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: \( 3.71654847808 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.750810334\) \(a_{4}=+0.500000000\) \(a_{5}=+0.593034073\)
\(a_{6}=-1.238009860\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=+2.065336826\) \(a_{10}=-0.419338414\)
\(a_{11}=-0.674346134\) \(a_{12}=+0.875405167\) \(a_{13}=-0.899567308\) \(a_{14}=-0.267261242\) \(a_{15}=+1.038290183\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.669771617\) \(a_{18}=-1.460413675\) \(a_{19}=-1.738297558\) \(a_{20}=+0.296517036\)
\(a_{21}=+0.661744105\) \(a_{22}=+0.476834724\) \(a_{23}=+0.831617434\) \(a_{24}=-0.619004930\) \(a_{25}=-0.648310589\)
\(a_{26}=+0.636090144\) \(a_{27}=+1.865202723\) \(a_{28}=+0.188982237\) \(a_{29}=-0.342674264\) \(a_{30}=-0.734182029\)
\(a_{31}=-0.361513474\) \(a_{32}=-0.176776696\) \(a_{33}=-1.180652180\) \(a_{34}=-0.473600051\) \(a_{35}=+0.224145811\)
\(a_{36}=+1.032668411\) \(a_{37}=-0.228878461\) \(a_{38}=+1.229161989\) \(a_{39}=-1.574971743\) \(a_{40}=-0.209669202\)
\(a_{41}=-0.041533732\) \(a_{42}=-0.467923743\) \(a_{43}=+0.628003691\) \(a_{44}=-0.337173067\) \(a_{45}=+1.224815109\)
\(a_{46}=-0.588042327\) \(a_{47}=+1.173662318\) \(a_{48}=+0.437702584\) \(a_{49}=+0.142857143\) \(a_{50}=+0.458424813\)
\(a_{51}=+1.172643067\) \(a_{52}=-0.449783654\) \(a_{53}=-0.141010228\) \(a_{54}=-1.318897494\) \(a_{55}=-0.399910234\)
\(a_{56}=-0.133630620\) \(a_{57}=-3.043429331\) \(a_{58}=+0.242307295\) \(a_{59}=-0.037392054\) \(a_{60}=+0.519145096\)
\(a_{61}=+0.345432087\) \(a_{62}=+0.255628629\) \(a_{63}=+0.780623951\) \(a_{64}=+0.125000011\) \(a_{65}=-0.533474081\)
\(a_{66}=+0.834847162\) \(a_{67}=-0.815573235\) \(a_{68}=+0.334885847\) \(a_{69}=+1.456004372\) \(a_{70}=-0.158494989\)
\(a_{71}=+1.830364043\) \(a_{72}=-0.730207028\) \(a_{73}=-1.373818763\) \(a_{74}=+0.161841605\) \(a_{75}=-1.135069554\)
\(a_{76}=-0.869149679\) \(a_{77}=-0.254878880\) \(a_{78}=+1.113673195\) \(a_{79}=+0.450458072\) \(a_{80}=+0.148258517\)
\(a_{81}=+1.200279378\) \(a_{82}=+0.029368781\) \(a_{83}=-0.372418796\) \(a_{84}=+0.330872051\) \(a_{85}=+0.397197386\)
\(a_{86}=-0.444065661\) \(a_{87}=-0.599957636\) \(a_{88}=+0.238417381\) \(a_{89}=+0.077512710\) \(a_{90}=-0.866075067\)
\(a_{91}=-0.340004517\) \(a_{92}=+0.415808651\) \(a_{93}=-0.632941563\) \(a_{94}=-0.829904578\) \(a_{95}=-1.030869674\)
\(a_{96}=-0.309502340\) \(a_{97}=+1.915680919\) \(a_{98}=-0.101015079\) \(a_{99}=-1.392752042\) \(a_{100}=-0.324155295\)

Showing 100 of 2000 available coefficients

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