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: \( 4.58940589267 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.983536717\) \(a_{4}=+0.500000000\) \(a_{5}=+0.547392116\)
\(a_{6}=+0.695465482\) \(a_{7}=+0.377964473\) \(a_{8}=-0.353553391\) \(a_{9}=-0.032655527\) \(a_{10}=-0.387064677\)
\(a_{11}=+1.494043157\) \(a_{12}=-0.491768358\) \(a_{13}=+1.247050383\) \(a_{14}=-0.267261242\) \(a_{15}=-0.538380245\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.553489479\) \(a_{18}=+0.023090944\) \(a_{19}=+0.387067211\) \(a_{20}=+0.273696058\)
\(a_{21}=-0.371741937\) \(a_{22}=-1.056448047\) \(a_{23}=+0.731981768\) \(a_{24}=+0.347732741\) \(a_{25}=-0.700361871\)
\(a_{26}=-0.881797782\) \(a_{27}=+1.015654626\) \(a_{28}=+0.188982237\) \(a_{29}=+1.562462938\) \(a_{30}=+0.380692322\)
\(a_{31}=+0.226645709\) \(a_{32}=-0.176776695\) \(a_{33}=-1.469446301\) \(a_{34}=+0.391376164\) \(a_{35}=+0.206894773\)
\(a_{36}=-0.016327763\) \(a_{37}=-1.641036248\) \(a_{38}=-0.273697850\) \(a_{39}=-1.226519840\) \(a_{40}=-0.193532339\)
\(a_{41}=+1.504477660\) \(a_{42}=+0.262861244\) \(a_{43}=+0.295835132\) \(a_{44}=+0.747021578\) \(a_{45}=-0.017875378\)
\(a_{46}=-0.517589272\) \(a_{47}=+1.017602523\) \(a_{48}=-0.245884179\) \(a_{49}=+0.142857143\) \(a_{50}=+0.495230628\)
\(a_{51}=+0.544377225\) \(a_{52}=+0.623525192\) \(a_{53}=-1.669982527\) \(a_{54}=-0.718176274\) \(a_{55}=+0.817827445\)
\(a_{56}=-0.133630621\) \(a_{57}=-0.380694814\) \(a_{58}=-1.104828139\) \(a_{59}=+1.165131096\) \(a_{60}=-0.269190122\)
\(a_{61}=-1.025085752\) \(a_{62}=-0.160262718\) \(a_{63}=-0.012342629\) \(a_{64}=+0.125000000\) \(a_{65}=+0.682625548\)
\(a_{66}=+1.039055444\) \(a_{67}=-0.440063941\) \(a_{68}=-0.276744739\) \(a_{69}=-0.719930945\) \(a_{70}=-0.146296697\)
\(a_{71}=-0.442256550\) \(a_{72}=+0.011545472\) \(a_{73}=-0.208266940\) \(a_{74}=+1.160387859\) \(a_{75}=+0.688831615\)
\(a_{76}=+0.193533605\) \(a_{77}=+0.564695234\) \(a_{78}=+0.867280496\) \(a_{79}=+0.035340000\) \(a_{80}=+0.136848029\)
\(a_{81}=-0.966278090\) \(a_{82}=-1.063826356\) \(a_{83}=+1.509626100\) \(a_{84}=-0.185870968\) \(a_{85}=-0.302975777\)
\(a_{86}=-0.209187028\) \(a_{87}=-1.536739668\) \(a_{88}=-0.528224024\) \(a_{89}=+0.768008400\) \(a_{90}=+0.012639801\)
\(a_{91}=+0.471340741\) \(a_{92}=+0.365990884\) \(a_{93}=-0.222914377\) \(a_{94}=-0.719553644\) \(a_{95}=+0.211877540\)
\(a_{96}=+0.173866370\) \(a_{97}=-0.229214900\) \(a_{98}=-0.101015254\) \(a_{99}=-0.048788766\) \(a_{100}=-0.350180936\)

Showing 100 of 148 available coefficients

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