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: \( 4.52208412029 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.324670114\) \(a_{4}=+0.500000000\) \(a_{5}=+0.131675401\)
\(a_{6}=+0.936683220\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+0.754750910\) \(a_{10}=+0.093108569\)
\(a_{11}=+0.105775293\) \(a_{12}=+0.662335057\) \(a_{13}=-1.844792128\) \(a_{14}=+0.267261242\) \(a_{15}=+0.174426468\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.979389415\) \(a_{18}=+0.533689486\) \(a_{19}=+1.658877222\) \(a_{20}=+0.065837700\)
\(a_{21}=+0.500678241\) \(a_{22}=+0.074794427\) \(a_{23}=-0.935168609\) \(a_{24}=+0.468341610\) \(a_{25}=-0.982661589\)
\(a_{26}=-1.304465023\) \(a_{27}=-0.324874140\) \(a_{28}=+0.188982237\) \(a_{29}=+0.351329384\) \(a_{30}=+0.123338138\)
\(a_{31}=+1.242793444\) \(a_{32}=+0.176776695\) \(a_{33}=+0.140117369\) \(a_{34}=-0.692532897\) \(a_{35}=+0.049768624\)
\(a_{36}=+0.377375454\) \(a_{37}=-0.232921024\) \(a_{38}=+1.173003331\) \(a_{39}=-2.443740995\) \(a_{40}=+0.046554283\)
\(a_{41}=+1.751988181\) \(a_{42}=+0.354032986\) \(a_{43}=-0.199391051\) \(a_{44}=+0.052887670\) \(a_{45}=+0.099382092\)
\(a_{46}=-0.661264034\) \(a_{47}=+0.018629284\) \(a_{48}=+0.331167550\) \(a_{49}=+0.142857143\) \(a_{50}=-0.694846673\)
\(a_{51}=-1.297367888\) \(a_{52}=-0.922396064\) \(a_{53}=+0.082727932\) \(a_{54}=-0.229720707\) \(a_{55}=+0.013928003\)
\(a_{56}=+0.133630622\) \(a_{57}=+2.197465078\) \(a_{58}=+0.248427391\) \(a_{59}=+0.529275258\) \(a_{60}=+0.087213236\)
\(a_{61}=-0.764828215\) \(a_{62}=+0.878787675\) \(a_{63}=+0.285269026\) \(a_{64}=+0.125000003\) \(a_{65}=-0.242913746\)
\(a_{66}=+0.099077947\) \(a_{67}=-0.022382454\) \(a_{68}=-0.489694705\) \(a_{69}=-1.238789911\) \(a_{70}=+0.035191737\)
\(a_{71}=+0.774516928\) \(a_{72}=+0.266844743\) \(a_{73}=+0.330874073\) \(a_{74}=-0.164700032\) \(a_{75}=-1.301702427\)
\(a_{76}=+0.829438614\) \(a_{77}=+0.039979331\) \(a_{78}=-1.727985863\) \(a_{79}=-0.361415242\) \(a_{80}=+0.032918706\)
\(a_{81}=-1.185101973\) \(a_{82}=+1.238842723\) \(a_{83}=+0.414895440\) \(a_{84}=+0.250339122\) \(a_{85}=-0.128961497\)
\(a_{86}=-0.140990755\) \(a_{87}=+0.465395534\) \(a_{88}=+0.037397220\) \(a_{89}=+1.384485212\) \(a_{90}=+0.070273784\)
\(a_{91}=-0.697265885\) \(a_{92}=-0.467584298\) \(a_{93}=+1.646291320\) \(a_{94}=+0.013172907\) \(a_{95}=+0.218433347\)
\(a_{96}=+0.234170785\) \(a_{97}=-0.013572598\) \(a_{98}=+0.101015234\) \(a_{99}=+0.079834000\) \(a_{100}=-0.491330793\)

Showing 100 of 2000 available coefficients

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