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: \( 37.8250722906 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.181244901\) \(a_{3}=+0.577471501\) \(a_{4}=+0.395339516\) \(a_{5}=-0.762277927\)
\(a_{6}=-0.682135265\) \(a_{7}=-1.165197083\) \(a_{8}=+0.714252114\) \(a_{9}=-0.666526666\) \(a_{10}=+0.900436914\)
\(a_{11}=+0.171078693\) \(a_{12}=+0.228297303\) \(a_{13}=+0.202233339\) \(a_{14}=+1.376383113\) \(a_{15}=-0.440193778\)
\(a_{16}=-1.239046183\) \(a_{17}=-1.892116596\) \(a_{18}=+0.787331227\) \(a_{19}=-1.305706679\) \(a_{20}=-0.301358586\)
\(a_{21}=-0.672868108\) \(a_{22}=-0.202085834\) \(a_{23}=+1.199122735\) \(a_{24}=+0.412460240\) \(a_{25}=-0.418932362\)
\(a_{26}=-0.238887101\) \(a_{27}=-0.962371655\) \(a_{28}=-0.460648451\) \(a_{29}=-0.515103931\) \(a_{30}=+0.519976656\)
\(a_{31}=+1.053915025\) \(a_{32}=+0.749364872\) \(a_{33}=+0.098793070\) \(a_{34}=+2.235053081\) \(a_{35}=+0.888204017\)
\(a_{36}=-0.263504329\) \(a_{37}=+0.443774581\) \(a_{38}=+1.542359336\) \(a_{39}=+0.116783990\) \(a_{40}=-0.544458621\)
\(a_{41}=+0.172122530\) \(a_{42}=+0.794822022\) \(a_{43}=-0.281197279\) \(a_{44}=+0.067634168\) \(a_{45}=+0.508078565\)
\(a_{46}=-1.416457617\) \(a_{47}=+1.460706163\) \(a_{48}=-0.715513859\) \(a_{49}=+0.357684243\) \(a_{50}=+0.494861717\)
\(a_{51}=-1.092643410\) \(a_{52}=+0.079950830\) \(a_{53}=+0.017324517\) \(a_{54}=+1.136796610\) \(a_{55}=-0.130409512\)
\(a_{56}=-0.832244480\) \(a_{57}=-0.754008385\) \(a_{58}=+0.608463892\) \(a_{59}=+1.045168180\) \(a_{60}=-0.174025995\)
\(a_{61}=-0.205890854\) \(a_{62}=-1.244931749\) \(a_{63}=+0.776634927\) \(a_{64}=+0.353862748\) \(a_{65}=-0.154158010\)
\(a_{66}=-0.116698809\) \(a_{67}=+0.561696385\) \(a_{68}=-0.748028459\) \(a_{69}=+0.692459205\) \(a_{70}=-1.049186466\)
\(a_{71}=+0.438341071\) \(a_{72}=-0.476068080\) \(a_{73}=+1.621215449\) \(a_{74}=-0.524206460\) \(a_{75}=-0.241921500\)
\(a_{76}=-0.516197439\) \(a_{77}=-0.199340394\) \(a_{78}=-0.137950493\) \(a_{79}=+0.477532821\) \(a_{80}=+0.944497556\)
\(a_{81}=+0.110784463\) \(a_{82}=-0.203318861\) \(a_{83}=-1.701355278\) \(a_{84}=-0.266011352\) \(a_{85}=+1.442318716\)
\(a_{86}=+0.332162852\) \(a_{87}=-0.297457840\) \(a_{88}=+0.122193318\) \(a_{89}=+0.045696074\) \(a_{90}=-0.600165214\)
\(a_{91}=-0.235641697\) \(a_{92}=+0.474060601\) \(a_{93}=+0.608605891\) \(a_{94}=-1.725451706\) \(a_{95}=+0.995311367\)
\(a_{96}=+0.432736857\) \(a_{97}=+0.474970269\) \(a_{98}=-0.422512688\) \(a_{99}=-0.114028511\) \(a_{100}=-0.165620517\)

Showing 100 of 5000 available coefficients

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