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: \( 9.83018076843 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.021255324\) \(a_{4}=+0.500000000\) \(a_{5}=-0.226031805\)
\(a_{6}=+0.015029783\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.999548211\) \(a_{10}=+0.159828622\)
\(a_{11}=+0.072118321\) \(a_{12}=-0.010627662\) \(a_{13}=+0.879945705\) \(a_{14}=-0.267261242\) \(a_{15}=+0.004804379\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.397728661\) \(a_{18}=+0.706787318\) \(a_{19}=+0.694177313\) \(a_{20}=-0.113015903\)
\(a_{21}=-0.008033757\) \(a_{22}=-0.050995354\) \(a_{23}=-1.266612112\) \(a_{24}=+0.007514892\) \(a_{25}=-0.948909623\)
\(a_{26}=-0.622215575\) \(a_{27}=+0.042501044\) \(a_{28}=+0.188982237\) \(a_{29}=-0.892421178\) \(a_{30}=-0.003397209\)
\(a_{31}=+0.253768808\) \(a_{32}=-0.176776695\) \(a_{33}=-0.001532898\) \(a_{34}=-0.988343415\) \(a_{35}=-0.085431992\)
\(a_{36}=-0.499774106\) \(a_{37}=-1.197926506\) \(a_{38}=-0.490857486\) \(a_{39}=-0.018703531\) \(a_{40}=+0.079914311\)
\(a_{41}=-0.156750275\) \(a_{42}=+0.005680724\) \(a_{43}=+0.201806144\) \(a_{44}=+0.036059161\) \(a_{45}=+0.225929687\)
\(a_{46}=+0.895630013\) \(a_{47}=-1.297762041\) \(a_{48}=-0.005313831\) \(a_{49}=+0.142857143\) \(a_{50}=+0.670980429\)
\(a_{51}=-0.029709175\) \(a_{52}=+0.439972853\) \(a_{53}=-1.585781529\) \(a_{54}=-0.030052777\) \(a_{55}=-0.016301034\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.014754963\) \(a_{58}=+0.631037066\) \(a_{59}=+0.217588770\) \(a_{60}=+0.002402190\)
\(a_{61}=-0.884305386\) \(a_{62}=-0.179441645\) \(a_{63}=-0.377793713\) \(a_{64}=+0.125000000\) \(a_{65}=-0.198895716\)
\(a_{66}=+0.001083923\) \(a_{67}=+0.269475547\) \(a_{68}=+0.698864331\) \(a_{69}=+0.026922250\) \(a_{70}=+0.060409541\)
\(a_{71}=+0.426343660\) \(a_{72}=+0.353393659\) \(a_{73}=-0.933415759\) \(a_{74}=+0.847061955\) \(a_{75}=+0.020169381\)
\(a_{76}=+0.347088657\) \(a_{77}=+0.027258163\) \(a_{78}=+0.013225393\) \(a_{79}=-0.865681666\) \(a_{80}=-0.056507951\)
\(a_{81}=+0.998644838\) \(a_{82}=+0.110839182\) \(a_{83}=-1.865505036\) \(a_{84}=-0.004016879\) \(a_{85}=-0.315931133\)
\(a_{86}=-0.142698493\) \(a_{87}=+0.018968700\) \(a_{88}=-0.025497677\) \(a_{89}=-0.068830991\) \(a_{90}=-0.159756414\)
\(a_{91}=+0.332588215\) \(a_{92}=-0.633306056\) \(a_{93}=-0.005393939\) \(a_{94}=+0.917656340\) \(a_{95}=-0.156906152\)
\(a_{96}=+0.003757446\) \(a_{97}=+0.857152512\) \(a_{98}=-0.101015254\) \(a_{99}=-0.072085739\) \(a_{100}=-0.474454811\)

Showing 100 of 208 available coefficients

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