Properties

Level $93$
Weight $0$
Character 93.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 93 = 3 \cdot 31 \)
Weight: \( 0 \)
Character: 93.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.55732466398 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.510369269\) \(a_{3}=-0.577350269\) \(a_{4}=+1.281215329\) \(a_{5}=-1.623446825\)
\(a_{6}=+0.872012104\) \(a_{7}=+0.158855953\) \(a_{8}=-0.424738991\) \(a_{9}=+0.333333333\) \(a_{10}=+2.452004194\)
\(a_{11}=-1.147928413\) \(a_{12}=-0.739710015\) \(a_{13}=-0.795459908\) \(a_{14}=-0.239931150\) \(a_{15}=+0.937297461\)
\(a_{16}=-0.639702609\) \(a_{17}=-1.303549145\) \(a_{18}=-0.503456423\) \(a_{19}=+0.811281775\) \(a_{20}=-2.079984958\)
\(a_{21}=-0.091715527\) \(a_{22}=+1.733795799\) \(a_{23}=+0.584558779\) \(a_{24}=+0.245223171\) \(a_{25}=+1.635579592\)
\(a_{26}=+1.201438200\) \(a_{27}=-0.192450090\) \(a_{28}=+0.203528683\) \(a_{29}=-0.122249616\) \(a_{30}=-1.415665281\)
\(a_{31}=-0.179605302\) \(a_{32}=+1.390926154\) \(a_{33}=+0.662756779\) \(a_{34}=+1.968840570\) \(a_{35}=-0.257894193\)
\(a_{36}=+0.427071776\) \(a_{37}=+0.353200019\) \(a_{38}=-1.225335061\) \(a_{39}=+0.459258992\) \(a_{40}=+0.689541167\)
\(a_{41}=-1.558123348\) \(a_{42}=+0.138524314\) \(a_{43}=+1.266530518\) \(a_{44}=-1.470743480\) \(a_{45}=-0.541148942\)
\(a_{46}=-0.882899616\) \(a_{47}=-0.601166179\) \(a_{48}=+0.369332474\) \(a_{49}=-0.974764786\) \(a_{50}=-2.470329153\)
\(a_{51}=+0.752604450\) \(a_{52}=-1.019155428\) \(a_{53}=+1.401149817\) \(a_{54}=+0.290670701\) \(a_{55}=+1.863600738\)
\(a_{56}=-0.067472317\) \(a_{57}=-0.468393751\) \(a_{58}=+0.184642064\) \(a_{59}=+1.832512122\) \(a_{60}=+1.200879875\)
\(a_{61}=-1.466063726\) \(a_{62}=+0.271270329\) \(a_{63}=+0.052951984\) \(a_{64}=-1.461109509\) \(a_{65}=+1.291386862\)
\(a_{66}=-1.001007471\) \(a_{67}=-0.187543247\) \(a_{68}=-1.670127147\) \(a_{69}=-0.337495169\) \(a_{70}=+0.389515464\)
\(a_{71}=-0.751218848\) \(a_{72}=-0.141579664\) \(a_{73}=-0.545465627\) \(a_{74}=-0.533462455\) \(a_{75}=-0.944302318\)
\(a_{76}=+1.039426646\) \(a_{77}=-0.182355263\) \(a_{78}=-0.693650668\) \(a_{79}=-1.408985167\) \(a_{80}=+1.038523170\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.353341622\) \(a_{83}=+1.758993257\) \(a_{84}=-0.117507340\) \(a_{85}=+2.116242720\)
\(a_{86}=-1.912928773\) \(a_{87}=+0.070580849\) \(a_{88}=+0.487569956\) \(a_{89}=+0.522809593\) \(a_{90}=+0.817334731\)
\(a_{91}=-0.126363542\) \(a_{92}=+0.748945669\) \(a_{93}=+0.103695169\) \(a_{94}=+0.907982923\) \(a_{95}=-1.317072821\)
\(a_{96}=-0.803051589\) \(a_{97}=+0.212889428\) \(a_{98}=+1.472254778\) \(a_{99}=-0.382642804\) \(a_{100}=+2.095529646\)

Showing 100 of 682 available coefficients

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