Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.58279102848 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.171605520\) \(a_{3}=+0.962837127\) \(a_{4}=+0.372659496\) \(a_{5}=+1.116721269\)
\(a_{6}=+1.128065293\) \(a_{7}=-0.377964473\) \(a_{8}=-0.734995598\) \(a_{9}=-0.072944667\) \(a_{10}=+1.308356803\)
\(a_{11}=+0.306910233\) \(a_{12}=+0.358810398\) \(a_{13}=-1.322338350\) \(a_{14}=-0.442825263\) \(a_{15}=+1.075220698\)
\(a_{16}=-1.233784396\) \(a_{17}=+1.345106643\) \(a_{18}=-0.085462375\) \(a_{19}=-0.739478269\) \(a_{20}=+0.416156785\)
\(a_{21}=-0.363918227\) \(a_{22}=+0.359577723\) \(a_{23}=+1.472071442\) \(a_{24}=-0.707681050\) \(a_{25}=+0.247066392\)
\(a_{26}=-1.549258910\) \(a_{27}=-1.033070961\) \(a_{28}=-0.140852050\) \(a_{29}=+1.056403351\) \(a_{30}=+1.259734505\)
\(a_{31}=-0.293208216\) \(a_{32}=-0.710513011\) \(a_{33}=+0.295504567\) \(a_{34}=+1.575934368\) \(a_{35}=-0.422080966\)
\(a_{36}=-0.027183523\) \(a_{37}=+0.245566465\) \(a_{38}=-0.866376822\) \(a_{39}=-1.273196457\) \(a_{40}=-0.820785217\)
\(a_{41}=+0.903227141\) \(a_{42}=-0.426368604\) \(a_{43}=+0.386773724\) \(a_{44}=+0.114373013\) \(a_{45}=-0.081458862\)
\(a_{46}=+1.724687027\) \(a_{47}=+0.504515348\) \(a_{48}=-1.187933423\) \(a_{49}=+0.142857143\) \(a_{50}=+0.289464349\)
\(a_{51}=+1.295118615\) \(a_{52}=-0.492781942\) \(a_{53}=-1.504548126\) \(a_{54}=-1.210351641\) \(a_{55}=+0.342733185\)
\(a_{56}=+0.277802224\) \(a_{57}=-0.711997132\) \(a_{58}=+1.237687998\) \(a_{59}=+0.359838620\) \(a_{60}=+0.400691203\)
\(a_{61}=-0.639591964\) \(a_{62}=-0.343524364\) \(a_{63}=+0.027570493\) \(a_{64}=+0.401343430\) \(a_{65}=-1.476683360\)
\(a_{66}=+0.346214782\) \(a_{67}=+0.253304582\) \(a_{68}=+0.501266763\) \(a_{69}=+1.417365037\) \(a_{70}=-0.494512390\)
\(a_{71}=+0.569414513\) \(a_{72}=+0.053614009\) \(a_{73}=-0.401930544\) \(a_{74}=+0.287707026\) \(a_{75}=+0.237884695\)
\(a_{76}=-0.275573599\) \(a_{77}=-0.116001165\) \(a_{78}=-1.491683998\) \(a_{79}=-0.065406296\) \(a_{80}=-1.377793276\)
\(a_{81}=-0.921734408\) \(a_{82}=+1.058225905\) \(a_{83}=-0.194420774\) \(a_{84}=-0.135617583\) \(a_{85}=+1.502109197\)
\(a_{86}=+0.453146230\) \(a_{87}=+1.017144367\) \(a_{88}=-0.225577670\) \(a_{89}=+0.201982412\) \(a_{90}=-0.095437652\)
\(a_{91}=+0.499796917\) \(a_{92}=+0.548581401\) \(a_{93}=-0.282311756\) \(a_{94}=+0.591092966\) \(a_{95}=-0.825791111\)
\(a_{96}=-0.684108306\) \(a_{97}=-1.110392876\) \(a_{98}=+0.167372217\) \(a_{99}=-0.022387465\) \(a_{100}=+0.092071637\)

Showing 100 of 1228 available coefficients

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