Properties

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

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.64274919042 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.080839253\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.764268765\) \(a_{7}=+1.531132989\) \(a_{8}=-0.353553391\) \(a_{9}=+0.168213492\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.915986378\) \(a_{12}=+0.540419627\) \(a_{13}=-0.806179942\) \(a_{14}=-1.082674520\) \(a_{15}=+0.483366009\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.603903079\) \(a_{18}=-0.118944901\) \(a_{19}=+0.890052229\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.654908637\) \(a_{22}=-0.647700179\) \(a_{23}=-1.219966175\) \(a_{24}=-0.382134383\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.570055304\) \(a_{27}=-0.899027509\) \(a_{28}=+0.765566495\) \(a_{29}=-1.437404645\) \(a_{30}=-0.341791383\)
\(a_{31}=+0.592768704\) \(a_{32}=-0.176776695\) \(a_{33}=+0.990034033\) \(a_{34}=+0.427023962\) \(a_{35}=+0.684743489\)
\(a_{36}=+0.084106746\) \(a_{37}=+0.980234058\) \(a_{38}=-0.629361967\) \(a_{39}=-0.871350927\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.087374596\) \(a_{42}=-1.170197119\) \(a_{43}=-1.137881900\) \(a_{44}=+0.457993189\) \(a_{45}=+0.075227360\)
\(a_{46}=+0.862646355\) \(a_{47}=-0.324142823\) \(a_{48}=+0.270209813\) \(a_{49}=+1.344368231\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.652722153\) \(a_{52}=-0.403089971\) \(a_{53}=-0.550686644\) \(a_{54}=+0.635708448\) \(a_{55}=+0.409641562\)
\(a_{56}=-0.541337260\) \(a_{57}=+0.962003387\) \(a_{58}=+1.016398572\) \(a_{59}=-1.437991096\) \(a_{60}=+0.241683004\)
\(a_{61}=+0.645030733\) \(a_{62}=-0.419150770\) \(a_{63}=+0.257557227\) \(a_{64}=+0.125000000\) \(a_{65}=-0.360534630\)
\(a_{66}=-0.700059778\) \(a_{67}=-0.159642106\) \(a_{68}=-0.301951539\) \(a_{69}=-1.318587329\) \(a_{70}=-0.484186765\)
\(a_{71}=+1.515932210\) \(a_{72}=-0.059472450\) \(a_{73}=-0.331655630\) \(a_{74}=-0.693130149\) \(a_{75}=+0.216167851\)
\(a_{76}=+0.445026115\) \(a_{77}=+1.402496961\) \(a_{78}=+0.616138149\) \(a_{79}=+0.877903180\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.139917713\) \(a_{82}=-0.061783169\) \(a_{83}=+0.333599001\) \(a_{84}=+0.827454319\) \(a_{85}=-0.270073667\)
\(a_{86}=+0.804604008\) \(a_{87}=-1.553603363\) \(a_{88}=-0.323850090\) \(a_{89}=-0.094085800\) \(a_{90}=-0.053193777\)
\(a_{91}=-1.234368704\) \(a_{92}=-0.609983087\) \(a_{93}=+0.640687683\) \(a_{94}=+0.229203588\) \(a_{95}=+0.398043458\)
\(a_{96}=-0.191067191\) \(a_{97}=+0.101263000\) \(a_{98}=-0.950611892\) \(a_{99}=+0.154081267\) \(a_{100}=+0.099975586\)

Showing 100 of 130 available coefficients

Rows: Cols: