Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 26.2369605037 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.051359362\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.036316553\) \(a_{7}=+1.675735128\) \(a_{8}=+0.353553391\) \(a_{9}=-0.997362216\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.404968252\) \(a_{12}=+0.025679681\) \(a_{13}=+1.668618648\) \(a_{14}=+1.184923673\) \(a_{15}=+0.022968605\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.141856111\) \(a_{18}=-0.705241586\) \(a_{19}=+0.796413651\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.086064688\) \(a_{22}=+0.286355797\) \(a_{23}=+1.239801190\) \(a_{24}=+0.018158277\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.179891561\) \(a_{27}=-0.102583250\) \(a_{28}=+0.837867564\) \(a_{29}=-1.598082602\) \(a_{30}=+0.016241256\)
\(a_{31}=+1.591877610\) \(a_{32}=+0.176776695\) \(a_{33}=+0.020798911\) \(a_{34}=-0.807414200\) \(a_{35}=+0.749411532\)
\(a_{36}=-0.498681108\) \(a_{37}=+0.981229654\) \(a_{38}=+0.563149493\) \(a_{39}=+0.085699190\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.621143815\) \(a_{42}=+0.060856924\) \(a_{43}=-0.796992803\) \(a_{44}=+0.202484126\) \(a_{45}=-0.446033943\)
\(a_{46}=+0.876671829\) \(a_{47}=-1.149713316\) \(a_{48}=+0.012839841\) \(a_{49}=+1.808088221\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.058645002\) \(a_{52}=+0.834309324\) \(a_{53}=-0.432012915\) \(a_{54}=-0.072537311\) \(a_{55}=+0.181107308\)
\(a_{56}=+0.592461836\) \(a_{57}=+0.040903297\) \(a_{58}=-1.130015045\) \(a_{59}=-0.682584822\) \(a_{60}=+0.011484303\)
\(a_{61}=-0.970928523\) \(a_{62}=+1.125627453\) \(a_{63}=-1.671314901\) \(a_{64}=+0.125000000\) \(a_{65}=+0.746228945\)
\(a_{66}=+0.014707051\) \(a_{67}=+0.353281606\) \(a_{68}=-0.570928056\) \(a_{69}=+0.063675398\) \(a_{70}=+0.529913976\)
\(a_{71}=+0.007441723\) \(a_{72}=-0.352620793\) \(a_{73}=+1.816680304\) \(a_{74}=+0.693834142\) \(a_{75}=+0.010271872\)
\(a_{76}=+0.398206825\) \(a_{77}=+0.678619526\) \(a_{78}=+0.060598478\) \(a_{79}=-1.017795557\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.992093606\) \(a_{82}=+0.439215004\) \(a_{83}=-0.967461321\) \(a_{84}=+0.043032344\) \(a_{85}=-0.510653577\)
\(a_{86}=-0.563559015\) \(a_{87}=-0.082076503\) \(a_{88}=+0.143177899\) \(a_{89}=-0.062192669\) \(a_{90}=-0.315393625\)
\(a_{91}=+2.796162884\) \(a_{92}=+0.619900595\) \(a_{93}=+0.081757819\) \(a_{94}=-0.812970082\) \(a_{95}=+0.356167012\)
\(a_{96}=+0.009079138\) \(a_{97}=+0.843273897\) \(a_{98}=+1.278511442\) \(a_{99}=-0.403900033\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

Rows: Cols: