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: \( 6.74067882534 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.790979790\) \(a_{3}=-0.577350269\) \(a_{4}=+2.207608607\) \(a_{5}=+1.599262916\)
\(a_{6}=+1.034022664\) \(a_{7}=+0.377964473\) \(a_{8}=-2.162802609\) \(a_{9}=+0.333333333\) \(a_{10}=-2.864247562\)
\(a_{11}=+0.772681755\) \(a_{12}=-1.274563424\) \(a_{13}=+1.364520470\) \(a_{14}=-0.676926732\) \(a_{15}=-0.923334875\)
\(a_{16}=+1.665927155\) \(a_{17}=-1.321489287\) \(a_{18}=-0.596993263\) \(a_{19}=+0.984471106\) \(a_{20}=+3.530546579\)
\(a_{21}=-0.218217890\) \(a_{22}=-1.383857408\) \(a_{23}=-0.966158816\) \(a_{24}=+1.248694669\) \(a_{25}=+1.557641876\)
\(a_{26}=-2.443828584\) \(a_{27}=-0.192450090\) \(a_{28}=+0.834397624\) \(a_{29}=+0.159306957\) \(a_{30}=+1.653674101\)
\(a_{31}=+0.690629106\) \(a_{32}=-0.820839257\) \(a_{33}=-0.446108019\) \(a_{34}=+2.366760605\) \(a_{35}=+0.604464565\)
\(a_{36}=+0.735869536\) \(a_{37}=+0.081285818\) \(a_{38}=-1.763167855\) \(a_{39}=-0.787806261\) \(a_{40}=-3.458890008\)
\(a_{41}=-0.565590552\) \(a_{42}=+0.390823831\) \(a_{43}=-0.002837707\) \(a_{44}=+1.705778894\) \(a_{45}=+0.533087639\)
\(a_{46}=+1.730370914\) \(a_{47}=+0.449403989\) \(a_{48}=-0.961823491\) \(a_{49}=+0.142857143\) \(a_{50}=-2.789705119\)
\(a_{51}=+0.762962195\) \(a_{52}=+3.012327134\) \(a_{53}=+0.556084572\) \(a_{54}=+0.344674221\) \(a_{55}=+1.235721277\)
\(a_{56}=-0.817462548\) \(a_{57}=-0.568384658\) \(a_{58}=-0.285315540\) \(a_{59}=-0.359671103\) \(a_{60}=-2.038362018\)
\(a_{61}=+0.724273665\) \(a_{62}=-1.236902772\) \(a_{63}=+0.125988158\) \(a_{64}=-0.195820636\) \(a_{65}=+2.182226986\)
\(a_{66}=+0.798970447\) \(a_{67}=-0.841645814\) \(a_{68}=-2.917331124\) \(a_{69}=+0.557812053\) \(a_{70}=-1.082583820\)
\(a_{71}=-0.448718304\) \(a_{72}=-0.720934203\) \(a_{73}=+1.717481426\) \(a_{74}=-0.145581257\) \(a_{75}=-0.899304956\)
\(a_{76}=+2.173326887\) \(a_{77}=+0.292046252\) \(a_{78}=+1.410945091\) \(a_{79}=+0.269973507\) \(a_{80}=+2.664255520\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.012961247\) \(a_{83}=-1.734261532\) \(a_{84}=-0.481739693\) \(a_{85}=-2.113408811\)
\(a_{86}=+0.005082276\) \(a_{87}=-0.091975914\) \(a_{88}=-1.671158116\) \(a_{89}=+1.842799580\) \(a_{90}=-0.954749187\)
\(a_{91}=+0.515740260\) \(a_{92}=-2.132900519\) \(a_{93}=-0.398734901\) \(a_{94}=-0.804873462\) \(a_{95}=+1.574428132\)
\(a_{96}=+0.473911766\) \(a_{97}=+0.217460748\) \(a_{98}=-0.255854256\) \(a_{99}=+0.257560585\) \(a_{100}=+3.438663612\)

Showing 100 of 240 available coefficients

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