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: \( 1.27404261148 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.594789813\) \(a_{3}=-0.577350268\) \(a_{4}=+1.543354551\) \(a_{5}=+0.685706616\)
\(a_{6}=+0.920752329\) \(a_{7}=-0.377964469\) \(a_{8}=-0.866536304\) \(a_{9}=+0.333333327\) \(a_{10}=-1.093557936\)
\(a_{11}=-0.247960731\) \(a_{12}=-0.891056154\) \(a_{13}=+0.615656577\) \(a_{14}=+0.602773869\) \(a_{15}=-0.395892909\)
\(a_{16}=-0.161411245\) \(a_{17}=+0.908259760\) \(a_{18}=-0.531596642\) \(a_{19}=+0.959812486\) \(a_{20}=+1.058288452\)
\(a_{21}=+0.218217977\) \(a_{22}=+0.395445279\) \(a_{23}=-1.686434812\) \(a_{24}=+0.500294865\) \(a_{25}=-0.529806284\)
\(a_{26}=-0.981842592\) \(a_{27}=-0.192450183\) \(a_{28}=-0.583333650\) \(a_{29}=+0.570627538\) \(a_{30}=+0.631366652\)
\(a_{31}=+0.178901141\) \(a_{32}=+1.123953339\) \(a_{33}=+0.143160151\) \(a_{34}=-1.448483395\) \(a_{35}=-0.259172614\)
\(a_{36}=+0.514451588\) \(a_{37}=+1.120269131\) \(a_{38}=-1.530699488\) \(a_{39}=-0.355449681\) \(a_{40}=-0.594189380\)
\(a_{41}=-0.274038582\) \(a_{42}=-0.348012313\) \(a_{43}=-0.145549183\) \(a_{44}=-0.382691951\) \(a_{45}=+0.228569265\)
\(a_{46}=+2.689508608\) \(a_{47}=+0.361919659\) \(a_{48}=+0.093192355\) \(a_{49}=+0.142856723\) \(a_{50}=+0.844927254\)
\(a_{51}=-0.524378971\) \(a_{52}=+0.950170658\) \(a_{53}=-0.410730952\) \(a_{54}=+0.306918856\) \(a_{55}=-0.170028578\)
\(a_{56}=+0.327513896\) \(a_{57}=-0.554150580\) \(a_{58}=-0.910032733\) \(a_{59}=+0.660812760\) \(a_{60}=-0.611007632\)
\(a_{61}=-1.413639859\) \(a_{62}=-0.285309475\) \(a_{63}=-0.125988100\) \(a_{64}=-1.631058013\) \(a_{65}=+0.422159320\)
\(a_{66}=-0.228309427\) \(a_{67}=-1.530745188\) \(a_{68}=+1.401767998\) \(a_{69}=+0.973662551\) \(a_{70}=+0.413318706\)
\(a_{71}=+0.651547885\) \(a_{72}=-0.288853589\) \(a_{73}=-0.649649359\) \(a_{74}=-1.786590336\) \(a_{75}=+0.305883711\)
\(a_{76}=+1.481332851\) \(a_{77}=+0.093721334\) \(a_{78}=+0.566867621\) \(a_{79}=+1.702888810\) \(a_{80}=-0.110675183\)
\(a_{81}=+0.111115708\) \(a_{82}=+0.437036005\) \(a_{83}=+1.012424235\) \(a_{84}=+0.336779077\) \(a_{85}=+0.622802521\)
\(a_{86}=+0.232119964\) \(a_{87}=-0.329454283\) \(a_{88}=+0.214868519\) \(a_{89}=-0.898215767\) \(a_{90}=-0.364519532\)
\(a_{91}=-0.232696242\) \(a_{92}=-2.602766806\) \(a_{93}=-0.103288218\) \(a_{94}=-0.577186707\) \(a_{95}=+0.658149834\)
\(a_{96}=-0.648914149\) \(a_{97}=-0.390214327\) \(a_{98}=-0.227828715\) \(a_{99}=-0.082654654\) \(a_{100}=-0.817678442\)

Showing 100 of 1500 available coefficients

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