Properties

Level $21$
Weight $0$
Character 21.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.09185429105 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.055262434\) \(a_{3}=+0.577350269\) \(a_{4}=+0.113578805\) \(a_{5}=-0.205580341\)
\(a_{6}=-0.609256050\) \(a_{7}=+0.377964473\) \(a_{8}=+0.935406988\) \(a_{9}=+0.333333333\) \(a_{10}=+0.216941211\)
\(a_{11}=+1.271471463\) \(a_{12}=+0.065574754\) \(a_{13}=-0.286610390\) \(a_{14}=-0.398851710\) \(a_{15}=-0.118691865\)
\(a_{16}=-1.100678660\) \(a_{17}=+1.433612839\) \(a_{18}=-0.351754145\) \(a_{19}=+0.263072306\) \(a_{20}=-0.023349569\)
\(a_{21}=+0.218217890\) \(a_{22}=-1.341736071\) \(a_{23}=+1.048690584\) \(a_{24}=+0.540057476\) \(a_{25}=-0.957736724\)
\(a_{26}=+0.302449178\) \(a_{27}=+0.192450090\) \(a_{28}=+0.042928753\) \(a_{29}=-0.066504408\) \(a_{30}=+0.125251066\)
\(a_{31}=+0.913191889\) \(a_{32}=+0.226097854\) \(a_{33}=+0.734084391\) \(a_{34}=-1.512837775\) \(a_{35}=-0.077702065\)
\(a_{36}=+0.037859602\) \(a_{37}=+0.670791769\) \(a_{38}=-0.277610323\) \(a_{39}=-0.165474587\) \(a_{40}=-0.192301287\)
\(a_{41}=-1.878526407\) \(a_{42}=-0.230277141\) \(a_{43}=+0.734054348\) \(a_{44}=+0.144412206\) \(a_{45}=-0.068526777\)
\(a_{46}=-1.106643771\) \(a_{47}=+1.108408003\) \(a_{48}=-0.635477133\) \(a_{49}=+0.142857137\) \(a_{50}=+1.010663602\)
\(a_{51}=+0.827696778\) \(a_{52}=-0.032552880\) \(a_{53}=+0.401243464\) \(a_{54}=-0.203085352\) \(a_{55}=-0.261389471\)
\(a_{56}=+0.353550656\) \(a_{57}=+0.151884785\) \(a_{58}=+0.070179472\) \(a_{59}=+1.467864235\) \(a_{60}=-0.013480620\)
\(a_{61}=-0.511629713\) \(a_{62}=-0.963657502\) \(a_{63}=+0.125988160\) \(a_{64}=+0.862086086\) \(a_{65}=+0.058921457\)
\(a_{66}=-0.774651681\) \(a_{67}=-1.740004357\) \(a_{68}=+0.162828034\) \(a_{69}=+0.605461784\) \(a_{70}=+0.081996064\)
\(a_{71}=-1.674617907\) \(a_{72}=+0.311802341\) \(a_{73}=-0.819164173\) \(a_{74}=-0.707861374\) \(a_{75}=-0.552949569\)
\(a_{76}=+0.029879447\) \(a_{77}=+0.480571063\) \(a_{78}=+0.174619119\) \(a_{79}=+1.573019135\) \(a_{80}=+0.226277888\)
\(a_{81}=+0.111111119\) \(a_{82}=+1.982338392\) \(a_{83}=-0.893997486\) \(a_{84}=+0.024784917\) \(a_{85}=-0.294722705\)
\(a_{86}=-0.774619921\) \(a_{87}=-0.038396249\) \(a_{88}=+1.189343390\) \(a_{89}=+1.219624219\) \(a_{90}=+0.072313585\)
\(a_{91}=-0.108328691\) \(a_{92}=+0.119108894\) \(a_{93}=+0.527231596\) \(a_{94}=-1.169661347\) \(a_{95}=-0.054082521\)
\(a_{96}=+0.130537654\) \(a_{97}=-0.405462083\) \(a_{98}=-0.150751778\) \(a_{99}=+0.423823807\) \(a_{100}=-0.108778604\)

Showing 100 of 1500 available coefficients

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