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: \( 6.37374126744 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.836118833\) \(a_{3}=-0.577350269\) \(a_{4}=+2.371332367\) \(a_{5}=+0.951986028\)
\(a_{6}=-1.060083702\) \(a_{7}=-0.377964473\) \(a_{8}=+2.517929185\) \(a_{9}=+0.333333333\) \(a_{10}=+1.747959474\)
\(a_{11}=-0.049639127\) \(a_{12}=-1.369089381\) \(a_{13}=+1.716512427\) \(a_{14}=-0.693987687\) \(a_{15}=-0.549629389\)
\(a_{16}=+2.251884829\) \(a_{17}=+1.310493794\) \(a_{18}=+0.612039611\) \(a_{19}=-0.250506163\) \(a_{20}=+2.257475281\)
\(a_{21}=+0.218217890\) \(a_{22}=-0.091143336\) \(a_{23}=-1.301108922\) \(a_{24}=-1.453727093\) \(a_{25}=-0.093722603\)
\(a_{26}=+3.151720794\) \(a_{27}=-0.192450090\) \(a_{28}=-0.896279389\) \(a_{29}=+0.438953455\) \(a_{30}=-1.009184873\)
\(a_{31}=-1.438160446\) \(a_{32}=+1.616798958\) \(a_{33}=+0.028659163\) \(a_{34}=+2.406222335\) \(a_{35}=-0.359816897\)
\(a_{36}=+0.790444122\) \(a_{37}=-0.651070709\) \(a_{38}=-0.459959083\) \(a_{39}=-0.991028912\) \(a_{40}=+2.397033404\)
\(a_{41}=-0.731826341\) \(a_{42}=+0.400673978\) \(a_{43}=-1.470067939\) \(a_{44}=-0.117710868\) \(a_{45}=+0.317328676\)
\(a_{46}=-2.388990595\) \(a_{47}=+1.822710543\) \(a_{48}=-1.300126312\) \(a_{49}=+0.142857143\) \(a_{50}=-0.172085836\)
\(a_{51}=-0.756613945\) \(a_{52}=+4.070421478\) \(a_{53}=+0.289328875\) \(a_{54}=-0.353361234\) \(a_{55}=-0.047255755\)
\(a_{56}=-0.951687778\) \(a_{57}=+0.144629800\) \(a_{58}=+0.805970705\) \(a_{59}=-0.583719518\) \(a_{60}=-1.303353961\)
\(a_{61}=-0.604002747\) \(a_{62}=-2.640633480\) \(a_{63}=-0.125988158\) \(a_{64}=+0.716750186\) \(a_{65}=+1.634095848\)
\(a_{66}=+0.052621629\) \(a_{67}=+0.715563872\) \(a_{68}=+3.107616350\) \(a_{69}=+0.751195587\) \(a_{70}=-0.660666581\)
\(a_{71}=-1.206561423\) \(a_{72}=+0.839309728\) \(a_{73}=+0.282250859\) \(a_{74}=-1.195443190\) \(a_{75}=+0.054110770\)
\(a_{76}=-0.594033372\) \(a_{77}=+0.018761826\) \(a_{78}=-1.819646849\) \(a_{79}=+0.283949336\) \(a_{80}=+2.143762894\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.343720127\) \(a_{83}=-0.784640820\) \(a_{84}=+0.517467146\) \(a_{85}=+1.247571781\)
\(a_{86}=-2.699219429\) \(a_{87}=-0.253429895\) \(a_{88}=-0.124987806\) \(a_{89}=+0.816831724\) \(a_{90}=+0.582653158\)
\(a_{91}=-0.648780715\) \(a_{92}=-3.085361701\) \(a_{93}=+0.830322321\) \(a_{94}=+3.346713154\) \(a_{95}=-0.238478367\)
\(a_{96}=-0.933459314\) \(a_{97}=+0.264169583\) \(a_{98}=+0.262302690\) \(a_{99}=-0.016546376\) \(a_{100}=-0.222247441\)

Showing 100 of 262 available coefficients

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