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: \( 5.47351318578 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.056960017\) \(a_{4}=+0.500000000\) \(a_{5}=-1.510850309\)
\(a_{6}=-0.040276814\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.996755556\) \(a_{10}=-1.068332499\)
\(a_{11}=-1.401922013\) \(a_{12}=-0.028480008\) \(a_{13}=+1.041763247\) \(a_{14}=-0.267261242\) \(a_{15}=+0.086058059\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.170214498\) \(a_{18}=-0.704812613\) \(a_{19}=+1.231565960\) \(a_{20}=-0.755425154\)
\(a_{21}=+0.021528863\) \(a_{22}=-0.991308562\) \(a_{23}=-1.295838865\) \(a_{24}=-0.020138407\) \(a_{25}=+1.282668655\)
\(a_{26}=+0.736637856\) \(a_{27}=+0.113735230\) \(a_{28}=-0.188982236\) \(a_{29}=+0.671475524\) \(a_{30}=+0.060852237\)
\(a_{31}=-0.814275591\) \(a_{32}=+0.176776696\) \(a_{33}=+0.079853502\) \(a_{34}=-0.120359826\) \(a_{35}=+0.571047739\)
\(a_{36}=-0.498377779\) \(a_{37}=-0.648219411\) \(a_{38}=+0.870848644\) \(a_{39}=-0.059338858\) \(a_{40}=-0.534166249\)
\(a_{41}=-0.360367268\) \(a_{42}=+0.015223204\) \(a_{43}=-0.468478785\) \(a_{44}=-0.700961012\) \(a_{45}=+1.505948421\)
\(a_{46}=-0.916296465\) \(a_{47}=+0.545106244\) \(a_{48}=-0.014240004\) \(a_{49}=+0.142857143\) \(a_{50}=+0.906983704\)
\(a_{51}=+0.009695420\) \(a_{52}=+0.520881623\) \(a_{53}=-1.946565656\) \(a_{54}=+0.080422952\) \(a_{55}=+2.118094308\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.070150020\) \(a_{58}=+0.474804897\) \(a_{59}=+0.034531231\) \(a_{60}=+0.043029030\)
\(a_{61}=-1.211240845\) \(a_{62}=-0.575779792\) \(a_{63}=+0.376738187\) \(a_{64}=+0.124999998\) \(a_{65}=-1.573948336\)
\(a_{66}=+0.056464960\) \(a_{67}=-0.900773110\) \(a_{68}=-0.085107245\) \(a_{69}=+0.073811007\) \(a_{70}=+0.403791720\)
\(a_{71}=+1.117886609\) \(a_{72}=-0.352406283\) \(a_{73}=+0.558122219\) \(a_{74}=-0.458360337\) \(a_{75}=-0.073060815\)
\(a_{76}=+0.615782904\) \(a_{77}=+0.529876716\) \(a_{78}=-0.041958907\) \(a_{79}=+0.509883859\) \(a_{80}=-0.377712577\)
\(a_{81}=+0.990277195\) \(a_{82}=-0.254818133\) \(a_{83}=+0.680736534\) \(a_{84}=+0.010764438\) \(a_{85}=+0.257168620\)
\(a_{86}=-0.331264538\) \(a_{87}=-0.038247263\) \(a_{88}=-0.495654277\) \(a_{89}=-1.592130532\) \(a_{90}=+1.064866356\)
\(a_{91}=-0.393749477\) \(a_{92}=-0.647919443\) \(a_{93}=+0.046381139\) \(a_{94}=+0.385448312\) \(a_{95}=-1.860711810\)
\(a_{96}=-0.010069192\) \(a_{97}=-1.362191199\) \(a_{98}=+0.101015267\) \(a_{99}=+1.397373561\) \(a_{100}=+0.641334275\)

Showing 100 of 2000 available coefficients

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