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: \( 5.27487748287 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.482127218\) \(a_{4}=+0.500000000\) \(a_{5}=+1.669617058\)
\(a_{6}=-1.048022206\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+1.196701090\) \(a_{10}=+1.180597544\)
\(a_{11}=+0.427011189\) \(a_{12}=-0.741063609\) \(a_{13}=+0.753162376\) \(a_{14}=+0.267261242\) \(a_{15}=-2.474584885\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.186781348\) \(a_{18}=+0.846195456\) \(a_{19}=-0.263142253\) \(a_{20}=+0.834808529\)
\(a_{21}=-0.560191433\) \(a_{22}=+0.301942507\) \(a_{23}=-0.982024522\) \(a_{24}=-0.524011103\) \(a_{25}=+1.787621121\)
\(a_{26}=+0.532566224\) \(a_{27}=-0.291536040\) \(a_{28}=+0.188982236\) \(a_{29}=-1.572167634\) \(a_{30}=-1.749795753\)
\(a_{31}=+0.869580151\) \(a_{32}=+0.176776695\) \(a_{33}=-0.632884905\) \(a_{34}=+0.839181139\) \(a_{35}=+0.631055932\)
\(a_{36}=+0.598350545\) \(a_{37}=+0.720900567\) \(a_{38}=-0.186069672\) \(a_{39}=-1.116282457\) \(a_{40}=+0.590298773\)
\(a_{41}=+0.415875407\) \(a_{42}=-0.396115161\) \(a_{43}=-0.945528065\) \(a_{44}=+0.213505596\) \(a_{45}=+1.998032553\)
\(a_{46}=-0.694396190\) \(a_{47}=-0.953477305\) \(a_{48}=-0.370531801\) \(a_{49}=+0.142857169\) \(a_{50}=+1.264038968\)
\(a_{51}=-1.758960938\) \(a_{52}=+0.376581188\) \(a_{53}=-0.748272672\) \(a_{54}=-0.206147111\) \(a_{55}=+0.712945165\)
\(a_{56}=+0.133630621\) \(a_{57}=+0.390010296\) \(a_{58}=-1.111690396\) \(a_{59}=+0.831839954\) \(a_{60}=-1.237292443\)
\(a_{61}=+0.104003071\) \(a_{62}=+0.614886020\) \(a_{63}=+0.452310498\) \(a_{64}=+0.124999999\) \(a_{65}=+1.257492752\)
\(a_{66}=-0.447517212\) \(a_{67}=-0.346690323\) \(a_{68}=+0.593390673\) \(a_{69}=+1.455485276\) \(a_{70}=+0.446223921\)
\(a_{71}=-0.003767622\) \(a_{72}=+0.423097727\) \(a_{73}=-1.638478225\) \(a_{74}=+0.509753666\) \(a_{75}=-2.649481896\)
\(a_{76}=-0.131571119\) \(a_{77}=+0.161395048\) \(a_{78}=-0.789330918\) \(a_{79}=-0.704666479\) \(a_{80}=+0.417404274\)
\(a_{81}=-0.764607639\) \(a_{82}=+0.294068345\) \(a_{83}=-1.022536172\) \(a_{84}=-0.280095717\) \(a_{85}=+1.981470382\)
\(a_{86}=-0.668589304\) \(a_{87}=+2.330152441\) \(a_{88}=+0.150971257\) \(a_{89}=+0.767878069\) \(a_{90}=+1.412822375\)
\(a_{91}=+0.284668614\) \(a_{92}=-0.491012254\) \(a_{93}=-1.288828421\) \(a_{94}=-0.674210244\) \(a_{95}=-0.439346798\)
\(a_{96}=-0.262005552\) \(a_{97}=-0.541986401\) \(a_{98}=+0.101015251\) \(a_{99}=+0.511004776\) \(a_{100}=+0.893810520\)

Showing 100 of 2000 available coefficients

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