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: \( 5.46083368454 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.972483823\) \(a_{3}=+0.577350269\) \(a_{4}=+2.890692432\) \(a_{5}=-0.713513080\)
\(a_{6}=+1.138814066\) \(a_{7}=+0.377964473\) \(a_{8}=+3.729360237\) \(a_{9}=+0.333333333\) \(a_{10}=-1.407393008\)
\(a_{11}=-0.258961304\) \(a_{12}=+1.668942054\) \(a_{13}=-0.502418359\) \(a_{14}=+0.745528809\) \(a_{15}=-0.411946969\)
\(a_{16}=+4.465410305\) \(a_{17}=+0.082875900\) \(a_{18}=+0.657494608\) \(a_{19}=-1.266322934\) \(a_{20}=-2.062546861\)
\(a_{21}=+0.218217890\) \(a_{22}=-0.510796982\) \(a_{23}=+0.090335270\) \(a_{24}=+2.153147137\) \(a_{25}=-0.490899084\)
\(a_{26}=-0.991012085\) \(a_{27}=+0.192450090\) \(a_{28}=+1.092579042\) \(a_{29}=-1.555473809\) \(a_{30}=-0.812558732\)
\(a_{31}=-0.689613420\) \(a_{32}=+5.078589354\) \(a_{33}=-0.149511378\) \(a_{34}=+0.163471372\) \(a_{35}=-0.269682595\)
\(a_{36}=+0.963564144\) \(a_{37}=+0.578114433\) \(a_{38}=-2.497801501\) \(a_{39}=-0.290071375\) \(a_{40}=-2.660947310\)
\(a_{41}=-0.252793378\) \(a_{42}=+0.430431258\) \(a_{43}=+0.643638227\) \(a_{44}=-0.748577481\) \(a_{45}=-0.237837693\)
\(a_{46}=+0.178184858\) \(a_{47}=+0.977217145\) \(a_{48}=+2.578105842\) \(a_{49}=+0.142857143\) \(a_{50}=-0.968290503\)
\(a_{51}=+0.047848423\) \(a_{52}=-1.452336948\) \(a_{53}=+1.356137086\) \(a_{54}=+0.379604689\) \(a_{55}=+0.184772277\)
\(a_{56}=+1.409565677\) \(a_{57}=-0.731111887\) \(a_{58}=-3.068146925\) \(a_{59}=+0.355547319\) \(a_{60}=-1.190811986\)
\(a_{61}=-1.052105444\) \(a_{62}=-1.360251315\) \(a_{63}=+0.125988158\) \(a_{64}=+5.552025039\) \(a_{65}=+0.358482071\)
\(a_{66}=-0.294908775\) \(a_{67}=+0.485506328\) \(a_{68}=+0.239568737\) \(a_{69}=+0.052155092\) \(a_{70}=-0.531944557\)
\(a_{71}=-0.459628228\) \(a_{72}=+1.243120079\) \(a_{73}=-0.196969519\) \(a_{74}=+1.140321368\) \(a_{75}=-0.283420719\)
\(a_{76}=-3.660550121\) \(a_{77}=-0.097878173\) \(a_{78}=-0.572161094\) \(a_{79}=+1.499544189\) \(a_{80}=-3.186128661\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.498630849\) \(a_{83}=+1.854214215\) \(a_{84}=+0.630800804\) \(a_{85}=-0.059133039\)
\(a_{86}=+1.269565991\) \(a_{87}=-0.898053222\) \(a_{88}=-0.965759989\) \(a_{89}=-0.176343168\) \(a_{90}=-0.469131003\)
\(a_{91}=-0.189896290\) \(a_{92}=+0.261131480\) \(a_{93}=-0.398148494\) \(a_{94}=+1.927545009\) \(a_{95}=+0.903537977\)
\(a_{96}=+2.932124930\) \(a_{97}=-0.887886721\) \(a_{98}=+0.281783403\) \(a_{99}=-0.086320435\) \(a_{100}=-1.419038268\)

Showing 100 of 226 available coefficients

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