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: \( 21.0495260714 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.566043284\) \(a_{4}=+0.500000000\) \(a_{5}=-1.037805774\)
\(a_{6}=+1.107359826\) \(a_{7}=+1.072001107\) \(a_{8}=-0.353553391\) \(a_{9}=+1.452491568\) \(a_{10}=+0.733839501\)
\(a_{11}=+0.160921124\) \(a_{12}=-0.783021642\) \(a_{13}=+1.436269518\) \(a_{14}=-0.758019253\) \(a_{15}=+1.625248763\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.690315652\) \(a_{18}=-1.027066637\) \(a_{19}=-0.238324979\) \(a_{20}=-0.518902887\)
\(a_{21}=-1.678800135\) \(a_{22}=-0.113788418\) \(a_{23}=-1.210640973\) \(a_{24}=+0.553679913\) \(a_{25}=+0.077040825\)
\(a_{26}=-1.015595916\) \(a_{27}=-0.708621381\) \(a_{28}=+0.536000554\) \(a_{29}=+0.888725717\) \(a_{30}=-1.149224422\)
\(a_{31}=+0.454681768\) \(a_{32}=-0.176776695\) \(a_{33}=-0.252009445\) \(a_{34}=+0.488126878\) \(a_{35}=-1.112528940\)
\(a_{36}=+0.726245784\) \(a_{37}=+1.109122265\) \(a_{38}=+0.168521209\) \(a_{39}=-2.249260232\) \(a_{40}=+0.366919750\)
\(a_{41}=+0.013110153\) \(a_{42}=+1.187090960\) \(a_{43}=+0.233835037\) \(a_{44}=+0.080460562\) \(a_{45}=-1.507404136\)
\(a_{46}=+0.856052442\) \(a_{47}=-0.258696818\) \(a_{48}=-0.391510821\) \(a_{49}=+0.149186374\) \(a_{50}=-0.054476090\)
\(a_{51}=+1.081064190\) \(a_{52}=+0.718134759\) \(a_{53}=-1.893914525\) \(a_{54}=+0.501070984\) \(a_{55}=-0.167004871\)
\(a_{56}=-0.379009626\) \(a_{57}=+0.373227233\) \(a_{58}=-0.628423981\) \(a_{59}=+1.309956277\) \(a_{60}=+0.812624382\)
\(a_{61}=-1.720337206\) \(a_{62}=-0.321508562\) \(a_{63}=+1.557072569\) \(a_{64}=+0.125000000\) \(a_{65}=-1.490568799\)
\(a_{66}=+0.178197587\) \(a_{67}=-0.770674561\) \(a_{68}=-0.345157826\) \(a_{69}=+1.895916166\) \(a_{70}=+0.786676757\)
\(a_{71}=+0.147753697\) \(a_{72}=-0.513533319\) \(a_{73}=-0.817036060\) \(a_{74}=-0.784267875\) \(a_{75}=-0.120649267\)
\(a_{76}=-0.119162490\) \(a_{77}=+0.172507623\) \(a_{78}=+1.590467163\) \(a_{79}=-0.178112955\) \(a_{80}=-0.259451444\)
\(a_{81}=-0.342759814\) \(a_{82}=-0.009270278\) \(a_{83}=+0.720715629\) \(a_{84}=-0.839400068\) \(a_{85}=+0.716413569\)
\(a_{86}=-0.165346340\) \(a_{87}=-1.391782940\) \(a_{88}=-0.056894209\) \(a_{89}=-0.253542718\) \(a_{90}=+1.065895687\)
\(a_{91}=+1.539682513\) \(a_{92}=-0.605320487\) \(a_{93}=-0.712051329\) \(a_{94}=+0.182926275\) \(a_{95}=+0.247335040\)
\(a_{96}=+0.276839957\) \(a_{97}=-0.956031700\) \(a_{98}=-0.105490697\) \(a_{99}=+0.233736575\) \(a_{100}=+0.038520413\)

Showing 100 of 1228 available coefficients

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