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: \( 7.95845200415 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.409485805\) \(a_{4}=+0.500000000\) \(a_{5}=-0.830310355\)
\(a_{6}=-0.996656971\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+0.986650236\) \(a_{10}=+0.587118083\)
\(a_{11}=+0.588968921\) \(a_{12}=+0.704742903\) \(a_{13}=-1.776714267\) \(a_{14}=+0.267261242\) \(a_{15}=-1.170310660\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.825263030\) \(a_{18}=-0.697667072\) \(a_{19}=-0.354560004\) \(a_{20}=-0.415155178\)
\(a_{21}=-0.532735560\) \(a_{22}=-0.416463918\) \(a_{23}=-1.344213167\) \(a_{24}=-0.498328486\) \(a_{25}=-0.310584714\)
\(a_{26}=+1.256326707\) \(a_{27}=-0.018816303\) \(a_{28}=-0.188982237\) \(a_{29}=-1.585107578\) \(a_{30}=+0.827534604\)
\(a_{31}=+0.387260406\) \(a_{32}=-0.176776695\) \(a_{33}=+0.830143334\) \(a_{34}=-0.583549085\) \(a_{35}=+0.313827816\)
\(a_{36}=+0.493325118\) \(a_{37}=-0.364229312\) \(a_{38}=+0.250711783\) \(a_{39}=-2.504253540\) \(a_{40}=+0.293559041\)
\(a_{41}=-1.541161187\) \(a_{42}=+0.376700927\) \(a_{43}=+1.372647106\) \(a_{44}=+0.294484461\) \(a_{45}=-0.819225908\)
\(a_{46}=+0.950502246\) \(a_{47}=+0.727515173\) \(a_{48}=+0.352371451\) \(a_{49}=+0.142857143\) \(a_{50}=+0.219616557\)
\(a_{51}=+1.163196526\) \(a_{52}=-0.888357134\) \(a_{53}=-1.404804238\) \(a_{54}=+0.013305136\) \(a_{55}=-0.489026994\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.499747292\) \(a_{58}=+1.120840317\) \(a_{59}=-0.206574984\) \(a_{60}=-0.585155330\)
\(a_{61}=-0.228050235\) \(a_{62}=-0.273834459\) \(a_{63}=-0.372918736\) \(a_{64}=+0.125000000\) \(a_{65}=+1.475224255\)
\(a_{66}=-0.586999981\) \(a_{67}=+1.546396312\) \(a_{68}=+0.412631515\) \(a_{69}=-1.894649379\) \(a_{70}=-0.221909777\)
\(a_{71}=-0.317314240\) \(a_{72}=-0.348833536\) \(a_{73}=+0.303859373\) \(a_{74}=+0.257549016\) \(a_{75}=-0.437764745\)
\(a_{76}=-0.177280002\) \(a_{77}=-0.222609328\) \(a_{78}=+1.770774660\) \(a_{79}=+1.550492519\) \(a_{80}=-0.207577589\)
\(a_{81}=-1.013171548\) \(a_{82}=+1.089765527\) \(a_{83}=+1.522609093\) \(a_{84}=-0.266367780\) \(a_{85}=-0.685224440\)
\(a_{86}=-0.970608077\) \(a_{87}=-2.234186631\) \(a_{88}=-0.208231959\) \(a_{89}=-0.990967717\) \(a_{90}=+0.579280195\)
\(a_{91}=+0.671534872\) \(a_{92}=-0.672106584\) \(a_{93}=+0.545838046\) \(a_{94}=-0.514430912\) \(a_{95}=+0.294394843\)
\(a_{96}=-0.249164243\) \(a_{97}=-0.270370901\) \(a_{98}=-0.101015254\) \(a_{99}=+0.581106325\) \(a_{100}=-0.155292357\)

Showing 100 of 192 available coefficients

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