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: \( 8.69750590723 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.099975295\) \(a_{3}=-0.836229188\) \(a_{4}=+0.209945651\) \(a_{5}=+1.289156473\)
\(a_{6}=+0.919831448\) \(a_{7}=+0.377964473\) \(a_{8}=+0.869040266\) \(a_{9}=-0.300720746\) \(a_{10}=-1.418040272\)
\(a_{11}=-1.172268409\) \(a_{12}=-0.175562681\) \(a_{13}=+1.142995895\) \(a_{14}=-0.415751583\) \(a_{15}=-1.078030270\)
\(a_{16}=-1.165868474\) \(a_{17}=-0.072162866\) \(a_{18}=+0.330785391\) \(a_{19}=+0.127735549\) \(a_{20}=+0.270652794\)
\(a_{21}=-0.316064924\) \(a_{22}=+1.289466290\) \(a_{23}=-1.044583759\) \(a_{24}=-0.726716836\) \(a_{25}=+0.661924412\)
\(a_{26}=-1.257267248\) \(a_{27}=+1.087700653\) \(a_{28}=+0.079351997\) \(a_{29}=-0.776618920\) \(a_{30}=+1.185806665\)
\(a_{31}=-1.444501524\) \(a_{32}=+0.413386253\) \(a_{33}=+0.980285060\) \(a_{34}=+0.079377370\) \(a_{35}=+0.487255347\)
\(a_{36}=-0.063135013\) \(a_{37}=-1.200327216\) \(a_{38}=-0.140505948\) \(a_{39}=-0.955806529\) \(a_{40}=+1.120328885\)
\(a_{41}=+0.594986834\) \(a_{42}=+0.347663608\) \(a_{43}=-1.840484371\) \(a_{44}=-0.246112654\) \(a_{45}=-0.387676096\)
\(a_{46}=+1.149016328\) \(a_{47}=+1.049909564\) \(a_{48}=+0.974933247\) \(a_{49}=+0.142857143\) \(a_{50}=-0.728100500\)
\(a_{51}=+0.060344695\) \(a_{52}=+0.239967017\) \(a_{53}=-0.207606331\) \(a_{54}=-1.196443847\) \(a_{55}=-1.511237408\)
\(a_{56}=+0.328466346\) \(a_{57}=-0.106816195\) \(a_{58}=+0.854261626\) \(a_{59}=-0.632141672\) \(a_{60}=-0.226327766\)
\(a_{61}=+0.650902590\) \(a_{62}=+1.588915990\) \(a_{63}=-0.113661758\) \(a_{64}=+0.711153808\) \(a_{65}=+1.473500557\)
\(a_{66}=-1.078289348\) \(a_{67}=-1.899749380\) \(a_{68}=-0.015150280\) \(a_{69}=+0.873511428\) \(a_{70}=-0.535968844\)
\(a_{71}=-0.850908442\) \(a_{72}=-0.261338437\) \(a_{73}=-0.153897005\) \(a_{74}=+1.320330284\) \(a_{75}=-0.553520513\)
\(a_{76}=+0.026817523\) \(a_{77}=-0.443075812\) \(a_{78}=+1.051363569\) \(a_{79}=+0.920942488\) \(a_{80}=-1.502986890\)
\(a_{81}=-0.608846288\) \(a_{82}=-0.654470818\) \(a_{83}=+0.914600039\) \(a_{84}=-0.066356456\) \(a_{85}=-0.093029226\)
\(a_{86}=+2.024487340\) \(a_{87}=+0.649431408\) \(a_{88}=-1.018748451\) \(a_{89}=-0.933224152\) \(a_{90}=+0.426434128\)
\(a_{91}=+0.432011841\) \(a_{92}=-0.219305817\) \(a_{93}=+1.207934336\) \(a_{94}=-1.154874582\) \(a_{95}=+0.164671110\)
\(a_{96}=-0.345685651\) \(a_{97}=-1.417798289\) \(a_{98}=-0.157139328\) \(a_{99}=+0.352525430\) \(a_{100}=+0.138968151\)

Showing 100 of 1228 available coefficients

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