Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.4385055061 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.786647124\) \(a_{3}=-0.577350269\) \(a_{4}=+2.192107945\) \(a_{5}=-1.077448678\)
\(a_{6}=-1.031521198\) \(a_{7}=+0.377964473\) \(a_{8}=+2.129876232\) \(a_{9}=+0.333333333\) \(a_{10}=-1.925020582\)
\(a_{11}=-0.530871790\) \(a_{12}=-1.265614112\) \(a_{13}=+1.058931429\) \(a_{14}=+0.675289139\) \(a_{15}=+0.622065284\)
\(a_{16}=+1.613229299\) \(a_{17}=+0.093711821\) \(a_{18}=+0.595549041\) \(a_{19}=+0.568138607\) \(a_{20}=-2.361883808\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.948480555\) \(a_{23}=-1.341710576\) \(a_{24}=-1.229684617\) \(a_{25}=+0.160895652\)
\(a_{26}=+1.891936792\) \(a_{27}=-0.192450087\) \(a_{28}=+0.828538925\) \(a_{29}=+0.015304152\) \(a_{30}=+1.111411148\)
\(a_{31}=-1.297506472\) \(a_{32}=+0.752395265\) \(a_{33}=+0.306498967\) \(a_{34}=+0.167429937\) \(a_{35}=-0.407237326\)
\(a_{36}=+0.730702677\) \(a_{37}=+1.052330818\) \(a_{38}=+1.015063173\) \(a_{39}=-0.611374406\) \(a_{40}=-2.294832304\)
\(a_{41}=+0.690467826\) \(a_{42}=-0.389878342\) \(a_{43}=+1.631937232\) \(a_{44}=-1.163728419\) \(a_{45}=-0.359149320\)
\(a_{46}=-2.397162944\) \(a_{47}=-0.245954425\) \(a_{48}=-0.931399150\) \(a_{49}=+0.142857143\) \(a_{50}=+0.287463756\)
\(a_{51}=-0.054104546\) \(a_{52}=+2.321291996\) \(a_{53}=+0.418601959\) \(a_{54}=-0.343840400\) \(a_{55}=+0.571987108\)
\(a_{56}=+0.805017556\) \(a_{57}=-0.328014961\) \(a_{58}=+0.027343124\) \(a_{59}=-0.589095855\) \(a_{60}=+1.363634337\)
\(a_{61}=+0.705272048\) \(a_{62}=-2.318186395\) \(a_{63}=+0.125988160\) \(a_{64}=-0.268964387\) \(a_{65}=-1.140944409\)
\(a_{66}=+0.547606499\) \(a_{67}=-0.516841186\) \(a_{68}=+0.205425715\) \(a_{69}=+0.774638611\) \(a_{70}=-0.727586957\)
\(a_{71}=+1.514790859\) \(a_{72}=+0.709959514\) \(a_{73}=-1.253966965\) \(a_{74}=+1.880136080\) \(a_{75}=-0.092890564\)
\(a_{76}=+1.245420965\) \(a_{77}=-0.200650711\) \(a_{78}=-1.092310128\) \(a_{79}=-0.911486473\) \(a_{80}=-1.738171955\)
\(a_{81}=+0.111111371\) \(a_{82}=+1.233622192\) \(a_{83}=-0.843175498\) \(a_{84}=-0.478357844\) \(a_{85}=-0.100969609\)
\(a_{86}=+2.915696290\) \(a_{87}=-0.008833053\) \(a_{88}=-1.130681813\) \(a_{89}=+0.063108711\) \(a_{90}=-0.641674398\)
\(a_{91}=+0.400239274\) \(a_{92}=-2.941178576\) \(a_{93}=+0.749101247\) \(a_{94}=-0.439458253\) \(a_{95}=-0.612147598\)
\(a_{96}=-0.434349611\) \(a_{97}=+0.136801631\) \(a_{98}=+0.255246459\) \(a_{99}=-0.176957672\) \(a_{100}=+0.352701801\)

Showing 100 of 1500 available coefficients

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