Properties

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

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 8.46236495549 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.069289125\) \(a_{3}=+0.208519494\) \(a_{4}=-0.995199017\) \(a_{5}=+1.463361336\)
\(a_{6}=-0.014448133\) \(a_{7}=-0.377964473\) \(a_{8}=+0.138245594\) \(a_{9}=-0.956519621\) \(a_{10}=-0.101395026\)
\(a_{11}=-0.677409507\) \(a_{12}=-0.207518395\) \(a_{13}=-1.797066744\) \(a_{14}=+0.026188828\) \(a_{15}=+0.305139365\)
\(a_{16}=+0.985620101\) \(a_{17}=-1.309983275\) \(a_{18}=+0.066276407\) \(a_{19}=+0.922659667\) \(a_{20}=-1.456335763\)
\(a_{21}=-0.078812961\) \(a_{22}=+0.046937112\) \(a_{23}=-0.237462511\) \(a_{24}=+0.028826901\) \(a_{25}=+1.141426399\)
\(a_{26}=+0.124517182\) \(a_{27}=-0.407972481\) \(a_{28}=+0.376149872\) \(a_{29}=-0.340871347\) \(a_{30}=-0.021142840\)
\(a_{31}=-0.564537258\) \(a_{32}=-0.206538348\) \(a_{33}=-0.141253088\) \(a_{34}=+0.090767595\) \(a_{35}=-0.553098596\)
\(a_{36}=+0.951927386\) \(a_{37}=+0.606815400\) \(a_{38}=-0.063930281\) \(a_{39}=-0.374723448\) \(a_{40}=+0.202303256\)
\(a_{41}=+0.462890112\) \(a_{42}=+0.005460881\) \(a_{43}=-0.226308968\) \(a_{44}=+0.674157276\) \(a_{45}=-1.399733830\)
\(a_{46}=+0.016453570\) \(a_{47}=-1.067099530\) \(a_{48}=+0.205521005\) \(a_{49}=+0.142857143\) \(a_{50}=-0.079088436\)
\(a_{51}=-0.273157049\) \(a_{52}=+1.788439057\) \(a_{53}=+0.709991755\) \(a_{54}=+0.028268056\) \(a_{55}=-0.991294881\)
\(a_{56}=-0.052251923\) \(a_{57}=+0.192392527\) \(a_{58}=+0.023618677\) \(a_{59}=-0.199946693\) \(a_{60}=-0.303674396\)
\(a_{61}=+0.983943374\) \(a_{62}=+0.039116292\) \(a_{63}=+0.361530434\) \(a_{64}=-0.971309240\) \(a_{65}=-2.629757990\)
\(a_{66}=+0.009787303\) \(a_{67}=+0.488013952\) \(a_{68}=+1.303694068\) \(a_{69}=-0.049515563\) \(a_{70}=+0.038323718\)
\(a_{71}=+0.836083084\) \(a_{72}=-0.132234623\) \(a_{73}=+0.850216062\) \(a_{74}=-0.042045708\) \(a_{75}=+0.238009655\)
\(a_{76}=-0.918229994\) \(a_{77}=+0.256036727\) \(a_{78}=+0.025964260\) \(a_{79}=-1.620097584\) \(a_{80}=+1.442318347\)
\(a_{81}=+0.871449405\) \(a_{82}=-0.032073251\) \(a_{83}=-0.679223874\) \(a_{84}=+0.078434581\) \(a_{85}=-1.916978875\)
\(a_{86}=+0.015680750\) \(a_{87}=-0.071078321\) \(a_{88}=-0.093648879\) \(a_{89}=+0.133306614\) \(a_{90}=+0.096986332\)
\(a_{91}=+0.679227385\) \(a_{92}=+0.236322458\) \(a_{93}=-0.117717023\) \(a_{94}=+0.073938392\) \(a_{95}=+1.350184483\)
\(a_{96}=-0.043067272\) \(a_{97}=-0.498240182\) \(a_{98}=-0.009898446\) \(a_{99}=+0.647955485\) \(a_{100}=-1.135946430\)

Showing 100 of 1228 available coefficients

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