Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 22.1410716544 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.306619558\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.216812769\) \(a_{7}=+0.280019311\) \(a_{8}=+0.353553391\) \(a_{9}=-0.905984447\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.263935320\) \(a_{12}=-0.153309779\) \(a_{13}=+0.059589801\) \(a_{14}=+0.198003554\) \(a_{15}=-0.137124435\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.633820180\) \(a_{18}=-0.640627746\) \(a_{19}=+1.237693941\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.085859397\) \(a_{22}=+0.186630455\) \(a_{23}=-1.607197132\) \(a_{24}=-0.108406384\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.042136352\) \(a_{27}=+0.584412108\) \(a_{28}=+0.140009656\) \(a_{29}=-1.789109537\) \(a_{30}=-0.096961618\)
\(a_{31}=-0.338207954\) \(a_{32}=+0.176776695\) \(a_{33}=-0.080927731\) \(a_{34}=-0.448178547\) \(a_{35}=+0.125228443\)
\(a_{36}=-0.452992223\) \(a_{37}=+0.527544551\) \(a_{38}=+0.875181779\) \(a_{39}=-0.018271398\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.035922667\) \(a_{42}=-0.060711762\) \(a_{43}=+0.412570540\) \(a_{44}=+0.131967660\) \(a_{45}=-0.405168562\)
\(a_{46}=-1.136459991\) \(a_{47}=+0.279385393\) \(a_{48}=-0.076654889\) \(a_{49}=-0.921589185\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.194341663\) \(a_{52}=+0.029794901\) \(a_{53}=+0.466454554\) \(a_{54}=+0.413241765\) \(a_{55}=+0.118035463\)
\(a_{56}=+0.099001777\) \(a_{57}=-0.379501169\) \(a_{58}=-1.265091486\) \(a_{59}=+0.141902462\) \(a_{60}=-0.068562217\)
\(a_{61}=-1.690264392\) \(a_{62}=-0.239149138\) \(a_{63}=-0.253693141\) \(a_{64}=+0.125000000\) \(a_{65}=+0.026649369\)
\(a_{66}=-0.057224547\) \(a_{67}=-0.808750159\) \(a_{68}=-0.316910090\) \(a_{69}=+0.492798074\) \(a_{70}=+0.088549881\)
\(a_{71}=-0.715554202\) \(a_{72}=-0.320313873\) \(a_{73}=-0.852446378\) \(a_{74}=+0.373030329\) \(a_{75}=-0.061323912\)
\(a_{76}=+0.618846970\) \(a_{77}=+0.073906987\) \(a_{78}=-0.012919830\) \(a_{79}=+0.454769949\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.726792264\) \(a_{82}=+0.732507942\) \(a_{83}=+0.654214806\) \(a_{84}=-0.042929699\) \(a_{85}=-0.283453001\)
\(a_{86}=+0.291731427\) \(a_{87}=+0.548575975\) \(a_{88}=+0.093315227\) \(a_{89}=+0.345360913\) \(a_{90}=-0.286497438\)
\(a_{91}=+0.016686295\) \(a_{92}=-0.803598566\) \(a_{93}=+0.103701173\) \(a_{94}=+0.197555306\) \(a_{95}=+0.553513557\)
\(a_{96}=-0.054203192\) \(a_{97}=-1.180162787\) \(a_{98}=-0.651661962\) \(a_{99}=-0.239121295\) \(a_{100}=+0.099975586\)

Showing 100 of 211 available coefficients

Rows: Cols: