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: \( 35.8416764326 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.497239259\) \(a_{3}=+1.533402492\) \(a_{4}=+1.241725398\) \(a_{5}=-0.828602113\)
\(a_{6}=-2.295870410\) \(a_{7}=+1.238720445\) \(a_{8}=-0.361920756\) \(a_{9}=+1.351323201\) \(a_{10}=+1.240615614\)
\(a_{11}=+0.324533876\) \(a_{12}=+1.904064819\) \(a_{13}=+0.420106725\) \(a_{14}=-1.854660881\) \(a_{15}=-1.270580545\)
\(a_{16}=-0.699843434\) \(a_{17}=-0.433745154\) \(a_{18}=-2.023254142\) \(a_{19}=+1.241574330\) \(a_{20}=-1.028896289\)
\(a_{21}=+1.899457017\) \(a_{22}=-0.485904860\) \(a_{23}=-0.832569395\) \(a_{24}=-0.554970189\) \(a_{25}=-0.313418538\)
\(a_{26}=-0.629000281\) \(a_{27}=+0.538719872\) \(a_{28}=+1.538150638\) \(a_{29}=-0.017359270\) \(a_{30}=+1.902363073\)
\(a_{31}=+0.096826797\) \(a_{32}=+1.409753820\) \(a_{33}=+0.497641054\) \(a_{34}=+0.649420272\) \(a_{35}=-1.026406378\)
\(a_{36}=+1.677972340\) \(a_{37}=+0.777857198\) \(a_{38}=-1.858933829\) \(a_{39}=+0.644192699\) \(a_{40}=+0.299888303\)
\(a_{41}=+1.645938888\) \(a_{42}=-2.843941616\) \(a_{43}=+1.377564304\) \(a_{44}=+0.402981957\) \(a_{45}=-1.119709260\)
\(a_{46}=+1.246555584\) \(a_{47}=-0.155408834\) \(a_{48}=-1.073141665\) \(a_{49}=+0.534428341\) \(a_{50}=+0.469262540\)
\(a_{51}=-0.665105899\) \(a_{52}=+0.521657190\) \(a_{53}=+0.394685431\) \(a_{54}=-0.806592542\) \(a_{55}=-0.268909456\)
\(a_{56}=-0.448318640\) \(a_{57}=+1.903833171\) \(a_{58}=+0.025990980\) \(a_{59}=-0.911955190\) \(a_{60}=-1.577712132\)
\(a_{61}=+1.413032392\) \(a_{62}=-0.144972880\) \(a_{63}=+1.673911678\) \(a_{64}=-1.410895334\) \(a_{65}=-0.348101327\)
\(a_{66}=-0.745087698\) \(a_{67}=+1.843654975\) \(a_{68}=-0.538592374\) \(a_{69}=-1.276663985\) \(a_{70}=+1.536775925\)
\(a_{71}=-0.041412487\) \(a_{72}=-0.489071914\) \(a_{73}=+0.529607717\) \(a_{74}=-1.164638335\) \(a_{75}=-0.480596767\)
\(a_{76}=+1.541694379\) \(a_{77}=+0.402006748\) \(a_{78}=-0.964510599\) \(a_{79}=+0.321973948\) \(a_{80}=+0.579891748\)
\(a_{81}=-0.525248807\) \(a_{82}=-2.464364321\) \(a_{83}=+1.314967278\) \(a_{84}=+2.358604020\) \(a_{85}=+0.359402151\)
\(a_{86}=-2.062543358\) \(a_{87}=-0.026618748\) \(a_{88}=-0.117455546\) \(a_{89}=-0.890911346\) \(a_{90}=+1.676472663\)
\(a_{91}=+0.520394789\) \(a_{92}=-1.033822563\) \(a_{93}=+0.148474451\) \(a_{94}=+0.232684208\) \(a_{95}=-1.028771113\)
\(a_{96}=+2.161720020\) \(a_{97}=-1.397117846\) \(a_{98}=-0.800167094\) \(a_{99}=+0.438550156\) \(a_{100}=-0.389179759\)

Showing 100 of 5000 available coefficients

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