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: \( 7.05035422681 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.257003712\) \(a_{3}=-1.348159450\) \(a_{4}=-0.933949092\) \(a_{5}=+0.789878662\)
\(a_{6}=+0.346481983\) \(a_{7}=+0.377964473\) \(a_{8}=+0.497032096\) \(a_{9}=+0.817533901\) \(a_{10}=-0.203001748\)
\(a_{11}=+0.631335199\) \(a_{12}=+1.259112294\) \(a_{13}=-1.342153511\) \(a_{14}=-0.097138273\) \(a_{15}=-1.064882383\)
\(a_{16}=+0.806209998\) \(a_{17}=+1.722943572\) \(a_{18}=-0.210109248\) \(a_{19}=-0.014737254\) \(a_{20}=-0.737706459\)
\(a_{21}=-0.509556376\) \(a_{22}=-0.162255490\) \(a_{23}=+1.013841239\) \(a_{24}=-0.670078517\) \(a_{25}=-0.376091699\)
\(a_{26}=+0.344938435\) \(a_{27}=+0.245993395\) \(a_{28}=-0.352999576\) \(a_{29}=+0.600205619\) \(a_{30}=+0.273678725\)
\(a_{31}=+1.184276187\) \(a_{32}=-0.704231058\) \(a_{33}=-0.851140514\) \(a_{34}=-0.442802894\) \(a_{35}=+0.298546072\)
\(a_{36}=-0.763535045\) \(a_{37}=-0.716304571\) \(a_{38}=+0.003787529\) \(a_{39}=+1.809436939\) \(a_{40}=+0.392595047\)
\(a_{41}=-0.427081870\) \(a_{42}=+0.130957880\) \(a_{43}=-0.059866175\) \(a_{44}=-0.589634935\) \(a_{45}=+0.645752584\)
\(a_{46}=-0.260560962\) \(a_{47}=+1.506826297\) \(a_{48}=-1.086899627\) \(a_{49}=+0.142857143\) \(a_{50}=+0.096656963\)
\(a_{51}=-2.322802658\) \(a_{52}=+1.253503053\) \(a_{53}=-0.823348972\) \(a_{54}=-0.063221216\) \(a_{55}=+0.498678202\)
\(a_{56}=+0.187860474\) \(a_{57}=+0.019868168\) \(a_{58}=-0.154255072\) \(a_{59}=-0.196779563\) \(a_{60}=+0.994545934\)
\(a_{61}=+1.644920892\) \(a_{62}=-0.304363376\) \(a_{63}=+0.308998770\) \(a_{64}=-0.625220002\) \(a_{65}=-1.060138420\)
\(a_{66}=+0.218746272\) \(a_{67}=+1.247166934\) \(a_{68}=-1.609141585\) \(a_{69}=-1.366819646\) \(a_{70}=-0.076727449\)
\(a_{71}=-0.415554142\) \(a_{72}=+0.406340588\) \(a_{73}=+1.042141754\) \(a_{74}=+0.184092934\) \(a_{75}=+0.507031578\)
\(a_{76}=+0.013763845\) \(a_{77}=+0.238622276\) \(a_{78}=-0.465032010\) \(a_{79}=-0.429000410\) \(a_{80}=+0.636808075\)
\(a_{81}=-1.149172221\) \(a_{82}=+0.109761626\) \(a_{83}=+0.653267368\) \(a_{84}=+0.475899715\) \(a_{85}=+1.360916364\)
\(a_{86}=+0.015385829\) \(a_{87}=-0.809172878\) \(a_{88}=+0.313793857\) \(a_{89}=+0.257451339\) \(a_{90}=-0.165960811\)
\(a_{91}=-0.507286345\) \(a_{92}=-0.946876104\) \(a_{93}=-1.596593133\) \(a_{94}=-0.387259952\) \(a_{95}=-0.011640642\)
\(a_{96}=+0.949415756\) \(a_{97}=-0.148436180\) \(a_{98}=-0.036714816\) \(a_{99}=+0.516137928\) \(a_{100}=+0.351250501\)

Showing 100 of 1228 available coefficients

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