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: \( 6.77498260248 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.682069925\) \(a_{4}=+0.500000000\) \(a_{5}=+1.673443402\)
\(a_{6}=-1.189403051\) \(a_{7}=-0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+1.829359233\) \(a_{10}=-1.183303177\)
\(a_{11}=-0.111583277\) \(a_{12}=+0.841034963\) \(a_{13}=+0.172703656\) \(a_{14}=+0.267261242\) \(a_{15}=+2.814848818\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.119904979\) \(a_{18}=-1.293552319\) \(a_{19}=+1.096565051\) \(a_{20}=+0.836721701\)
\(a_{21}=-0.635762673\) \(a_{22}=+0.078901292\) \(a_{23}=-0.207356731\) \(a_{24}=-0.594701525\) \(a_{25}=+1.800412820\)
\(a_{26}=-0.122119926\) \(a_{27}=+1.395040224\) \(a_{28}=-0.188982237\) \(a_{29}=+0.074773290\) \(a_{30}=-1.990398687\)
\(a_{31}=+0.663479403\) \(a_{32}=-0.176776696\) \(a_{33}=-0.187690875\) \(a_{34}=+0.791892406\) \(a_{35}=-0.632502153\)
\(a_{36}=+0.914679616\) \(a_{37}=-1.174517848\) \(a_{38}=-0.775388584\) \(a_{39}=+0.290499626\) \(a_{40}=-0.591651586\)
\(a_{41}=+1.203416675\) \(a_{42}=+0.449552098\) \(a_{43}=-1.747289202\) \(a_{44}=-0.055791646\) \(a_{45}=+3.061329146\)
\(a_{46}=+0.146623371\) \(a_{47}=+1.050840910\) \(a_{48}=+0.420517481\) \(a_{49}=+0.142857143\) \(a_{50}=-1.273084114\)
\(a_{51}=-1.883758485\) \(a_{52}=+0.086351830\) \(a_{53}=-1.274040161\) \(a_{54}=-0.986442402\) \(a_{55}=-0.186728299\)
\(a_{56}=+0.133630622\) \(a_{57}=+1.844499095\) \(a_{58}=-0.052872710\) \(a_{59}=-0.390667881\) \(a_{60}=+1.407424421\)
\(a_{61}=+0.239128879\) \(a_{62}=-0.469150782\) \(a_{63}=-0.691432802\) \(a_{64}=+0.124999996\) \(a_{65}=+0.289009798\)
\(a_{66}=+0.132717467\) \(a_{67}=+0.886937617\) \(a_{68}=-0.559952466\) \(a_{69}=-0.348788548\) \(a_{70}=+0.447246612\)
\(a_{71}=-0.581015053\) \(a_{72}=-0.646776099\) \(a_{73}=-1.732565237\) \(a_{74}=+0.830509533\) \(a_{75}=+3.028420256\)
\(a_{76}=+0.548282529\) \(a_{77}=+0.042174512\) \(a_{78}=-0.205414248\) \(a_{79}=-1.305476197\) \(a_{80}=+0.418360838\)
\(a_{81}=+0.517195973\) \(a_{82}=-0.850944079\) \(a_{83}=-0.101178150\) \(a_{84}=-0.317881361\) \(a_{85}=-1.874097586\)
\(a_{86}=+1.235520016\) \(a_{87}=+0.125773922\) \(a_{88}=+0.039450633\) \(a_{89}=+0.098229150\) \(a_{90}=-2.164686611\)
\(a_{91}=-0.065275829\) \(a_{92}=-0.103678231\) \(a_{93}=+1.116018744\) \(a_{94}=-0.743056714\) \(a_{95}=+1.835039566\)
\(a_{96}=-0.297350790\) \(a_{97}=-0.113939894\) \(a_{98}=-0.101015241\) \(a_{99}=-0.204125886\) \(a_{100}=+0.900206427\)

Showing 100 of 2000 available coefficients

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