Properties

Level $58$
Weight $0$
Character 58.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 58 = 2 \cdot 29 \)
Weight: \( 0 \)
Character: 58.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.56349435606 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.045402508\) \(a_{4}=+0.500000000\) \(a_{5}=+1.283828995\)
\(a_{6}=+0.032104421\) \(a_{7}=+0.896258895\) \(a_{8}=-0.353553391\) \(a_{9}=-0.997938612\) \(a_{10}=-0.907804188\)
\(a_{11}=+0.030119280\) \(a_{12}=-0.022701254\) \(a_{13}=-0.629854580\) \(a_{14}=-0.633750743\) \(a_{15}=-0.058289056\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.381489855\) \(a_{18}=+0.705649160\) \(a_{19}=-1.438793678\) \(a_{20}=+0.641914498\)
\(a_{21}=-0.040692402\) \(a_{22}=-0.021297547\) \(a_{23}=+1.033361424\) \(a_{24}=+0.016052211\) \(a_{25}=+0.648216889\)
\(a_{26}=+0.445374445\) \(a_{27}=+0.090711424\) \(a_{28}=+0.448129448\) \(a_{29}=+0.185695338\) \(a_{30}=+0.041216587\)
\(a_{31}=-0.539990297\) \(a_{32}=-0.176776695\) \(a_{33}=-0.001367491\) \(a_{34}=+0.269754064\) \(a_{35}=+1.150643157\)
\(a_{36}=-0.498969306\) \(a_{37}=+0.714001868\) \(a_{38}=+1.017380766\) \(a_{39}=+0.028596978\) \(a_{40}=-0.453902094\)
\(a_{41}=-1.389442282\) \(a_{42}=+0.028773873\) \(a_{43}=+0.566485150\) \(a_{44}=+0.015059640\) \(a_{45}=-1.281182526\)
\(a_{46}=-0.730696870\) \(a_{47}=-0.547214170\) \(a_{48}=-0.011350627\) \(a_{49}=-0.196719993\) \(a_{50}=-0.458358558\)
\(a_{51}=+0.017320596\) \(a_{52}=-0.314927290\) \(a_{53}=+0.435389485\) \(a_{54}=-0.064142663\) \(a_{55}=+0.038668005\)
\(a_{56}=-0.316875371\) \(a_{57}=+0.065324842\) \(a_{58}=-0.131306433\) \(a_{59}=+0.479088370\) \(a_{60}=-0.029144528\)
\(a_{61}=+0.590002250\) \(a_{62}=+0.381830801\) \(a_{63}=-0.894411358\) \(a_{64}=+0.125000000\) \(a_{65}=-0.808625572\)
\(a_{66}=+0.000966962\) \(a_{67}=+1.849073909\) \(a_{68}=-0.190744928\) \(a_{69}=-0.046917200\) \(a_{70}=-0.813627579\)
\(a_{71}=-1.148619353\) \(a_{72}=+0.352824580\) \(a_{73}=+1.738704688\) \(a_{74}=-0.504875563\) \(a_{75}=-0.029430673\)
\(a_{76}=-0.719396839\) \(a_{77}=+0.026994673\) \(a_{78}=-0.020221117\) \(a_{79}=+0.220628053\) \(a_{80}=+0.320957249\)
\(a_{81}=+0.993820086\) \(a_{82}=+0.982484060\) \(a_{83}=-0.522253824\) \(a_{84}=-0.020346201\) \(a_{85}=-0.489767737\)
\(a_{86}=-0.400565491\) \(a_{87}=-0.008431034\) \(a_{88}=-0.010648774\) \(a_{89}=+1.873562894\) \(a_{90}=+0.905932852\)
\(a_{91}=-0.564512770\) \(a_{92}=+0.516680712\) \(a_{93}=+0.024516914\) \(a_{94}=+0.386938851\) \(a_{95}=-1.847165042\)
\(a_{96}=+0.008026105\) \(a_{97}=-1.240321502\) \(a_{98}=+0.139102041\) \(a_{99}=-0.030057193\) \(a_{100}=+0.324108444\)

Showing 100 of 408 available coefficients

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