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: \( 3.92021463299 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.164711547\) \(a_{3}=+0.898554031\) \(a_{4}=+0.356552987\) \(a_{5}=+1.167494614\)
\(a_{6}=-1.046556255\) \(a_{7}=-1.794633622\) \(a_{8}=+0.749430167\) \(a_{9}=-0.192600651\) \(a_{10}=-1.359794458\)
\(a_{11}=-0.238737907\) \(a_{12}=+0.320382123\) \(a_{13}=-0.423024965\) \(a_{14}=+2.090230502\) \(a_{15}=+1.049056992\)
\(a_{16}=-1.229422957\) \(a_{17}=-1.181059960\) \(a_{18}=+0.224324206\) \(a_{19}=-1.474829947\) \(a_{20}=+0.416273693\)
\(a_{21}=-1.612575275\) \(a_{22}=+0.278060795\) \(a_{23}=+1.091717708\) \(a_{24}=+0.673403497\) \(a_{25}=+0.363043670\)
\(a_{26}=+0.492702062\) \(a_{27}=-1.071616125\) \(a_{28}=-0.639881978\) \(a_{29}=-0.185695338\) \(a_{30}=-1.221848789\)
\(a_{31}=+1.397300229\) \(a_{32}=+0.682492944\) \(a_{33}=-0.214518906\) \(a_{34}=+1.375594171\) \(a_{35}=-2.095225084\)
\(a_{36}=-0.068672341\) \(a_{37}=-0.761892700\) \(a_{38}=+1.717751474\) \(a_{39}=-0.380110787\) \(a_{40}=+0.874955684\)
\(a_{41}=-1.051873512\) \(a_{42}=+1.878185038\) \(a_{43}=+0.284698275\) \(a_{44}=-0.085122707\) \(a_{45}=-0.224860219\)
\(a_{46}=-1.271536231\) \(a_{47}=+0.415358867\) \(a_{48}=-1.104702948\) \(a_{49}=+2.220709843\) \(a_{50}=-0.422841153\)
\(a_{51}=-1.061246189\) \(a_{52}=-0.150830819\) \(a_{53}=-0.495893044\) \(a_{54}=+1.248123689\) \(a_{55}=-0.278725200\)
\(a_{56}=-1.344952564\) \(a_{57}=-1.325214413\) \(a_{58}=+0.216281484\) \(a_{59}=+0.640364288\) \(a_{60}=+0.374044333\)
\(a_{61}=+0.524539412\) \(a_{62}=-1.627451684\) \(a_{63}=+0.345647585\) \(a_{64}=+0.434515527\) \(a_{65}=-0.493879396\)
\(a_{66}=+0.249852684\) \(a_{67}=-1.123797880\) \(a_{68}=-0.421110473\) \(a_{69}=+0.980967335\) \(a_{70}=+2.440332830\)
\(a_{71}=+0.102669743\) \(a_{72}=-0.144340707\) \(a_{73}=+0.623971496\) \(a_{74}=+0.887385179\) \(a_{75}=+0.326214360\)
\(a_{76}=-0.525855075\) \(a_{77}=+0.428447109\) \(a_{78}=+0.442719430\) \(a_{79}=-0.192815796\) \(a_{80}=-1.435344680\)
\(a_{81}=-0.770304348\) \(a_{82}=+1.225129199\) \(a_{83}=+1.034810045\) \(a_{84}=-0.574968474\) \(a_{85}=-1.378881178\)
\(a_{86}=-0.331591361\) \(a_{87}=-0.166857277\) \(a_{88}=-0.178917405\) \(a_{89}=+0.319519974\) \(a_{90}=+0.261897267\)
\(a_{91}=+0.759174824\) \(a_{92}=+0.389255182\) \(a_{93}=+1.255549765\) \(a_{94}=-0.483773279\) \(a_{95}=-1.721856012\)
\(a_{96}=+0.613256792\) \(a_{97}=-0.695120404\) \(a_{98}=-2.586486360\) \(a_{99}=+0.045981119\) \(a_{100}=+0.129444282\)

Showing 100 of 1500 available coefficients

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