Properties

Level $29$
Weight $0$
Character 29.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.21206072001 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.509775466\) \(a_{3}=-1.639470890\) \(a_{4}=+1.279421952\) \(a_{5}=+0.410536596\)
\(a_{6}=-2.475232918\) \(a_{7}=-0.482761470\) \(a_{8}=+0.421864400\) \(a_{9}=+1.687864783\) \(a_{10}=+0.619818082\)
\(a_{11}=+1.408798373\) \(a_{12}=-2.097575032\) \(a_{13}=-0.272051424\) \(a_{14}=-0.728861426\) \(a_{15}=-0.673062800\)
\(a_{16}=-0.642501433\) \(a_{17}=+0.244736721\) \(a_{18}=+2.548296834\) \(a_{19}=-0.313143267\) \(a_{20}=+0.525249533\)
\(a_{21}=+0.791473386\) \(a_{22}=+2.126969231\) \(a_{23}=-0.917020030\) \(a_{24}=-0.691634398\) \(a_{25}=-0.831459703\)
\(a_{26}=-0.410736567\) \(a_{27}=-1.127734285\) \(a_{28}=-0.617655588\) \(a_{29}=+0.185695298\) \(a_{30}=-1.016173692\)
\(a_{31}=+1.171555923\) \(a_{32}=-1.391897336\) \(a_{33}=-2.309683900\) \(a_{34}=+0.369497444\) \(a_{35}=-0.198191248\)
\(a_{36}=+2.159491293\) \(a_{37}=+1.702378354\) \(a_{38}=-0.472776071\) \(a_{39}=+0.446020392\) \(a_{40}=+0.173190748\)
\(a_{41}=+0.030741381\) \(a_{42}=+1.194947136\) \(a_{43}=-0.151846879\) \(a_{44}=+1.802447599\) \(a_{45}=+0.692930221\)
\(a_{46}=-1.384494384\) \(a_{47}=-0.596568232\) \(a_{48}=+1.053362401\) \(a_{49}=-0.766941337\) \(a_{50}=-1.255317523\)
\(a_{51}=-0.401238701\) \(a_{52}=-0.348068551\) \(a_{53}=+1.012938296\) \(a_{54}=-1.702625492\) \(a_{55}=+0.578363259\)
\(a_{56}=-0.203659859\) \(a_{57}=+0.513389327\) \(a_{58}=+0.280358292\) \(a_{59}=+1.199799241\) \(a_{60}=-0.861131222\)
\(a_{61}=-0.273821823\) \(a_{62}=+1.768786373\) \(a_{63}=-0.814836098\) \(a_{64}=-1.458950994\) \(a_{65}=-0.111687087\)
\(a_{66}=-3.487104131\) \(a_{67}=-0.732539071\) \(a_{68}=+0.313121502\) \(a_{69}=+1.503427658\) \(a_{70}=-0.299224258\)
\(a_{71}=+0.427304739\) \(a_{72}=+0.712050036\) \(a_{73}=-1.059390175\) \(a_{74}=+2.570209082\) \(a_{75}=+1.363153861\)
\(a_{76}=-0.400642367\) \(a_{77}=-0.680113535\) \(a_{78}=+0.673390583\) \(a_{79}=+0.038133835\) \(a_{80}=-0.263770208\)
\(a_{81}=+0.161022743\) \(a_{82}=+0.046412540\) \(a_{83}=-0.132004170\) \(a_{84}=+1.012628453\) \(a_{85}=+0.100473464\)
\(a_{86}=-0.229254763\) \(a_{87}=-0.304442136\) \(a_{88}=+0.594321933\) \(a_{89}=-1.260454788\) \(a_{90}=+1.046169038\)
\(a_{91}=+0.131335949\) \(a_{92}=-1.173255559\) \(a_{93}=-1.920731907\) \(a_{94}=-0.900683982\) \(a_{95}=-0.128556787\)
\(a_{96}=+2.281975147\) \(a_{97}=+0.888128838\) \(a_{98}=-1.157909221\) \(a_{99}=+2.377861107\) \(a_{100}=-1.063787704\)

Showing 100 of 1500 available coefficients

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