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: \( 12.3624041926 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.772786700\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.253549497\) \(a_{7}=-0.377572230\) \(a_{8}=-0.353553391\) \(a_{9}=+2.142772682\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.091063548\) \(a_{12}=+0.886393350\) \(a_{13}=+0.692464939\) \(a_{14}=+0.266983884\) \(a_{15}=+0.792814314\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.441547818\) \(a_{18}=-1.515169094\) \(a_{19}=+1.410356242\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.669355028\) \(a_{22}=-0.771498434\) \(a_{23}=-0.950211028\) \(a_{24}=-0.626774748\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.489646654\) \(a_{27}=+2.025892212\) \(a_{28}=-0.188786115\) \(a_{29}=+1.813793865\) \(a_{30}=-0.560604378\)
\(a_{31}=-0.748569241\) \(a_{32}=-0.176776695\) \(a_{33}=+1.934222947\) \(a_{34}=+1.019328237\) \(a_{35}=-0.168855435\)
\(a_{36}=+1.071386341\) \(a_{37}=-0.045548449\) \(a_{38}=-0.997272463\) \(a_{39}=+1.227592635\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.051098846\) \(a_{42}=+0.473305479\) \(a_{43}=-0.522225066\) \(a_{44}=+0.545531774\) \(a_{45}=+0.958277076\)
\(a_{46}=+0.671900662\) \(a_{47}=+1.231489069\) \(a_{48}=+0.443196675\) \(a_{49}=-0.857439211\) \(a_{50}=-0.141421356\)
\(a_{51}=-2.555556798\) \(a_{52}=+0.346232470\) \(a_{53}=+0.822795161\) \(a_{54}=-1.432522121\) \(a_{55}=+0.487938452\)
\(a_{56}=+0.133491942\) \(a_{57}=+2.500260788\) \(a_{58}=-1.282545942\) \(a_{59}=-0.070278854\) \(a_{60}=+0.396407157\)
\(a_{61}=+1.029618399\) \(a_{62}=+0.529318386\) \(a_{63}=-0.809051460\) \(a_{64}=+0.125000000\) \(a_{65}=+0.309679735\)
\(a_{66}=-1.367702162\) \(a_{67}=+1.237837199\) \(a_{68}=-0.720773909\) \(a_{69}=-1.684521473\) \(a_{70}=+0.119398823\)
\(a_{71}=+0.965218232\) \(a_{72}=-0.757584547\) \(a_{73}=+0.372942217\) \(a_{74}=+0.032207617\) \(a_{75}=+0.354557340\)
\(a_{76}=+0.705178121\) \(a_{77}=-0.411955296\) \(a_{78}=-0.868039076\) \(a_{79}=+0.047870582\) \(a_{80}=+0.111803399\)
\(a_{81}=+1.448702084\) \(a_{82}=-0.036132341\) \(a_{83}=-0.529530898\) \(a_{84}=-0.334677514\) \(a_{85}=-0.644679783\)
\(a_{86}=+0.369268886\) \(a_{87}=+3.215469633\) \(a_{88}=-0.385749217\) \(a_{89}=-0.582601173\) \(a_{90}=-0.677604218\)
\(a_{91}=-0.261455503\) \(a_{92}=-0.475105514\) \(a_{93}=-1.327053572\) \(a_{94}=-0.870794272\) \(a_{95}=+0.630730486\)
\(a_{96}=-0.313387374\) \(a_{97}=-1.272598074\) \(a_{98}=+0.606301081\) \(a_{99}=+2.337901201\) \(a_{100}=+0.099975586\)

Showing 100 of 150 available coefficients

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