Properties

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

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 7.96478111463 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.206738088\) \(a_{4}=+0.500000000\) \(a_{5}=+0.568558674\)
\(a_{6}=-0.853292685\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.456216812\) \(a_{10}=+0.402031694\)
\(a_{11}=-0.339663243\) \(a_{12}=-0.603369044\) \(a_{13}=-0.468778138\) \(a_{14}=+0.267261242\) \(a_{15}=-0.686101408\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.630413192\) \(a_{18}=+0.322594002\) \(a_{19}=-0.672994243\) \(a_{20}=+0.284279337\)
\(a_{21}=-0.456104125\) \(a_{22}=-0.240178182\) \(a_{23}=-1.340758784\) \(a_{24}=-0.426646342\) \(a_{25}=-0.676741034\)
\(a_{26}=-0.331476200\) \(a_{27}=+0.656203884\) \(a_{28}=+0.188982237\) \(a_{29}=+0.933251791\) \(a_{30}=-0.485146958\)
\(a_{31}=-0.495283656\) \(a_{32}=+0.176776695\) \(a_{33}=+0.409884572\) \(a_{34}=-1.152876224\) \(a_{35}=+0.214894980\)
\(a_{36}=+0.228108406\) \(a_{37}=+0.048657295\) \(a_{38}=-0.475878793\) \(a_{39}=+0.565692434\) \(a_{40}=+0.201015847\)
\(a_{41}=-1.929140771\) \(a_{42}=-0.322514320\) \(a_{43}=+1.449957237\) \(a_{44}=-0.169831621\) \(a_{45}=+0.259386026\)
\(a_{46}=-0.948059628\) \(a_{47}=+0.793371212\) \(a_{48}=-0.301684522\) \(a_{49}=+0.142857143\) \(a_{50}=-0.478528174\)
\(a_{51}=+1.967481697\) \(a_{52}=-0.234389069\) \(a_{53}=-0.547486694\) \(a_{54}=+0.464006216\) \(a_{55}=-0.193118483\)
\(a_{56}=+0.133630621\) \(a_{57}=+0.812127786\) \(a_{58}=+0.659908670\) \(a_{59}=-1.322606743\) \(a_{60}=-0.343050704\)
\(a_{61}=-1.738516858\) \(a_{62}=-0.350218431\) \(a_{63}=+0.172433747\) \(a_{64}=+0.125000000\) \(a_{65}=-0.266527877\)
\(a_{66}=+0.289832160\) \(a_{67}=-1.031581709\) \(a_{68}=-0.815206596\) \(a_{69}=+1.617944691\) \(a_{70}=+0.151953697\)
\(a_{71}=+1.836556691\) \(a_{72}=+0.161297001\) \(a_{73}=+0.247653658\) \(a_{74}=+0.034405903\) \(a_{75}=+0.816649181\)
\(a_{76}=-0.336497121\) \(a_{77}=-0.128380639\) \(a_{78}=+0.400004956\) \(a_{79}=+0.431733790\) \(a_{80}=+0.142139669\)
\(a_{81}=-1.248083032\) \(a_{82}=-1.364108521\) \(a_{83}=-0.212464050\) \(a_{84}=-0.228052063\) \(a_{85}=-0.926985563\)
\(a_{86}=+1.025274595\) \(a_{87}=-1.126190482\) \(a_{88}=-0.120089091\) \(a_{89}=+1.738141340\) \(a_{90}=+0.183413618\)
\(a_{91}=-0.177181482\) \(a_{92}=-0.670379392\) \(a_{93}=+0.597677651\) \(a_{94}=+0.560998164\) \(a_{95}=-0.382636715\)
\(a_{96}=-0.213323171\) \(a_{97}=-0.439681100\) \(a_{98}=+0.101015254\) \(a_{99}=-0.154960082\) \(a_{100}=-0.338370517\)

Showing 100 of 178 available coefficients

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