Properties

Level $23$
Weight $0$
Character 23.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.57958924015 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.951519979\) \(a_{3}=-0.031708747\) \(a_{4}=-0.094609729\) \(a_{5}=+1.040653188\)
\(a_{6}=+0.030171506\) \(a_{7}=+0.607443624\) \(a_{8}=+1.041543027\) \(a_{9}=-0.998994555\) \(a_{10}=-0.990202300\)
\(a_{11}=+0.513049466\) \(a_{12}=+0.002999956\) \(a_{13}=-1.140010011\) \(a_{14}=-0.577994744\) \(a_{15}=-0.032997809\)
\(a_{16}=-0.896439269\) \(a_{17}=+1.556687632\) \(a_{18}=+0.950563277\) \(a_{19}=+0.705256468\) \(a_{20}=-0.098455916\)
\(a_{21}=-0.019261274\) \(a_{22}=-0.488176817\) \(a_{23}=-0.208514418\) \(a_{24}=-0.033026024\) \(a_{25}=+0.082959063\)
\(a_{26}=+1.084742304\) \(a_{27}=+0.063385606\) \(a_{28}=-0.057470086\) \(a_{29}=-1.644961232\) \(a_{30}=+0.031398101\)
\(a_{31}=+1.258230971\) \(a_{32}=-0.188563123\) \(a_{33}=-0.016268143\) \(a_{34}=-1.481219395\) \(a_{35}=+0.632138112\)
\(a_{36}=+0.094514600\) \(a_{37}=-0.388851734\) \(a_{38}=-0.671065615\) \(a_{39}=+0.036148243\) \(a_{40}=+1.083885051\)
\(a_{41}=-0.305626157\) \(a_{42}=+0.018327539\) \(a_{43}=-0.240092099\) \(a_{44}=-0.048539523\) \(a_{45}=-1.039606796\)
\(a_{46}=+0.198405617\) \(a_{47}=+1.291383102\) \(a_{48}=+0.028424957\) \(a_{49}=-0.631012246\) \(a_{50}=-0.078937196\)
\(a_{51}=-0.049360555\) \(a_{52}=+0.107856020\) \(a_{53}=+1.476716507\) \(a_{54}=-0.060312682\) \(a_{55}=+0.533906594\)
\(a_{56}=+0.632678702\) \(a_{57}=-0.022362887\) \(a_{58}=+1.565213423\) \(a_{59}=-0.876903803\) \(a_{60}=+0.003121936\)
\(a_{61}=-0.173143767\) \(a_{62}=-1.197231945\) \(a_{63}=-0.606832911\) \(a_{64}=+1.075860884\) \(a_{65}=-1.186355097\)
\(a_{66}=+0.015479534\) \(a_{67}=-1.053730593\) \(a_{68}=-0.147277874\) \(a_{69}=+0.006611675\) \(a_{70}=-0.601491964\)
\(a_{71}=+0.612705060\) \(a_{72}=-1.040495743\) \(a_{73}=-0.116543270\) \(a_{74}=+0.370000226\) \(a_{75}=-0.002630580\)
\(a_{76}=-0.066724060\) \(a_{77}=+0.311648646\) \(a_{78}=-0.034395789\) \(a_{79}=-0.663667366\) \(a_{80}=-0.932882456\)
\(a_{81}=+0.996984680\) \(a_{82}=+0.290809436\) \(a_{83}=+0.252236433\) \(a_{84}=+0.001822281\) \(a_{85}=+1.619971979\)
\(a_{86}=+0.228452385\) \(a_{87}=+0.052159632\) \(a_{88}=+0.534363027\) \(a_{89}=+0.589892547\) \(a_{90}=+0.989206779\)
\(a_{91}=-0.692491822\) \(a_{92}=+0.019727349\) \(a_{93}=-0.039896945\) \(a_{94}=-1.228776735\) \(a_{95}=+0.733927436\)
\(a_{96}=+0.005979137\) \(a_{97}=+0.524248445\) \(a_{98}=+0.600420747\) \(a_{99}=-0.512533612\) \(a_{100}=-0.007848740\)

Showing 100 of 1500 available coefficients

Rows: Cols: