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: \( 2.65932874893 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.436150589\) \(a_{3}=-0.577350269\) \(a_{4}=-0.809772663\) \(a_{5}=+0.055166721\)
\(a_{6}=+0.251811660\) \(a_{7}=-0.377964473\) \(a_{8}=+0.789333413\) \(a_{9}=+0.333333333\) \(a_{10}=-0.024060998\)
\(a_{11}=-0.699982667\) \(a_{12}=+0.467522466\) \(a_{13}=-1.755221224\) \(a_{14}=+0.164849427\) \(a_{15}=-0.031850521\)
\(a_{16}=+0.465504433\) \(a_{17}=-0.089148277\) \(a_{18}=-0.145383531\) \(a_{19}=+0.079949502\) \(a_{20}=-0.044672504\)
\(a_{21}=+0.218217891\) \(a_{22}=+0.305297849\) \(a_{23}=+1.590583109\) \(a_{24}=-0.455721859\) \(a_{25}=-0.996956628\)
\(a_{26}=+0.765540769\) \(a_{27}=-0.192450090\) \(a_{28}=+0.306065301\) \(a_{29}=-0.324263124\) \(a_{30}=+0.013891617\)
\(a_{31}=-0.246883062\) \(a_{32}=-0.992363403\) \(a_{33}=+0.404135205\) \(a_{34}=+0.038882099\) \(a_{35}=-0.020851110\)
\(a_{36}=-0.269924239\) \(a_{37}=-0.695555206\) \(a_{38}=-0.034870051\) \(a_{39}=+1.013377409\) \(a_{40}=+0.043544852\)
\(a_{41}=-1.514564410\) \(a_{42}=-0.095175930\) \(a_{43}=+1.391777108\) \(a_{44}=+0.566826815\) \(a_{45}=+0.018388981\)
\(a_{46}=-0.693733907\) \(a_{47}=-0.352975722\) \(a_{48}=-0.268758988\) \(a_{49}=+0.142857145\) \(a_{50}=+0.434823191\)
\(a_{51}=+0.051469468\) \(a_{52}=+1.421330484\) \(a_{53}=+1.464979661\) \(a_{54}=+0.083937575\) \(a_{55}=-0.038615721\)
\(a_{56}=-0.298339759\) \(a_{57}=-0.046159294\) \(a_{58}=+0.141427624\) \(a_{59}=-1.229893116\) \(a_{60}=+0.025792166\)
\(a_{61}=-1.368958012\) \(a_{62}=+0.107677294\) \(a_{63}=-0.125987665\) \(a_{64}=-0.032684362\) \(a_{65}=-0.096829021\)
\(a_{66}=-0.176265154\) \(a_{67}=-1.445778706\) \(a_{68}=+0.072189965\) \(a_{69}=-0.918321927\) \(a_{70}=+0.009094261\)
\(a_{71}=+1.039233947\) \(a_{72}=+0.263110863\) \(a_{73}=+0.581943669\) \(a_{74}=+0.303366816\) \(a_{75}=+0.575593239\)
\(a_{76}=-0.064740950\) \(a_{77}=+0.264568566\) \(a_{78}=-0.441985009\) \(a_{79}=-0.324617963\) \(a_{80}=+0.025680226\)
\(a_{81}=+0.111111218\) \(a_{82}=+0.660578287\) \(a_{83}=+1.362157175\) \(a_{84}=-0.176706794\) \(a_{85}=-0.004918238\)
\(a_{86}=-0.607024247\) \(a_{87}=+0.187213373\) \(a_{88}=-0.552519621\) \(a_{89}=+0.550784037\) \(a_{90}=-0.008020658\)
\(a_{91}=+0.663411239\) \(a_{92}=-1.288010478\) \(a_{93}=+0.142538446\) \(a_{94}=+0.153950418\) \(a_{95}=+0.004410518\)
\(a_{96}=+0.572941245\) \(a_{97}=+0.961891926\) \(a_{98}=-0.062307255\) \(a_{99}=-0.233327616\) \(a_{100}=+0.807308394\)

Showing 100 of 1500 available coefficients

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