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: \( 6.7163141939 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.120589041\) \(a_{4}=+0.500000000\) \(a_{5}=-1.507600273\)
\(a_{6}=+0.085269329\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.985458283\) \(a_{10}=+1.066034376\)
\(a_{11}=+0.668220775\) \(a_{12}=-0.060294520\) \(a_{13}=+0.859013382\) \(a_{14}=+0.267261242\) \(a_{15}=+0.181800071\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.490008716\) \(a_{18}=+0.696824235\) \(a_{19}=-1.316526530\) \(a_{20}=-0.753800136\)
\(a_{21}=+0.045578373\) \(a_{22}=-0.472503441\) \(a_{23}=+1.292916438\) \(a_{24}=+0.042634664\) \(a_{25}=+1.272858583\)
\(a_{26}=-0.607414187\) \(a_{27}=+0.239424510\) \(a_{28}=-0.188982237\) \(a_{29}=+0.930271614\) \(a_{30}=-0.128552063\)
\(a_{31}=-0.362941629\) \(a_{32}=-0.176776695\) \(a_{33}=-0.080580102\) \(a_{34}=-1.053595267\) \(a_{35}=+0.569819343\)
\(a_{36}=-0.492729142\) \(a_{37}=-1.466055568\) \(a_{38}=+0.930924837\) \(a_{39}=-0.103587600\) \(a_{40}=+0.533017188\)
\(a_{41}=+0.678229537\) \(a_{42}=-0.032228777\) \(a_{43}=+0.649199026\) \(a_{44}=+0.334110387\) \(a_{45}=+1.485677177\)
\(a_{46}=-0.914229981\) \(a_{47}=-0.798556540\) \(a_{48}=-0.030147260\) \(a_{49}=+0.142857143\) \(a_{50}=-0.900046936\)
\(a_{51}=-0.179678722\) \(a_{52}=+0.429506691\) \(a_{53}=+0.407136057\) \(a_{54}=-0.169298695\) \(a_{55}=-1.007409823\)
\(a_{56}=+0.133630621\) \(a_{57}=+0.158758672\) \(a_{58}=-0.657801366\) \(a_{59}=-0.616898802\) \(a_{60}=+0.090900036\)
\(a_{61}=+1.227947946\) \(a_{62}=+0.256638487\) \(a_{63}=+0.372468221\) \(a_{64}=+0.125000000\) \(a_{65}=-1.295048809\)
\(a_{66}=+0.056978737\) \(a_{67}=+0.958984657\) \(a_{68}=+0.745004358\) \(a_{69}=-0.155911553\) \(a_{70}=-0.402923121\)
\(a_{71}=+0.397096760\) \(a_{72}=+0.348412117\) \(a_{73}=-1.202110500\) \(a_{74}=+1.036657834\) \(a_{75}=-0.153492796\)
\(a_{76}=-0.658263265\) \(a_{77}=-0.252563713\) \(a_{78}=+0.073247494\) \(a_{79}=+1.115560301\) \(a_{80}=-0.376900068\)
\(a_{81}=+0.956586311\) \(a_{82}=-0.479580705\) \(a_{83}=-0.019562900\) \(a_{84}=+0.022789187\) \(a_{85}=-2.246337547\)
\(a_{86}=-0.459053034\) \(a_{87}=-0.112180562\) \(a_{88}=-0.236251721\) \(a_{89}=+1.216106000\) \(a_{90}=-1.050532406\)
\(a_{91}=-0.324676540\) \(a_{92}=+0.646458219\) \(a_{93}=+0.043766783\) \(a_{94}=+0.564664744\) \(a_{95}=+1.984795756\)
\(a_{96}=+0.021317332\) \(a_{97}=-1.492936000\) \(a_{98}=-0.101015254\) \(a_{99}=-0.658503698\) \(a_{100}=+0.636429292\)

Showing 100 of 148 available coefficients

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