Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 45.3984695313 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.002577740\) \(a_{3}=-0.987369980\) \(a_{4}=+0.005162125\) \(a_{5}=+1.332515816\)
\(a_{6}=-0.989915163\) \(a_{7}=+1.553936610\) \(a_{8}=-0.997402309\) \(a_{9}=-0.025100522\) \(a_{10}=+1.335950695\)
\(a_{11}=+0.356235891\) \(a_{12}=-0.005096927\) \(a_{13}=-0.246185894\) \(a_{14}=+1.557942254\) \(a_{15}=-1.315686115\)
\(a_{16}=-1.005135477\) \(a_{17}=-0.464444195\) \(a_{18}=-0.025165224\) \(a_{19}=-0.509407149\) \(a_{20}=+0.006878613\)
\(a_{21}=-1.534310361\) \(a_{22}=+0.357154180\) \(a_{23}=+1.328961721\) \(a_{24}=+0.984805098\) \(a_{25}=+0.775598400\)
\(a_{26}=-0.246820498\) \(a_{27}=+1.012153482\) \(a_{28}=+0.008021615\) \(a_{29}=+1.935043282\) \(a_{30}=-1.319077612\)
\(a_{31}=-0.248669548\) \(a_{32}=-0.010324146\) \(a_{33}=-0.351736624\) \(a_{34}=-0.465641412\) \(a_{35}=+2.070645110\)
\(a_{36}=-0.000129572\) \(a_{37}=+0.071097852\) \(a_{38}=-0.510720268\) \(a_{39}=+0.243076562\) \(a_{40}=-1.329054351\)
\(a_{41}=-0.265281326\) \(a_{42}=-1.538265413\) \(a_{43}=+1.166783613\) \(a_{44}=+0.001838934\) \(a_{45}=-0.033446842\)
\(a_{46}=+1.332387439\) \(a_{47}=+0.482652285\) \(a_{48}=+0.992440596\) \(a_{49}=+1.414718987\) \(a_{50}=+0.777597691\)
\(a_{51}=+0.458578256\) \(a_{52}=-0.001270842\) \(a_{53}=+1.280914590\) \(a_{54}=+1.014762551\) \(a_{55}=+0.474689958\)
\(a_{56}=-1.549899962\) \(a_{57}=+0.502973327\) \(a_{58}=+1.940031321\) \(a_{59}=-0.782719732\) \(a_{60}=-0.006791736\)
\(a_{61}=-0.025430925\) \(a_{62}=-0.249310553\) \(a_{63}=-0.039004620\) \(a_{64}=+0.994784718\) \(a_{65}=-0.328046598\)
\(a_{66}=-0.352643309\) \(a_{67}=+0.276513687\) \(a_{68}=-0.002397516\) \(a_{69}=-1.312176907\) \(a_{70}=+2.075982687\)
\(a_{71}=-0.848033527\) \(a_{72}=+0.025035318\) \(a_{73}=+0.109151121\) \(a_{74}=+0.071281124\) \(a_{75}=-0.765802577\)
\(a_{76}=-0.002629623\) \(a_{77}=+0.553567992\) \(a_{78}=+0.243703150\) \(a_{79}=+1.079806859\) \(a_{80}=-1.339358921\)
\(a_{81}=-0.974269442\) \(a_{82}=-0.265965152\) \(a_{83}=+1.862411384\) \(a_{84}=-0.007920301\) \(a_{85}=-0.618879236\)
\(a_{86}=+1.169791278\) \(a_{87}=-1.910603648\) \(a_{88}=-0.355310500\) \(a_{89}=+1.425065078\) \(a_{90}=-0.033533060\)
\(a_{91}=-0.382557274\) \(a_{92}=+0.006860266\) \(a_{93}=+0.245528846\) \(a_{94}=+0.483896438\) \(a_{95}=-0.678793083\)
\(a_{96}=+0.010193752\) \(a_{97}=-1.205664890\) \(a_{98}=+1.418365765\) \(a_{99}=-0.008941707\) \(a_{100}=+0.004003736\)

Showing 100 of 5000 available coefficients

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