Properties

Level $28$
Weight $0$
Character 28.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 28 = 2^{2} \cdot 7 \)
Weight: \( 0 \)
Character: 28.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 8.64784692286 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.375415108\) \(a_{4}=+0.000000000\) \(a_{5}=-1.174891869\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.377964473\) \(a_{8}=+0.000000000\) \(a_{9}=+0.891766718\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.648148747\) \(a_{12}=+0.000000000\) \(a_{13}=-0.690045952\) \(a_{14}=+0.000000000\) \(a_{15}=-1.615964027\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.170896672\) \(a_{18}=+0.000000000\) \(a_{19}=-0.467311403\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.519858046\) \(a_{22}=+0.000000000\) \(a_{23}=+1.397280841\) \(a_{24}=+0.000000000\) \(a_{25}=+0.380370905\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.148865691\) \(a_{28}=+0.000000000\) \(a_{29}=-1.317597442\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.020816613\) \(a_{32}=+0.000000000\) \(a_{33}=+0.891473579\) \(a_{34}=+0.000000000\) \(a_{35}=-0.444067386\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.852411098\) \(a_{38}=+0.000000000\) \(a_{39}=-0.949099627\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.222981663\) \(a_{42}=+0.000000000\) \(a_{43}=-0.150515056\) \(a_{44}=+0.000000000\) \(a_{45}=-1.047729467\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.403525610\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.000000000\)
\(a_{51}=-1.610468972\) \(a_{52}=+0.000000000\) \(a_{53}=+1.724457165\) \(a_{54}=+0.000000000\) \(a_{55}=-0.761504694\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.642747163\) \(a_{58}=+0.000000000\) \(a_{59}=-1.419580858\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.375114440\) \(a_{62}=+0.000000000\) \(a_{63}=+0.337056138\) \(a_{64}=+0.000000000\) \(a_{65}=+0.810729378\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.074252564\) \(a_{68}=+0.000000000\) \(a_{69}=+1.921841178\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.093893047\) \(a_{72}=+0.000000000\) \(a_{73}=-1.282940652\) \(a_{74}=+0.000000000\) \(a_{75}=+0.523167889\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.244977200\) \(a_{78}=+0.000000000\) \(a_{79}=-1.007893870\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.096518838\) \(a_{82}=+0.000000000\) \(a_{83}=-1.426181240\) \(a_{84}=+0.000000000\) \(a_{85}=+1.375676980\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.812243427\) \(a_{88}=+0.000000000\) \(a_{89}=+1.538377719\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.260812854\) \(a_{92}=+0.000000000\) \(a_{93}=-1.404046592\) \(a_{94}=+0.000000000\) \(a_{95}=+0.549040368\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.321165705\) \(a_{98}=+0.000000000\) \(a_{99}=+0.577997482\) \(a_{100}=+0.000000000\)

Showing 100 of 372 available coefficients

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