Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 21.7535258027 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.836096282\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.298316132\) \(a_{7}=-0.636542366\) \(a_{8}=+0.353553391\) \(a_{9}=+2.371249557\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.642432642\) \(a_{12}=+0.918048141\) \(a_{13}=-0.484678272\) \(a_{14}=-0.450103424\) \(a_{15}=-0.821127220\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.572479298\) \(a_{18}=+1.676726641\) \(a_{19}=-0.456623909\) \(a_{20}=-0.223606798\)
\(a_{21}=-1.168753072\) \(a_{22}=-1.161375259\) \(a_{23}=+0.729907567\) \(a_{24}=+0.649158066\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.342719293\) \(a_{27}=+2.517746213\) \(a_{28}=-0.318271183\) \(a_{29}=-1.089089112\) \(a_{30}=-0.580624625\)
\(a_{31}=-0.272398514\) \(a_{32}=+0.176776695\) \(a_{33}=-3.015664468\) \(a_{34}=-1.111910775\) \(a_{35}=+0.284670400\)
\(a_{36}=+1.185624778\) \(a_{37}=-0.435955643\) \(a_{38}=-0.322881863\) \(a_{39}=-0.889915973\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.770567060\) \(a_{42}=-0.826433223\) \(a_{43}=+0.906695208\) \(a_{44}=-0.821216321\) \(a_{45}=-1.060455040\)
\(a_{46}=+0.516122590\) \(a_{47}=+0.888699582\) \(a_{48}=+0.459024070\) \(a_{49}=-0.594813816\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.887223393\) \(a_{52}=-0.242339136\) \(a_{53}=-0.516966977\) \(a_{54}=+1.780315420\) \(a_{55}=+0.734518207\)
\(a_{56}=-0.225051712\) \(a_{57}=-0.838405462\) \(a_{58}=-0.770102296\) \(a_{59}=+0.938581289\) \(a_{60}=-0.410563610\)
\(a_{61}=-1.511355162\) \(a_{62}=-0.192614837\) \(a_{63}=-1.509400804\) \(a_{64}=+0.125000000\) \(a_{65}=+0.216754713\)
\(a_{66}=-2.132396795\) \(a_{67}=+0.872282149\) \(a_{68}=-0.786239649\) \(a_{69}=+1.340180569\) \(a_{70}=+0.201292370\)
\(a_{71}=+0.435065008\) \(a_{72}=+0.838363321\) \(a_{73}=-0.915199871\) \(a_{74}=-0.308267191\) \(a_{75}=+0.367219256\)
\(a_{76}=-0.228311955\) \(a_{77}=+1.045477960\) \(a_{78}=-0.629265619\) \(a_{79}=+0.955750843\) \(a_{80}=-0.111803399\)
\(a_{81}=+2.251574903\) \(a_{82}=-1.251979975\) \(a_{83}=+0.631968266\) \(a_{84}=-0.584376536\) \(a_{85}=+0.703234121\)
\(a_{86}=+0.641130330\) \(a_{87}=-1.999672468\) \(a_{88}=-0.580687630\) \(a_{89}=+1.310696696\) \(a_{90}=-0.749854950\)
\(a_{91}=+0.308518254\) \(a_{92}=+0.364953783\) \(a_{93}=-0.500149899\) \(a_{94}=+0.628405501\) \(a_{95}=+0.204208420\)
\(a_{96}=+0.324579033\) \(a_{97}=+0.947403733\) \(a_{98}=-0.420596883\) \(a_{99}=-3.894617675\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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