75}=+0.231261090\)
\(a_{76}=+0.711747586\) \(a_{77}=+0.004549292\) \(a_{78}=-0.057941120\) \(a_{79}=-0.559829767\) \(a_{80}=-0.217428261\)
\(a_{81}=-0.891518549\) \(a_{82}=-0.780508019\) \(a_{83}=+0.645593977\) \(a_{84}=+0.029126015\) \(a_{85}=+1.474079131\)
\(a_{86}=+0.310983022\) \(a_{87}=+0.558091118\) \(a_{88}=+0.026212865\) \(a_{89}=-1.298744788\) \(a_{90}=-0.060718945\)
\(a_{91}=+0.005296140\) \(a_{92}=-0.379506476\) \(a_{93}=-0.090578916\) \(a_{94}=+0.495581231\) \(a_{95}=-1.238032353\)
\(a_{96}=+0.167823095\) \(a_{97}=+0.579940112\) \(a_{98}=+0.704444501\) \(a_{99}=+0.007320195\) \(a_{100}=-0.121799607\)

Showing 100 of 5000 available coefficients

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