Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 10.9447198479 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.632994497\) \(a_{4}=+0.500000000\) \(a_{5}=-0.863609979\)
\(a_{6}=-0.447594701\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.599317967\) \(a_{10}=-0.610664472\)
\(a_{11}=-0.116130877\) \(a_{12}=-0.316497249\) \(a_{13}=-0.643123602\) \(a_{14}=+0.267261242\) \(a_{15}=+0.546660364\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.948366675\) \(a_{18}=-0.423781798\) \(a_{19}=+0.484618479\) \(a_{20}=-0.431804989\)
\(a_{21}=-0.239249432\) \(a_{22}=-0.082116930\) \(a_{23}=-0.079517405\) \(a_{24}=-0.223797351\) \(a_{25}=-0.254177804\)
\(a_{26}=-0.454757060\) \(a_{27}=+1.012359472\) \(a_{28}=+0.188982237\) \(a_{29}=+0.482540701\) \(a_{30}=+0.386547251\)
\(a_{31}=+1.049215559\) \(a_{32}=+0.176776695\) \(a_{33}=+0.073510206\) \(a_{34}=+0.670596507\) \(a_{35}=-0.326413891\)
\(a_{36}=-0.299658983\) \(a_{37}=+1.114892116\) \(a_{38}=+0.342677013\) \(a_{39}=+0.407093701\) \(a_{40}=-0.305332236\)
\(a_{41}=+0.556091948\) \(a_{42}=-0.169174895\) \(a_{43}=+1.544547599\) \(a_{44}=-0.058065438\) \(a_{45}=+0.517576976\)
\(a_{46}=-0.056227297\) \(a_{47}=+1.938459285\) \(a_{48}=-0.158248624\) \(a_{49}=+0.142857143\) \(a_{50}=-0.179730849\)
\(a_{51}=-0.600310887\) \(a_{52}=-0.321561801\) \(a_{53}=-1.823994177\) \(a_{54}=+0.715846248\) \(a_{55}=+0.100291784\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.306760830\) \(a_{58}=+0.341207802\) \(a_{59}=+0.803835320\) \(a_{60}=+0.273330182\)
\(a_{61}=+0.126472047\) \(a_{62}=+0.741907437\) \(a_{63}=-0.226520899\) \(a_{64}=+0.125000000\) \(a_{65}=+0.555407960\)
\(a_{66}=+0.051979565\) \(a_{67}=-0.116187065\) \(a_{68}=+0.474183338\) \(a_{69}=+0.050334080\) \(a_{70}=-0.230809475\)
\(a_{71}=-0.796199700\) \(a_{72}=-0.211890899\) \(a_{73}=-1.816572363\) \(a_{74}=+0.788347775\) \(a_{75}=+0.160893151\)
\(a_{76}=+0.242309239\) \(a_{77}=-0.043893346\) \(a_{78}=+0.287858717\) \(a_{79}=-0.641650183\) \(a_{80}=-0.215902495\)
\(a_{81}=-0.041500008\) \(a_{82}=+0.393216387\) \(a_{83}=+1.300310082\) \(a_{84}=-0.119624716\) \(a_{85}=-0.819018925\)
\(a_{86}=+1.092160081\) \(a_{87}=-0.305445608\) \(a_{88}=-0.041058465\) \(a_{89}=-0.553297962\) \(a_{90}=+0.365982190\)
\(a_{91}=-0.243077873\) \(a_{92}=-0.039758703\) \(a_{93}=-0.664147676\) \(a_{94}=+1.370697705\) \(a_{95}=-0.418521353\)
\(a_{96}=-0.111898675\) \(a_{97}=+0.846217819\) \(a_{98}=+0.101015254\) \(a_{99}=+0.069599320\) \(a_{100}=-0.127088902\)

Showing 100 of 210 available coefficients

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