Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 7.33182919217 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.690425141\) \(a_{3}=+0.146033531\) \(a_{4}=+1.857537157\) \(a_{5}=+0.235973027\)
\(a_{6}=-0.246858753\) \(a_{7}=+0.377964473\) \(a_{8}=-1.449602369\) \(a_{9}=-0.978674208\) \(a_{10}=-0.398894737\)
\(a_{11}=+1.346388945\) \(a_{12}=+0.271262711\) \(a_{13}=-1.714737776\) \(a_{14}=-0.638920647\) \(a_{15}=+0.034459974\)
\(a_{16}=+0.592907131\) \(a_{17}=-0.850984768\) \(a_{18}=+1.654375485\) \(a_{19}=-0.090161873\) \(a_{20}=+0.438328665\)
\(a_{21}=+0.055195487\) \(a_{22}=-2.275969722\) \(a_{23}=+0.285993987\) \(a_{24}=-0.211690553\) \(a_{25}=-0.944316731\)
\(a_{26}=+2.898635846\) \(a_{27}=-0.288952782\) \(a_{28}=+0.702083052\) \(a_{29}=-1.128651307\) \(a_{30}=-0.058252007\)
\(a_{31}=-1.083792390\) \(a_{32}=+0.447337248\) \(a_{33}=+0.196617932\) \(a_{34}=+1.438526046\) \(a_{35}=+0.089189421\)
\(a_{36}=-1.817923705\) \(a_{37}=+0.095704089\) \(a_{38}=+0.152411897\) \(a_{39}=-0.250409213\) \(a_{40}=-0.342067058\)
\(a_{41}=+0.466456271\) \(a_{42}=-0.093303838\) \(a_{43}=-0.670822774\) \(a_{44}=+2.500967493\) \(a_{45}=-0.230940715\)
\(a_{46}=-0.483451426\) \(a_{47}=-0.236882685\) \(a_{48}=+0.086584322\) \(a_{49}=+0.142857143\) \(a_{50}=+1.596296742\)
\(a_{51}=-0.124272311\) \(a_{52}=-3.185189133\) \(a_{53}=-1.255352842\) \(a_{54}=+0.488453047\) \(a_{55}=+0.317711474\)
\(a_{56}=-0.547898195\) \(a_{57}=-0.013166657\) \(a_{58}=+1.907900545\) \(a_{59}=+1.418510264\) \(a_{60}=+0.064010683\)
\(a_{61}=-0.420964282\) \(a_{62}=+1.832069904\) \(a_{63}=-0.369904081\) \(a_{64}=-1.349097261\) \(a_{65}=-0.404631863\)
\(a_{66}=-0.332367896\) \(a_{67}=-0.025468183\) \(a_{68}=-1.580735826\) \(a_{69}=+0.041764712\) \(a_{70}=-0.150768039\)
\(a_{71}=+0.889050251\) \(a_{72}=+1.418688449\) \(a_{73}=-1.338562945\) \(a_{74}=-0.161780599\) \(a_{75}=-0.137901907\)
\(a_{76}=-0.167479029\) \(a_{77}=+0.508887188\) \(a_{78}=+0.423298029\) \(a_{79}=+0.611992188\) \(a_{80}=+0.139910090\)
\(a_{81}=+0.936477412\) \(a_{82}=-0.788509408\) \(a_{83}=-0.977651303\) \(a_{84}=+0.102527668\) \(a_{85}=-0.200809451\)
\(a_{86}=+1.133975682\) \(a_{87}=-0.164820936\) \(a_{88}=-1.951728604\) \(a_{89}=+1.332747965\) \(a_{90}=+0.390387990\)
\(a_{91}=-0.648109960\) \(a_{92}=+0.531244458\) \(a_{93}=-0.158270030\) \(a_{94}=+0.400432446\) \(a_{95}=-0.021275770\)
\(a_{96}=+0.065326238\) \(a_{97}=+0.160797637\) \(a_{98}=-0.241489306\) \(a_{99}=-1.317676134\) \(a_{100}=-1.754103415\)

Showing 100 of 1228 available coefficients

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