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: \( 5.81798310167 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.671872556\) \(a_{3}=+0.577350269\) \(a_{4}=-0.548587269\) \(a_{5}=-0.296460810\)
\(a_{6}=+0.387905801\) \(a_{7}=+0.377964473\) \(a_{8}=-1.040453286\) \(a_{9}=+0.333333333\) \(a_{10}=-0.199183882\)
\(a_{11}=-1.195021328\) \(a_{12}=-0.316727007\) \(a_{13}=-1.723408512\) \(a_{14}=+0.253943956\) \(a_{15}=-0.171161729\)
\(a_{16}=-0.150464740\) \(a_{17}=-0.024943261\) \(a_{18}=+0.223957519\) \(a_{19}=-0.554493740\) \(a_{20}=+0.162634626\)
\(a_{21}=+0.218217890\) \(a_{22}=-0.802902034\) \(a_{23}=-0.097506497\) \(a_{24}=-0.600705985\) \(a_{25}=-0.912110988\)
\(a_{26}=-1.157910882\) \(a_{27}=+0.192450090\) \(a_{28}=-0.207346498\) \(a_{29}=+1.169794407\) \(a_{30}=-0.114998868\)
\(a_{31}=+0.773163906\) \(a_{32}=+0.939360157\) \(a_{33}=-0.689945886\) \(a_{34}=-0.016758693\) \(a_{35}=-0.112051654\)
\(a_{36}=-0.182862423\) \(a_{37}=+1.717270345\) \(a_{38}=-0.372549126\) \(a_{39}=-0.995010368\) \(a_{40}=+0.308453624\)
\(a_{41}=-1.621164200\) \(a_{42}=+0.146614612\) \(a_{43}=-0.335273097\) \(a_{44}=+0.655573487\) \(a_{45}=-0.098820270\)
\(a_{46}=-0.065511939\) \(a_{47}=+0.318038676\) \(a_{48}=-0.086870858\) \(a_{49}=+0.142857143\) \(a_{50}=-0.612822341\)
\(a_{51}=-0.014400998\) \(a_{52}=+0.945439969\) \(a_{53}=-1.211092975\) \(a_{54}=+0.129301934\) \(a_{55}=+0.354276991\)
\(a_{56}=-0.393254378\) \(a_{57}=-0.320137110\) \(a_{58}=+0.785952758\) \(a_{59}=-0.008538896\) \(a_{60}=+0.093897145\)
\(a_{61}=+0.076792808\) \(a_{62}=+0.519467610\) \(a_{63}=+0.125988158\) \(a_{64}=+0.781595049\) \(a_{65}=+0.510923084\)
\(a_{66}=-0.463555705\) \(a_{67}=-0.839024182\) \(a_{68}=+0.013683555\) \(a_{69}=-0.056295402\) \(a_{70}=-0.075284431\)
\(a_{71}=-0.631250168\) \(a_{72}=-0.346817762\) \(a_{73}=+1.581705996\) \(a_{74}=+1.153786816\) \(a_{75}=-0.526607524\)
\(a_{76}=+0.304188206\) \(a_{77}=-0.451675607\) \(a_{78}=-0.668520159\) \(a_{79}=-1.639792999\) \(a_{80}=+0.044606899\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.089215734\) \(a_{83}=-0.137891530\) \(a_{84}=-0.119711556\) \(a_{85}=+0.007394699\)
\(a_{86}=-0.225260792\) \(a_{87}=+0.675381116\) \(a_{88}=+1.243363868\) \(a_{89}=-0.456554013\) \(a_{90}=-0.066394627\)
\(a_{91}=-0.651387190\) \(a_{92}=+0.053490823\) \(a_{93}=+0.446386389\) \(a_{94}=+0.213681458\) \(a_{95}=+0.164385663\)
\(a_{96}=+0.542339839\) \(a_{97}=+1.255905871\) \(a_{98}=+0.095981794\) \(a_{99}=-0.398340443\) \(a_{100}=+0.500372476\)

Showing 100 of 238 available coefficients

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