Properties

Level $41$
Weight $0$
Character 41.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 41 \)
Weight: \( 0 \)
Character: 41.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.86739746584 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.843917120\) \(a_{3}=-0.236289016\) \(a_{4}=-0.287803894\) \(a_{5}=+1.219604898\)
\(a_{6}=-0.199408346\) \(a_{7}=-1.174720396\) \(a_{8}=-1.086799754\) \(a_{9}=-0.944167501\) \(a_{10}=+1.029245453\)
\(a_{11}=+1.380894826\) \(a_{12}=+0.068004899\) \(a_{13}=+0.459062142\) \(a_{14}=-0.991366654\) \(a_{15}=-0.288179241\)
\(a_{16}=-0.629365024\) \(a_{17}=+0.634870212\) \(a_{18}=-0.796799118\) \(a_{19}=+0.951868736\) \(a_{20}=-0.351007039\)
\(a_{21}=+0.277573527\) \(a_{22}=+1.165360785\) \(a_{23}=-0.809600670\) \(a_{24}=+0.256798845\) \(a_{25}=+0.487436106\)
\(a_{26}=+0.387410401\) \(a_{27}=+0.459385426\) \(a_{28}=+0.338089105\) \(a_{29}=+0.003463732\) \(a_{30}=-0.243199396\)
\(a_{31}=-1.006466922\) \(a_{32}=+0.555667835\) \(a_{33}=-0.326290280\) \(a_{34}=+0.535777841\) \(a_{35}=-1.432694749\)
\(a_{36}=+0.271735083\) \(a_{37}=-0.641095799\) \(a_{38}=+0.803298323\) \(a_{39}=-0.108471342\) \(a_{40}=-1.325466302\)
\(a_{41}=+0.156173762\) \(a_{42}=+0.234249051\) \(a_{43}=+0.962135426\) \(a_{44}=-0.397426908\) \(a_{45}=-1.151511308\)
\(a_{46}=-0.683235866\) \(a_{47}=-1.104565883\) \(a_{48}=+0.148712042\) \(a_{49}=+0.379968009\) \(a_{50}=+0.411355675\)
\(a_{51}=-0.150012858\) \(a_{52}=-0.132119872\) \(a_{53}=-0.702634095\) \(a_{54}=+0.387683226\) \(a_{55}=+1.684146092\)
\(a_{56}=+1.276685837\) \(a_{57}=-0.224916127\) \(a_{58}=+0.002923103\) \(a_{59}=+1.262473353\) \(a_{60}=+0.082939108\)
\(a_{61}=-0.184448106\) \(a_{62}=-0.849374667\) \(a_{63}=+1.109132821\) \(a_{64}=+1.098302623\) \(a_{65}=+0.559874437\)
\(a_{66}=-0.275361953\) \(a_{67}=-0.459230343\) \(a_{68}=-0.182718119\) \(a_{69}=+0.191299746\) \(a_{70}=-1.209075627\)
\(a_{71}=+0.994805783\) \(a_{72}=+1.026121007\) \(a_{73}=-0.660558421\) \(a_{74}=-0.541031721\) \(a_{75}=-0.115175798\)
\(a_{76}=-0.273951529\) \(a_{77}=-1.622165317\) \(a_{78}=-0.091540823\) \(a_{79}=-0.602682048\) \(a_{80}=-0.767576666\)
\(a_{81}=+0.835619770\) \(a_{82}=+0.131797711\) \(a_{83}=-0.752439499\) \(a_{84}=-0.079886742\) \(a_{85}=+0.774290820\)
\(a_{86}=+0.811962558\) \(a_{87}=-0.000818442\) \(a_{88}=-1.500756157\) \(a_{89}=+1.334395591\) \(a_{90}=-0.971780107\)
\(a_{91}=-0.539269662\) \(a_{92}=+0.233006225\) \(a_{93}=+0.237817079\) \(a_{94}=-0.932162059\) \(a_{95}=+1.160903772\)
\(a_{96}=-0.131298206\) \(a_{97}=-0.566989591\) \(a_{98}=+0.320661508\) \(a_{99}=-1.303796017\) \(a_{100}=-0.140286010\)

Showing 100 of 546 available coefficients

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