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: \( 25.0775787865 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.109630859\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.784627505\) \(a_{7}=+0.955470795\) \(a_{8}=-0.353553391\) \(a_{9}=+0.231280643\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.585850533\) \(a_{12}=-0.554815429\) \(a_{13}=-1.343658101\) \(a_{14}=-0.675619878\) \(a_{15}=-0.496242006\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.460572438\) \(a_{18}=-0.163540111\) \(a_{19}=+1.132513090\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.060219879\) \(a_{22}=+1.121365666\) \(a_{23}=+0.440839938\) \(a_{24}=+0.392313752\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.950109755\) \(a_{27}=+0.852994720\) \(a_{28}=+0.477735398\) \(a_{29}=-1.268826561\) \(a_{30}=+0.350896088\)
\(a_{31}=-1.208131002\) \(a_{32}=-0.176776695\) \(a_{33}=+1.759708689\) \(a_{34}=+1.032780675\) \(a_{35}=+0.427299530\)
\(a_{36}=+0.115640321\) \(a_{37}=+1.066893360\) \(a_{38}=-0.800807686\) \(a_{39}=+1.490964493\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.436012858\) \(a_{42}=+0.749688666\) \(a_{43}=-1.091989889\) \(a_{44}=-0.792925266\) \(a_{45}=+0.103431848\)
\(a_{46}=-0.311720909\) \(a_{47}=-1.097137495\) \(a_{48}=-0.277407715\) \(a_{49}=-0.087075560\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.620696248\) \(a_{52}=-0.671829051\) \(a_{53}=-0.987835703\) \(a_{54}=-0.603158351\) \(a_{55}=-0.709213919\)
\(a_{56}=-0.337809939\) \(a_{57}=-1.256671473\) \(a_{58}=+0.897195866\) \(a_{59}=+1.416361470\) \(a_{60}=-0.248121003\)
\(a_{61}=-0.173587323\) \(a_{62}=+0.854277624\) \(a_{63}=+0.220981900\) \(a_{64}=+0.125000000\) \(a_{65}=-0.600902171\)
\(a_{66}=-1.244301947\) \(a_{67}=+0.775850675\) \(a_{68}=-0.730286219\) \(a_{69}=-0.489169599\) \(a_{70}=-0.302146395\)
\(a_{71}=-1.108154100\) \(a_{72}=-0.081770055\) \(a_{73}=-0.153193409\) \(a_{74}=-0.754407530\) \(a_{75}=-0.221926172\)
\(a_{76}=+0.566256545\) \(a_{77}=-1.515233870\) \(a_{78}=-1.054271103\) \(a_{79}=+1.803586048\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.177789907\) \(a_{82}=+0.308307649\) \(a_{83}=-0.866395524\) \(a_{84}=-0.530109939\) \(a_{85}=-0.653187851\)
\(a_{86}=+0.772153455\) \(a_{87}=+1.407929107\) \(a_{88}=+0.560682833\) \(a_{89}=-0.057158070\) \(a_{90}=-0.073137361\)
\(a_{91}=-1.283826074\) \(a_{92}=+0.220419969\) \(a_{93}=+1.340579441\) \(a_{94}=+0.775793362\) \(a_{95}=+0.506475251\)
\(a_{96}=+0.196156876\) \(a_{97}=-0.674566536\) \(a_{98}=+0.061571719\) \(a_{99}=-0.366776531\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

Rows: Cols: