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: \( 8.49946505045 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.002762662\) \(a_{4}=+0.500000000\) \(a_{5}=-0.186624017\)
\(a_{6}=-0.001953497\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.999992368\) \(a_{10}=-0.131963108\)
\(a_{11}=+0.037233914\) \(a_{12}=-0.001381331\) \(a_{13}=+0.412005216\) \(a_{14}=-0.267261242\) \(a_{15}=+0.000515579\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.942815282\) \(a_{18}=-0.707101384\) \(a_{19}=-1.529530297\) \(a_{20}=-0.093312008\)
\(a_{21}=+0.001044188\) \(a_{22}=+0.026328353\) \(a_{23}=-0.711525496\) \(a_{24}=-0.000976748\) \(a_{25}=-0.965171476\)
\(a_{26}=+0.291331682\) \(a_{27}=+0.005525302\) \(a_{28}=-0.188982237\) \(a_{29}=-0.650839984\) \(a_{30}=+0.000364569\)
\(a_{31}=-0.486592157\) \(a_{32}=+0.176776695\) \(a_{33}=-0.000102865\) \(a_{34}=-0.666671079\) \(a_{35}=+0.070537248\)
\(a_{36}=-0.499996184\) \(a_{37}=+0.579719651\) \(a_{38}=-1.081541245\) \(a_{39}=-0.001138231\) \(a_{40}=-0.065981554\)
\(a_{41}=+1.384894179\) \(a_{42}=+0.000738352\) \(a_{43}=+0.517847869\) \(a_{44}=+0.018616957\) \(a_{45}=+0.186622592\)
\(a_{46}=-0.503124503\) \(a_{47}=-0.082778879\) \(a_{48}=-0.000690665\) \(a_{49}=+0.142857143\) \(a_{50}=-0.682479296\)
\(a_{51}=+0.002604680\) \(a_{52}=+0.206002608\) \(a_{53}=-1.332568760\) \(a_{54}=+0.003906979\) \(a_{55}=-0.006948743\)
\(a_{56}=-0.133630621\) \(a_{57}=+0.004225575\) \(a_{58}=-0.460213366\) \(a_{59}=+0.964331001\) \(a_{60}=+0.000257790\)
\(a_{61}=+1.024936924\) \(a_{62}=-0.344072614\) \(a_{63}=+0.377961588\) \(a_{64}=+0.125000000\) \(a_{65}=-0.076890068\)
\(a_{66}=-0.000072736\) \(a_{67}=+1.699703653\) \(a_{68}=-0.471407641\) \(a_{69}=+0.001965704\) \(a_{70}=+0.049877366\)
\(a_{71}=-0.876966796\) \(a_{72}=-0.353550692\) \(a_{73}=-0.873965012\) \(a_{74}=+0.409923696\) \(a_{75}=+0.002666442\)
\(a_{76}=-0.764765148\) \(a_{77}=-0.014073097\) \(a_{78}=-0.000804851\) \(a_{79}=-1.482559048\) \(a_{80}=-0.046656004\)
\(a_{81}=+0.999977101\) \(a_{82}=+0.979268065\) \(a_{83}=-0.596253078\) \(a_{84}=+0.000522094\) \(a_{85}=+0.175951973\)
\(a_{86}=+0.366173740\) \(a_{87}=+0.001798052\) \(a_{88}=+0.013164177\) \(a_{89}=+1.444280150\) \(a_{90}=+0.131962101\)
\(a_{91}=-0.155723334\) \(a_{92}=-0.355762748\) \(a_{93}=+0.001344293\) \(a_{94}=-0.058533507\) \(a_{95}=+0.285447076\)
\(a_{96}=-0.000488374\) \(a_{97}=-0.966755195\) \(a_{98}=+0.101015254\) \(a_{99}=-0.037233644\) \(a_{100}=-0.482585738\)

Showing 100 of 190 available coefficients

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