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: \( 2.94495321818 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.243560463\) \(a_{4}=+0.500000000\) \(a_{5}=-1.407191466\)
\(a_{6}=+0.879330036\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.546442624\) \(a_{10}=-0.995034628\)
\(a_{11}=+1.241451955\) \(a_{12}=+0.621780231\) \(a_{13}=-0.169215948\) \(a_{14}=-0.267261242\) \(a_{15}=-1.749927671\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.217795948\) \(a_{18}=+0.386393285\) \(a_{19}=-0.368631295\) \(a_{20}=-0.703595733\)
\(a_{21}=-0.470021675\) \(a_{22}=+0.877839096\) \(a_{23}=+1.491501692\) \(a_{24}=+0.439665018\) \(a_{25}=+0.980187822\)
\(a_{26}=-0.119653745\) \(a_{27}=-0.564026020\) \(a_{28}=-0.188982237\) \(a_{29}=-0.663473607\) \(a_{30}=-1.237385722\)
\(a_{31}=-1.604237414\) \(a_{32}=+0.176776696\) \(a_{33}=+1.543820566\) \(a_{34}=+0.154004992\) \(a_{35}=+0.531868380\)
\(a_{36}=+0.273221311\) \(a_{37}=-0.358311905\) \(a_{38}=-0.260661686\) \(a_{39}=-0.210430264\) \(a_{40}=-0.497517333\)
\(a_{41}=+0.972842582\) \(a_{42}=-0.332355508\) \(a_{43}=-0.086646015\) \(a_{44}=+0.620725977\) \(a_{45}=-0.768949398\)
\(a_{46}=+1.054650961\) \(a_{47}=-0.384570080\) \(a_{48}=+0.310890116\) \(a_{49}=+0.142857143\) \(a_{50}=+0.693097456\)
\(a_{51}=+0.270842431\) \(a_{52}=-0.084607974\) \(a_{53}=+0.396253767\) \(a_{54}=-0.398826624\) \(a_{55}=-1.746960598\)
\(a_{56}=-0.133630619\) \(a_{57}=-0.458415303\) \(a_{58}=-0.469146687\) \(a_{59}=+1.403860317\) \(a_{60}=-0.874963836\)
\(a_{61}=-0.098890657\) \(a_{62}=-1.134367149\) \(a_{63}=-0.206535910\) \(a_{64}=+0.124999940\) \(a_{65}=+0.238119193\)
\(a_{66}=+1.091646028\) \(a_{67}=+0.205036319\) \(a_{68}=+0.108898442\) \(a_{69}=+1.854771613\) \(a_{70}=+0.376087787\)
\(a_{71}=-1.340811818\) \(a_{72}=+0.193196951\) \(a_{73}=-0.222410446\) \(a_{74}=-0.253361359\) \(a_{75}=+1.218922326\)
\(a_{76}=-0.184313849\) \(a_{77}=-0.469226492\) \(a_{78}=-0.148794578\) \(a_{79}=+1.264494386\) \(a_{80}=-0.351797866\)
\(a_{81}=-1.247843076\) \(a_{82}=+0.687903570\) \(a_{83}=+0.282874883\) \(a_{84}=-0.235010830\) \(a_{85}=-0.306480657\)
\(a_{86}=-0.061267955\) \(a_{87}=-0.825069509\) \(a_{88}=+0.438919512\) \(a_{89}=-1.028061100\) \(a_{90}=-0.543729830\)
\(a_{91}=+0.063957860\) \(a_{92}=+0.745751191\) \(a_{93}=-1.994966343\) \(a_{94}=-0.271932047\) \(a_{95}=+0.518736919\)
\(a_{96}=+0.219831632\) \(a_{97}=-0.026286114\) \(a_{98}=+0.101012225\) \(a_{99}=+0.678392215\) \(a_{100}=+0.490096328\)

Showing 100 of 2000 available coefficients

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