Properties

Level 10
Weight 0
Character 10.1
Symmetry odd
Fricke sign -1

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: \(-1\)
Spectral parameter: \( 23.9165494096 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.534501759\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.085056599\) \(a_{7}=-0.974357004\) \(a_{8}=-0.353553391\) \(a_{9}=+1.354695648\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.436929830\) \(a_{12}=-0.767250879\) \(a_{13}=+0.361387630\) \(a_{14}=+0.688974445\) \(a_{15}=-0.686250049\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.604485998\) \(a_{18}=-0.957914479\) \(a_{19}=-1.854844002\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.495152536\) \(a_{22}=+1.016062827\) \(a_{23}=-0.707643209\) \(a_{24}=+0.542528300\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.255539644\) \(a_{27}=-0.544281095\) \(a_{28}=-0.487178502\) \(a_{29}=+0.768218720\) \(a_{30}=+0.485252063\)
\(a_{31}=+1.571337895\) \(a_{32}=-0.176776695\) \(a_{33}=+2.204971352\) \(a_{34}=-0.427436148\) \(a_{35}=-0.435745699\)
\(a_{36}=+0.677347824\) \(a_{37}=-1.071586438\) \(a_{38}=+1.311572772\) \(a_{39}=-0.554549955\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.002976754\) \(a_{42}=-1.057232497\) \(a_{43}=-0.897527209\) \(a_{44}=-0.718464915\) \(a_{45}=+0.605838311\)
\(a_{46}=+0.500379312\) \(a_{47}=-1.561676509\) \(a_{48}=-0.383625440\) \(a_{49}=-0.050628429\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.927584827\) \(a_{52}=+0.180693815\) \(a_{53}=-0.314155978\) \(a_{54}=+0.384864853\) \(a_{55}=-0.642614556\)
\(a_{56}=+0.344487222\) \(a_{57}=+2.846261383\) \(a_{58}=-0.543212666\) \(a_{59}=-1.056508452\) \(a_{60}=-0.343125024\)
\(a_{61}=-0.910944464\) \(a_{62}=-1.111103681\) \(a_{63}=-1.319957192\) \(a_{64}=+0.125000000\) \(a_{65}=+0.161617462\)
\(a_{66}=-1.559150195\) \(a_{67}=-0.682796453\) \(a_{68}=+0.302242999\) \(a_{69}=+1.085879749\) \(a_{70}=+0.308118739\)
\(a_{71}=-0.403636758\) \(a_{72}=-0.478957239\) \(a_{73}=-1.703095432\) \(a_{74}=+0.757726037\) \(a_{75}=-0.306900352\)
\(a_{76}=-0.927422001\) \(a_{77}=+1.400082644\) \(a_{78}=+0.392126033\) \(a_{79}=+0.089428591\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.519495350\) \(a_{82}=+0.709211664\) \(a_{83}=-0.648853593\) \(a_{84}=+0.747576268\) \(a_{85}=+0.270334357\)
\(a_{86}=+0.634647576\) \(a_{87}=-1.178832977\) \(a_{88}=+0.508031414\) \(a_{89}=+0.898428421\) \(a_{90}=-0.428392378\)
\(a_{91}=-0.352120569\) \(a_{92}=-0.353821604\) \(a_{93}=-2.411220763\) \(a_{94}=+1.104272050\) \(a_{95}=-0.829511455\)
\(a_{96}=+0.271264150\) \(a_{97}=-0.646882518\) \(a_{98}=+0.035799706\) \(a_{99}=-1.946602587\) \(a_{100}=+0.099975586\)

Showing 100 of 220 available coefficients

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