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: \( 5.1066115556 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.838269125\) \(a_{3}=+0.577350269\) \(a_{4}=-0.297304873\) \(a_{5}=+0.892244056\)
\(a_{6}=-0.483974905\) \(a_{7}=-0.377964473\) \(a_{8}=+1.087490622\) \(a_{9}=+0.333333333\) \(a_{10}=-0.747940644\)
\(a_{11}=-1.677127498\) \(a_{12}=-0.171649049\) \(a_{13}=-0.662068852\) \(a_{14}=+0.316835948\) \(a_{15}=+0.515137346\)
\(a_{16}=-0.614304939\) \(a_{17}=-0.510729319\) \(a_{18}=-0.279423042\) \(a_{19}=-0.171549324\) \(a_{20}=-0.265268506\)
\(a_{21}=-0.218217890\) \(a_{22}=+1.405884201\) \(a_{23}=-0.843603494\) \(a_{24}=+0.627863003\) \(a_{25}=-0.203900545\)
\(a_{26}=+0.554991877\) \(a_{27}=+0.192450090\) \(a_{28}=+0.112370680\) \(a_{29}=-1.992209991\) \(a_{30}=-0.431823732\)
\(a_{31}=+1.676092292\) \(a_{32}=-0.572537758\) \(a_{33}=-0.968290012\) \(a_{34}=+0.428128619\) \(a_{35}=-0.337236554\)
\(a_{36}=-0.099101624\) \(a_{37}=-0.097461154\) \(a_{38}=+0.143804502\) \(a_{39}=-0.382245630\) \(a_{40}=+0.970307043\)
\(a_{41}=+0.085783756\) \(a_{42}=+0.182925320\) \(a_{43}=-0.757320556\) \(a_{44}=+0.498618179\) \(a_{45}=+0.297414685\)
\(a_{46}=+0.707166763\) \(a_{47}=+1.152262776\) \(a_{48}=-0.354669122\) \(a_{49}=+0.142857143\) \(a_{50}=+0.170923532\)
\(a_{51}=-0.294869710\) \(a_{52}=+0.196836296\) \(a_{53}=-1.098625758\) \(a_{54}=-0.161324968\) \(a_{55}=-1.496407041\)
\(a_{56}=-0.411032820\) \(a_{57}=-0.099044048\) \(a_{58}=+1.670008127\) \(a_{59}=-0.380041657\) \(a_{60}=-0.153152843\)
\(a_{61}=-0.221323892\) \(a_{62}=-1.405016419\) \(a_{63}=-0.125988158\) \(a_{64}=+1.094245664\) \(a_{65}=-0.590726997\)
\(a_{66}=+0.811687622\) \(a_{67}=-0.728586964\) \(a_{68}=+0.151842316\) \(a_{69}=-0.487054704\) \(a_{70}=+0.282694991\)
\(a_{71}=+1.078893769\) \(a_{72}=+0.362496874\) \(a_{73}=+1.304060671\) \(a_{74}=+0.081698677\) \(a_{75}=-0.117722035\)
\(a_{76}=+0.051002450\) \(a_{77}=+0.633894611\) \(a_{78}=+0.320424710\) \(a_{79}=+0.343741922\) \(a_{80}=-0.548109930\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.071909874\) \(a_{83}=-1.167245631\) \(a_{84}=+0.064877242\) \(a_{85}=-0.455695199\)
\(a_{86}=+0.634838440\) \(a_{87}=-1.150202975\) \(a_{88}=-1.823860425\) \(a_{89}=+1.138572745\) \(a_{90}=-0.249313548\)
\(a_{91}=+0.250238505\) \(a_{92}=+0.250807430\) \(a_{93}=+0.967692336\) \(a_{94}=-0.965906309\) \(a_{95}=-0.153063864\)
\(a_{96}=-0.330554829\) \(a_{97}=-0.373467132\) \(a_{98}=-0.119752732\) \(a_{99}=-0.559042499\) \(a_{100}=+0.060620626\)

Showing 100 of 226 available coefficients

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