Properties

Level $15$
Weight $0$
Character 15.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.49290270259 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.881838111\) \(a_{3}=+0.577350269\) \(a_{4}=-0.222361546\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.509129471\) \(a_{7}=-1.740205188\) \(a_{8}=+1.077924997\) \(a_{9}=+0.333333333\) \(a_{10}=+0.394369992\)
\(a_{11}=+0.058907224\) \(a_{12}=-0.128380498\) \(a_{13}=-1.081305487\) \(a_{14}=+1.534579255\) \(a_{15}=-0.258198890\)
\(a_{16}=-0.728193797\) \(a_{17}=-0.269112022\) \(a_{18}=-0.293946037\) \(a_{19}=+0.921442691\) \(a_{20}=+0.099443106\)
\(a_{21}=-1.004707934\) \(a_{22}=-0.051946635\) \(a_{23}=-0.732933493\) \(a_{24}=+0.622340287\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.953536388\) \(a_{27}=+0.192450090\) \(a_{28}=+0.386954716\) \(a_{29}=+0.113496132\) \(a_{30}=+0.227689621\)
\(a_{31}=-0.692575194\) \(a_{32}=-0.435775954\) \(a_{33}=+0.034010101\) \(a_{34}=+0.237313236\) \(a_{35}=+0.778243419\)
\(a_{36}=-0.074120515\) \(a_{37}=-1.509996449\) \(a_{38}=-0.812563282\) \(a_{39}=-0.624292014\) \(a_{40}=-0.482062713\)
\(a_{41}=+0.961724872\) \(a_{42}=+0.885989746\) \(a_{43}=-0.365486415\) \(a_{44}=-0.013098701\) \(a_{45}=-0.149071199\)
\(a_{46}=+0.646328687\) \(a_{47}=+0.164518213\) \(a_{48}=-0.420422885\) \(a_{49}=+2.028314095\) \(a_{50}=-0.176367623\)
\(a_{51}=-0.155371898\) \(a_{52}=+0.240440760\) \(a_{53}=+1.035211369\) \(a_{54}=-0.169709824\) \(a_{55}=-0.026344112\)
\(a_{56}=-1.875810672\) \(a_{57}=+0.531995185\) \(a_{58}=-0.100085214\) \(a_{59}=-1.763961400\) \(a_{60}=+0.057413510\)
\(a_{61}=-0.845375476\) \(a_{62}=+0.610739203\) \(a_{63}=-0.580068401\) \(a_{64}=+1.112477633\) \(a_{65}=+0.483574517\)
\(a_{66}=-0.029991398\) \(a_{67}=-0.801668347\) \(a_{68}=+0.059840162\) \(a_{69}=-0.423159352\) \(a_{70}=-0.686284749\)
\(a_{71}=+0.753004931\) \(a_{72}=+0.359308304\) \(a_{73}=+0.835769965\) \(a_{74}=+1.331572416\) \(a_{75}=+0.115470054\)
\(a_{76}=-0.204893422\) \(a_{77}=-0.102510656\) \(a_{78}=+0.550524490\) \(a_{79}=-1.066624954\) \(a_{80}=+0.325658166\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.848085644\) \(a_{83}=-0.727957610\) \(a_{84}=+0.223408408\) \(a_{85}=+0.120350555\)
\(a_{86}=+0.322299850\) \(a_{87}=+0.065527022\) \(a_{88}=+0.063497568\) \(a_{89}=-0.211120777\) \(a_{90}=+0.131456663\)
\(a_{91}=+1.881693420\) \(a_{92}=+0.162976235\) \(a_{93}=-0.399858470\) \(a_{94}=-0.145078429\) \(a_{95}=-0.412081696\)
\(a_{96}=-0.251595366\) \(a_{97}=-1.185198411\) \(a_{98}=-1.788644628\) \(a_{99}=+0.019635715\) \(a_{100}=-0.044472494\)

Showing 100 of 1500 available coefficients

Rows: Cols: