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: \( 23.2637115379 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.447094173\) \(a_{3}=-1.536666654\) \(a_{4}=+1.094081547\) \(a_{5}=+0.106965525\)
\(a_{6}=+2.223701362\) \(a_{7}=+0.619998838\) \(a_{8}=-0.136144858\) \(a_{9}=+1.361344407\) \(a_{10}=-0.154789188\)
\(a_{11}=-0.329116931\) \(a_{12}=-1.681238630\) \(a_{13}=-0.641450303\) \(a_{14}=-0.897196708\) \(a_{15}=-0.164370356\)
\(a_{16}=-0.897067116\) \(a_{17}=+1.381730459\) \(a_{18}=-1.969993559\) \(a_{19}=+1.259881379\) \(a_{20}=+0.117029007\)
\(a_{21}=-0.952731539\) \(a_{22}=+0.476263193\) \(a_{23}=+0.183350565\) \(a_{24}=+0.209209264\) \(a_{25}=-0.988558376\)
\(a_{26}=+0.928238996\) \(a_{27}=-0.555265901\) \(a_{28}=+0.678329287\) \(a_{29}=-0.564950862\) \(a_{30}=+0.237859384\)
\(a_{31}=-0.973055413\) \(a_{32}=+1.434285455\) \(a_{33}=+0.505743013\) \(a_{34}=-1.999494096\) \(a_{35}=+0.066318501\)
\(a_{36}=+1.489421794\) \(a_{37}=+0.339380917\) \(a_{38}=-1.823167002\) \(a_{39}=+0.985695291\) \(a_{40}=-0.014562806\)
\(a_{41}=-0.866111825\) \(a_{42}=+1.378692260\) \(a_{43}=-0.360708915\) \(a_{44}=-0.360080760\) \(a_{45}=+0.145616920\)
\(a_{46}=-0.265325535\) \(a_{47}=-0.562113453\) \(a_{48}=+1.378493123\) \(a_{49}=-0.615601441\) \(a_{50}=+1.430537067\)
\(a_{51}=-2.123259121\) \(a_{52}=-0.701798940\) \(a_{53}=+1.345819988\) \(a_{54}=+0.803522050\) \(a_{55}=-0.035204167\)
\(a_{56}=-0.084409653\) \(a_{57}=-1.936017701\) \(a_{58}=+0.817537096\) \(a_{59}=+1.119179866\) \(a_{60}=-0.179834569\)
\(a_{61}=-1.559361199\) \(a_{62}=+1.408102809\) \(a_{63}=+0.844031950\) \(a_{64}=-1.178479009\) \(a_{65}=-0.068613069\)
\(a_{66}=-0.731857767\) \(a_{67}=+0.012857103\) \(a_{68}=+1.511725798\) \(a_{69}=-0.281748700\) \(a_{70}=-0.095969117\)
\(a_{71}=+0.267018223\) \(a_{72}=-0.185340041\) \(a_{73}=-1.454215153\) \(a_{74}=-0.491116148\) \(a_{75}=+1.519084693\)
\(a_{76}=+1.378412968\) \(a_{77}=-0.204052114\) \(a_{78}=-1.426393913\) \(a_{79}=+0.060533389\) \(a_{80}=-0.095955255\)
\(a_{81}=-0.508085813\) \(a_{82}=+1.253345375\) \(a_{83}=+0.091229955\) \(a_{84}=-1.042365997\) \(a_{85}=+0.147797524\)
\(a_{86}=+0.521979770\) \(a_{87}=+0.868141151\) \(a_{88}=+0.044807578\) \(a_{89}=-1.572097524\) \(a_{90}=-0.210721396\)
\(a_{91}=-0.397698442\) \(a_{92}=+0.200600470\) \(a_{93}=+1.495261807\) \(a_{94}=+0.813431103\) \(a_{95}=+0.134763873\)
\(a_{96}=-2.204018630\) \(a_{97}=+0.048943530\) \(a_{98}=+0.890833257\) \(a_{99}=-0.448041491\) \(a_{100}=-1.081563479\)

Showing 100 of 5000 available coefficients

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