Properties

Level $67$
Weight $0$
Character 67.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 67 \)
Weight: \( 0 \)
Character: 67.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.84247476 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.815400450\) \(a_{3}=+0.395104130\) \(a_{4}=-0.335122106\) \(a_{5}=-0.614680650\)
\(a_{6}=-0.322168085\) \(a_{7}=+0.013302187\) \(a_{8}=+1.088659166\) \(a_{9}=-0.843892726\) \(a_{10}=+0.501210879\)
\(a_{11}=-0.971452010\) \(a_{12}=-0.132408128\) \(a_{13}=+1.648143780\) \(a_{14}=-0.010846609\) \(a_{15}=-0.242862863\)
\(a_{16}=-0.552571068\) \(a_{17}=+0.619524910\) \(a_{18}=+0.688110509\) \(a_{19}=+1.881417253\) \(a_{20}=+0.205993074\)
\(a_{21}=+0.005255749\) \(a_{22}=+0.792122406\) \(a_{23}=-0.917394640\) \(a_{24}=+0.430133733\) \(a_{25}=-0.622167699\)
\(a_{26}=-1.343897180\) \(a_{27}=-0.728529632\) \(a_{28}=-0.004457857\) \(a_{29}=-0.278454560\) \(a_{30}=+0.198030488\)
\(a_{31}=+0.458020268\) \(a_{32}=-0.638092469\) \(a_{33}=-0.383824701\) \(a_{34}=-0.505160891\) \(a_{35}=-0.008176597\)
\(a_{36}=+0.282807108\) \(a_{37}=-0.803001898\) \(a_{38}=-1.534108475\) \(a_{39}=+0.651188414\) \(a_{40}=-0.669177724\)
\(a_{41}=-0.575078054\) \(a_{42}=-0.004285540\) \(a_{43}=+1.185085878\) \(a_{44}=+0.325555044\) \(a_{45}=+0.518724530\)
\(a_{46}=+0.748044002\) \(a_{47}=+0.617105129\) \(a_{48}=-0.218323111\) \(a_{49}=-0.999823052\) \(a_{50}=+0.507315821\)
\(a_{51}=+0.244776851\) \(a_{52}=-0.552329415\) \(a_{53}=+0.130460771\) \(a_{54}=+0.594043389\) \(a_{55}=+0.597132753\)
\(a_{56}=+0.014481548\) \(a_{57}=+0.743355727\) \(a_{58}=+0.227051973\) \(a_{59}=+1.363108656\) \(a_{60}=+0.081388714\)
\(a_{61}=-1.102187025\) \(a_{62}=-0.373469933\) \(a_{63}=-0.011225619\) \(a_{64}=+1.072871954\) \(a_{65}=-1.013082090\)
\(a_{66}=+0.312970834\) \(a_{67}=-0.122169444\) \(a_{68}=-0.207616493\) \(a_{69}=-0.362466411\) \(a_{70}=+0.006667201\)
\(a_{71}=-0.666942266\) \(a_{72}=-0.918711552\) \(a_{73}=+1.616833935\) \(a_{74}=+0.654768109\) \(a_{75}=-0.245821027\)
\(a_{76}=-0.630504513\) \(a_{77}=-0.012922436\) \(a_{78}=-0.530979326\) \(a_{79}=+0.649029835\) \(a_{80}=+0.339654743\)
\(a_{81}=+0.556047660\) \(a_{82}=+0.468918904\) \(a_{83}=+0.228233092\) \(a_{84}=-0.001761318\) \(a_{85}=-0.380809975\)
\(a_{86}=-0.966319558\) \(a_{87}=-0.110018547\) \(a_{88}=-1.057580135\) \(a_{89}=+0.540247208\) \(a_{90}=-0.422968215\)
\(a_{91}=+0.021923917\) \(a_{92}=+0.307439224\) \(a_{93}=+0.180965700\) \(a_{94}=-0.503187800\) \(a_{95}=-1.156470780\)
\(a_{96}=-0.252112970\) \(a_{97}=-0.087591047\) \(a_{98}=+0.815256166\) \(a_{99}=+0.819801285\) \(a_{100}=+0.208502149\)

Showing 100 of 546 available coefficients

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