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: \( 28.522720264 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.082217403\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.058136483\) \(a_{7}=-1.668828225\) \(a_{8}=+0.353553391\) \(a_{9}=-0.993240299\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.805805904\) \(a_{12}=+0.041108702\) \(a_{13}=-1.640470665\) \(a_{14}=-1.180039754\) \(a_{15}=+0.036768740\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.582021675\) \(a_{18}=-0.702326951\) \(a_{19}=+0.885891672\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.137206723\) \(a_{22}=+1.276897600\) \(a_{23}=-1.281479222\) \(a_{24}=+0.029068242\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.159987932\) \(a_{27}=-0.163879041\) \(a_{28}=-0.834414112\) \(a_{29}=-1.161080579\) \(a_{30}=+0.025999426\)
\(a_{31}=-0.083127040\) \(a_{32}=+0.176776695\) \(a_{33}=+0.148468672\) \(a_{34}=+0.411551473\) \(a_{35}=-0.746322671\)
\(a_{36}=-0.496620149\) \(a_{37}=-0.126890463\) \(a_{38}=+0.626420009\) \(a_{39}=-0.134875238\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.048145992\) \(a_{42}=-0.097019804\) \(a_{43}=+1.466989981\) \(a_{44}=+0.902902952\) \(a_{45}=-0.444190565\)
\(a_{46}=-0.906142648\) \(a_{47}=-0.395132449\) \(a_{48}=+0.020554351\) \(a_{49}=+1.784987643\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.047852311\) \(a_{52}=-0.820235333\) \(a_{53}=+0.623188240\) \(a_{54}=-0.115879981\) \(a_{55}=+0.807580951\)
\(a_{56}=-0.590019877\) \(a_{57}=+0.072835713\) \(a_{58}=-0.821007951\) \(a_{59}=+0.273766807\) \(a_{60}=+0.018384370\)
\(a_{61}=+0.606240666\) \(a_{62}=-0.058779694\) \(a_{63}=+1.657547444\) \(a_{64}=+0.125000000\) \(a_{65}=-0.733640785\)
\(a_{66}=+0.104983205\) \(a_{67}=+0.030552143\) \(a_{68}=+0.291010837\) \(a_{69}=-0.105359894\) \(a_{70}=-0.527729821\)
\(a_{71}=-0.913872338\) \(a_{72}=-0.351163475\) \(a_{73}=+1.512899691\) \(a_{74}=-0.089725107\) \(a_{75}=+0.016443481\)
\(a_{76}=+0.442945836\) \(a_{77}=-3.013579860\) \(a_{78}=-0.095371195\) \(a_{79}=+0.059121510\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.979766589\) \(a_{82}=+0.034044357\) \(a_{83}=-0.952023002\) \(a_{84}=-0.068603361\) \(a_{85}=+0.260288006\)
\(a_{86}=+1.037318564\) \(a_{87}=-0.095461030\) \(a_{88}=+0.638448800\) \(a_{89}=+1.615623900\) \(a_{90}=-0.314090161\)
\(a_{91}=+2.737663748\) \(a_{92}=-0.640739611\) \(a_{93}=-0.006834489\) \(a_{94}=-0.279400834\) \(a_{95}=+0.396182800\)
\(a_{96}=+0.014534121\) \(a_{97}=-0.897136316\) \(a_{98}=+1.262176867\) \(a_{99}=-1.793599195\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

Rows: Cols: