Properties

Level $439$
Weight $0$
Character 439.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 439 \)
Weight: \( 0 \)
Character: 439.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.4383034261 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.316770318\) \(a_{3}=+1.180855827\) \(a_{4}=-0.899656566\) \(a_{5}=+0.235510567\)
\(a_{6}=-0.374060074\) \(a_{7}=+0.522248719\) \(a_{8}=+0.601754813\) \(a_{9}=+0.394420483\) \(a_{10}=-0.074602757\)
\(a_{11}=+0.347628475\) \(a_{12}=-1.062364698\) \(a_{13}=+0.994943969\) \(a_{14}=-0.165432892\) \(a_{15}=+0.278104028\)
\(a_{16}=+0.709038503\) \(a_{17}=-0.557947973\) \(a_{18}=-0.124940704\) \(a_{19}=+1.182028758\) \(a_{20}=-0.211878627\)
\(a_{21}=+0.616700442\) \(a_{22}=-0.110118381\) \(a_{23}=+0.672005890\) \(a_{24}=+0.710585676\) \(a_{25}=-0.944534772\)
\(a_{26}=-0.315168718\) \(a_{27}=-0.715102101\) \(a_{28}=-0.469844481\) \(a_{29}=+1.188812298\) \(a_{30}=-0.088095103\)
\(a_{31}=+1.648887074\) \(a_{32}=-0.826357170\) \(a_{33}=+0.410499110\) \(a_{34}=+0.176741354\) \(a_{35}=+0.122995093\)
\(a_{36}=-0.354842983\) \(a_{37}=+0.917038633\) \(a_{38}=-0.374431619\) \(a_{39}=+1.174885382\) \(a_{40}=+0.141719608\)
\(a_{41}=-1.379418111\) \(a_{42}=-0.195352388\) \(a_{43}=-0.488937861\) \(a_{44}=-0.312746237\) \(a_{45}=+0.092890193\)
\(a_{46}=-0.212871514\) \(a_{47}=+0.061266062\) \(a_{48}=+0.837272236\) \(a_{49}=-0.727256283\) \(a_{50}=+0.299200592\)
\(a_{51}=-0.658856115\) \(a_{52}=-0.895107878\) \(a_{53}=-1.020303103\) \(a_{54}=+0.226523120\) \(a_{55}=+0.081870186\)
\(a_{56}=+0.314265675\) \(a_{57}=+1.395805542\) \(a_{58}=-0.376580447\) \(a_{59}=-1.051496101\) \(a_{60}=-0.250198113\)
\(a_{61}=+0.323274049\) \(a_{62}=-0.522318490\) \(a_{63}=+0.205985597\) \(a_{64}=-0.447273080\) \(a_{65}=+0.234319814\)
\(a_{66}=-0.130033941\) \(a_{67}=+1.517541122\) \(a_{68}=+0.501961565\) \(a_{69}=+0.793542073\) \(a_{70}=-0.038961188\)
\(a_{71}=-0.324896467\) \(a_{72}=+0.237344436\) \(a_{73}=+1.131325050\) \(a_{74}=-0.290490618\) \(a_{75}=-1.115359393\)
\(a_{76}=-1.063419934\) \(a_{77}=+0.181548535\) \(a_{78}=-0.372168826\) \(a_{79}=-0.392481704\) \(a_{80}=+0.166986068\)
\(a_{81}=-1.238852952\) \(a_{82}=+0.436958715\) \(a_{83}=+1.100701857\) \(a_{84}=-0.554818606\) \(a_{85}=-0.131402627\)
\(a_{86}=+0.154881009\) \(a_{87}=+1.403815904\) \(a_{88}=+0.209187091\) \(a_{89}=-0.712502807\) \(a_{90}=-0.029424849\)
\(a_{91}=+0.519608213\) \(a_{92}=-0.604574522\) \(a_{93}=+1.947097917\) \(a_{94}=-0.019407253\) \(a_{95}=+0.278380256\)
\(a_{96}=-0.975808685\) \(a_{97}=-1.811474361\) \(a_{98}=+0.230373209\) \(a_{99}=+0.137111789\) \(a_{100}=+0.849756907\)

Showing 100 of 1372 available coefficients

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