Properties

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

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 24.5039253761 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.556066500\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.393198393\) \(a_{7}=+0.040371033\) \(a_{8}=+0.353553391\) \(a_{9}=-0.690790048\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.960295116\) \(a_{12}=+0.278033250\) \(a_{13}=+1.719668514\) \(a_{14}=+0.028546631\) \(a_{15}=+0.248680499\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.122717510\) \(a_{18}=-0.488462327\) \(a_{19}=+0.090099062\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.022448979\) \(a_{22}=+1.386137970\) \(a_{23}=-1.458261254\) \(a_{24}=+0.196599196\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.215989268\) \(a_{27}=-0.940191704\) \(a_{28}=+0.020185516\) \(a_{29}=+1.058560040\) \(a_{30}=+0.175843667\)
\(a_{31}=-0.092847024\) \(a_{32}=+0.176776695\) \(a_{33}=+1.090054444\) \(a_{34}=+0.086774384\) \(a_{35}=+0.018054475\)
\(a_{36}=-0.345395024\) \(a_{37}=-1.755156111\) \(a_{38}=+0.063709658\) \(a_{39}=+0.956250052\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.384583610\) \(a_{42}=+0.015873825\) \(a_{43}=+1.148642540\) \(a_{44}=+0.980147558\) \(a_{45}=-0.308930701\)
\(a_{46}=-1.031146421\) \(a_{47}=+0.960857634\) \(a_{48}=+0.139016625\) \(a_{49}=-0.998370180\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.068239096\) \(a_{52}=+0.859834257\) \(a_{53}=-1.353583378\) \(a_{54}=-0.664815929\) \(a_{55}=+0.876670627\)
\(a_{56}=+0.014273315\) \(a_{57}=+0.050101070\) \(a_{58}=+0.748514982\) \(a_{59}=-0.331820040\) \(a_{60}=+0.124340249\)
\(a_{61}=+1.383192979\) \(a_{62}=-0.065652760\) \(a_{63}=-0.027887907\) \(a_{64}=+0.125000000\) \(a_{65}=+0.769059139\)
\(a_{66}=+0.770784889\) \(a_{67}=-0.713227637\) \(a_{68}=+0.061358755\) \(a_{69}=-0.810890231\) \(a_{70}=+0.012766441\)
\(a_{71}=+1.677314355\) \(a_{72}=-0.244231164\) \(a_{73}=+0.134547569\) \(a_{74}=-1.241082788\) \(a_{75}=+0.111213300\)
\(a_{76}=+0.045049531\) \(a_{77}=+0.079139138\) \(a_{78}=+0.676170896\) \(a_{79}=+1.022245681\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.167980938\) \(a_{82}=+0.979048460\) \(a_{83}=+0.566977829\) \(a_{84}=+0.011224489\) \(a_{85}=+0.054880939\)
\(a_{86}=+0.812212929\) \(a_{87}=+0.588629776\) \(a_{88}=+0.693068985\) \(a_{89}=-1.391917218\) \(a_{90}=-0.218446994\)
\(a_{91}=+0.069424793\) \(a_{92}=-0.729130627\) \(a_{93}=-0.051629120\) \(a_{94}=+0.679428948\) \(a_{95}=+0.040293525\)
\(a_{96}=+0.098299598\) \(a_{97}=+0.672270183\) \(a_{98}=-0.705954324\) \(a_{99}=-1.354152357\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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