Properties

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

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 16.1380731715 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.161855592\) \(a_{3}=-1.281972561\) \(a_{4}=+0.349908418\) \(a_{5}=-0.756806414\)
\(a_{6}=-1.489466989\) \(a_{7}=-0.298519117\) \(a_{8}=-0.755312541\) \(a_{9}=+0.643453648\) \(a_{10}=-0.879299764\)
\(a_{11}=+0.764090704\) \(a_{12}=-0.448572990\) \(a_{13}=+0.162602318\) \(a_{14}=-0.346836105\) \(a_{15}=+0.970205057\)
\(a_{16}=-1.227472517\) \(a_{17}=+0.416417433\) \(a_{18}=+0.747600219\) \(a_{19}=-0.755676384\) \(a_{20}=-0.264812935\)
\(a_{21}=+0.382693316\) \(a_{22}=+0.887763058\) \(a_{23}=-1.601644488\) \(a_{24}=+0.968289952\) \(a_{25}=-0.427244052\)
\(a_{26}=+0.188920412\) \(a_{27}=+0.457082641\) \(a_{28}=-0.104454352\) \(a_{29}=-1.484372131\) \(a_{30}=+1.127238171\)
\(a_{31}=+0.959375991\) \(a_{32}=-0.670833268\) \(a_{33}=-0.979543317\) \(a_{34}=+0.483816923\) \(a_{35}=+0.225921182\)
\(a_{36}=+0.225149848\) \(a_{37}=+0.400473807\) \(a_{38}=-0.877986833\) \(a_{39}=-0.208451710\) \(a_{40}=+0.571625375\)
\(a_{41}=-0.390411276\) \(a_{42}=+0.444634370\) \(a_{43}=+0.158052513\) \(a_{44}=+0.267361769\) \(a_{45}=-0.486969847\)
\(a_{46}=-1.860879605\) \(a_{47}=+1.561732882\) \(a_{48}=+1.573586086\) \(a_{49}=-0.910886337\) \(a_{50}=-0.496395891\)
\(a_{51}=-0.533835722\) \(a_{52}=+0.056895919\) \(a_{53}=+0.427814002\) \(a_{54}=+0.531064021\) \(a_{55}=-0.578268746\)
\(a_{56}=+0.225475236\) \(a_{57}=+0.968756381\) \(a_{58}=-1.724626059\) \(a_{59}=+0.224223615\) \(a_{60}=+0.339482916\)
\(a_{61}=-0.548055569\) \(a_{62}=+1.114656360\) \(a_{63}=-0.192083214\) \(a_{64}=+0.448061133\) \(a_{65}=-0.123058477\)
\(a_{66}=-1.138087881\) \(a_{67}=-0.737407248\) \(a_{68}=+0.145707965\) \(a_{69}=+2.053264286\) \(a_{70}=+0.262487789\)
\(a_{71}=-0.724996821\) \(a_{72}=-0.486008609\) \(a_{73}=-0.779493711\) \(a_{74}=+0.465292733\) \(a_{75}=+0.547715152\)
\(a_{76}=-0.264417528\) \(a_{77}=-0.228095682\) \(a_{78}=-0.242190785\) \(a_{79}=+0.968006375\) \(a_{80}=+0.928959074\)
\(a_{81}=-1.229421051\) \(a_{82}=-0.453601524\) \(a_{83}=-0.266400378\) \(a_{84}=+0.133907613\) \(a_{85}=-0.315147384\)
\(a_{86}=+0.183634196\) \(a_{87}=+1.902924343\) \(a_{88}=-0.577127291\) \(a_{89}=-0.194150327\) \(a_{90}=-0.565788640\)
\(a_{91}=-0.048539900\) \(a_{92}=-0.560428889\) \(a_{93}=-1.229893697\) \(a_{94}=+1.814508083\) \(a_{95}=+0.571900737\)
\(a_{96}=+0.859989844\) \(a_{97}=-0.905148258\) \(a_{98}=-1.058318379\) \(a_{99}=+0.491656959\) \(a_{100}=-0.149496305\)

Showing 100 of 6000 available coefficients

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