Properties

Level $51$
Weight $0$
Character 51.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 2.50163374451 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.022263453\) \(a_{3}=-0.577350269\) \(a_{4}=-0.999504339\) \(a_{5}=+1.090768842\)
\(a_{6}=-0.012853810\) \(a_{7}=-0.583821790\) \(a_{8}=-0.044515870\) \(a_{9}=+0.333333333\) \(a_{10}=+0.024284280\)
\(a_{11}=-1.559434354\) \(a_{12}=+0.577064099\) \(a_{13}=-0.509057415\) \(a_{14}=-0.012997889\) \(a_{15}=-0.629755684\)
\(a_{16}=+0.998513262\) \(a_{17}=+0.242535625\) \(a_{18}=+0.007421151\) \(a_{19}=-0.619745436\) \(a_{20}=-1.090228190\)
\(a_{21}=+0.337069667\) \(a_{22}=-0.034718393\) \(a_{23}=-1.424800609\) \(a_{24}=+0.025701250\) \(a_{25}=+0.189776666\)
\(a_{26}=-0.011333376\) \(a_{27}=-0.192450090\) \(a_{28}=+0.583532412\) \(a_{29}=+0.892972462\) \(a_{30}=-0.014020536\)
\(a_{31}=+1.425016016\) \(a_{32}=+0.066746223\) \(a_{33}=+0.900339844\) \(a_{34}=+0.005399680\) \(a_{35}=-0.636814617\)
\(a_{36}=-0.333168113\) \(a_{37}=-0.343611061\) \(a_{38}=-0.013797673\) \(a_{39}=+0.293904435\) \(a_{40}=-0.048556524\)
\(a_{41}=-0.861250329\) \(a_{42}=+0.007504335\) \(a_{43}=+0.284479996\) \(a_{44}=+1.558661402\) \(a_{45}=+0.363589614\)
\(a_{46}=-0.031720981\) \(a_{47}=-1.481480052\) \(a_{48}=-0.576491900\) \(a_{49}=-0.659152118\) \(a_{50}=+0.004225084\)
\(a_{51}=-0.140028008\) \(a_{52}=+0.508805095\) \(a_{53}=+1.035102796\) \(a_{54}=-0.004284603\) \(a_{55}=-1.700982404\)
\(a_{56}=+0.025989335\) \(a_{57}=+0.357810194\) \(a_{58}=+0.019880650\) \(a_{59}=-0.029129451\) \(a_{60}=+0.629443539\)
\(a_{61}=-1.869174044\) \(a_{62}=+0.031725777\) \(a_{63}=-0.194607263\) \(a_{64}=-0.997027260\) \(a_{65}=-0.555263967\)
\(a_{66}=+0.020044673\) \(a_{67}=+1.147022555\) \(a_{68}=-0.242415410\) \(a_{69}=+0.822609015\) \(a_{70}=-0.014177692\)
\(a_{71}=-0.609585425\) \(a_{72}=-0.014838623\) \(a_{73}=+1.319040230\) \(a_{74}=-0.007649969\) \(a_{75}=-0.109567609\)
\(a_{76}=+0.619438252\) \(a_{77}=+0.910431755\) \(a_{78}=+0.006543327\) \(a_{79}=+0.800192841\) \(a_{80}=+1.089147154\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.019174406\) \(a_{83}=-0.951548433\) \(a_{84}=-0.336902595\) \(a_{85}=+0.264550303\)
\(a_{86}=+0.006333507\) \(a_{87}=-0.515557892\) \(a_{88}=+0.069419577\) \(a_{89}=-0.425567388\) \(a_{90}=+0.008094760\)
\(a_{91}=+0.297198811\) \(a_{92}=+1.424094391\) \(a_{93}=-0.822733380\) \(a_{94}=-0.032982861\) \(a_{95}=-0.675999011\)
\(a_{96}=-0.038535950\) \(a_{97}=+0.685310413\) \(a_{98}=-0.014675002\) \(a_{99}=-0.519811451\) \(a_{100}=-0.189682601\)

Showing 100 of 456 available coefficients

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