Properties

Level $947$
Weight $0$
Character 947.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 947 \)
Weight: \( 0 \)
Character: 947.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.43597663517 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.582532580\) \(a_{3}=+0.274881182\) \(a_{4}=+1.504408507\) \(a_{5}=-1.271133037\)
\(a_{6}=+0.435009669\) \(a_{7}=-0.056760442\) \(a_{8}=+0.798243852\) \(a_{9}=-0.924439339\) \(a_{10}=-2.011609269\)
\(a_{11}=+0.856998528\) \(a_{12}=+0.413535350\) \(a_{13}=-0.694811912\) \(a_{14}=-0.089825625\) \(a_{15}=-0.349411938\)
\(a_{16}=-0.241161191\) \(a_{17}=-0.351683941\) \(a_{18}=-1.462955536\) \(a_{19}=+0.767328269\) \(a_{20}=-1.912304780\)
\(a_{21}=-0.015602808\) \(a_{22}=+1.356227049\) \(a_{23}=+0.538480888\) \(a_{24}=+0.219423481\) \(a_{25}=+0.615779647\)
\(a_{26}=-1.099563169\) \(a_{27}=-0.528993728\) \(a_{28}=-0.085391568\) \(a_{29}=-0.268716019\) \(a_{30}=-0.552955160\)
\(a_{31}=-1.319296147\) \(a_{32}=-1.179889986\) \(a_{33}=+0.235572567\) \(a_{34}=-0.556551250\) \(a_{35}=+0.072150539\)
\(a_{36}=-1.390735979\) \(a_{37}=+1.072000072\) \(a_{38}=+1.214322392\) \(a_{39}=-0.190992382\) \(a_{40}=-1.014675064\)
\(a_{41}=+0.521770811\) \(a_{42}=-0.024691773\) \(a_{43}=+0.011992252\) \(a_{44}=+1.289275108\) \(a_{45}=+1.175086087\)
\(a_{46}=+0.852162933\) \(a_{47}=+1.038116126\) \(a_{48}=-0.066291029\) \(a_{49}=-0.996778016\) \(a_{50}=+0.974491515\)
\(a_{51}=-0.096671913\) \(a_{52}=-1.045283249\) \(a_{53}=+1.497352050\) \(a_{54}=-0.837150140\) \(a_{55}=-1.089358370\)
\(a_{56}=-0.045309102\) \(a_{57}=+0.210925154\) \(a_{58}=-0.425251615\) \(a_{59}=-1.757346481\) \(a_{60}=-0.525658171\)
\(a_{61}=+1.790039956\) \(a_{62}=-2.087828109\) \(a_{63}=+0.052472152\) \(a_{64}=-1.626052985\) \(a_{65}=+0.883199598\)
\(a_{66}=+0.372801835\) \(a_{67}=+1.100200504\) \(a_{68}=-0.529077002\) \(a_{69}=+0.148018837\) \(a_{70}=+0.114180458\)
\(a_{71}=-1.253113850\) \(a_{72}=-0.737929130\) \(a_{73}=+1.220700823\) \(a_{74}=+1.696474393\) \(a_{75}=+0.169267609\)
\(a_{76}=+1.154376469\) \(a_{77}=-0.048643482\) \(a_{78}=-0.302250610\) \(a_{79}=+0.117473994\) \(a_{80}=+0.306548568\)
\(a_{81}=+0.779028364\) \(a_{82}=+0.825719988\) \(a_{83}=-0.403375830\) \(a_{84}=-0.023472370\) \(a_{85}=+0.447037374\)
\(a_{86}=+0.018977681\) \(a_{87}=-0.073864365\) \(a_{88}=+0.684093204\) \(a_{89}=-0.037075890\) \(a_{90}=+1.859612182\)
\(a_{91}=+0.039438448\) \(a_{92}=+0.810095496\) \(a_{93}=-0.362650091\) \(a_{94}=+1.642852116\) \(a_{95}=-0.975377024\)
\(a_{96}=-0.324331451\) \(a_{97}=-0.510784544\) \(a_{98}=-1.577433937\) \(a_{99}=-0.792242303\) \(a_{100}=+0.926385658\)

Showing 100 of 2472 available coefficients

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