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: \( 2.77837816936 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.725392743\) \(a_{3}=+0.577350269\) \(a_{4}=+1.976980117\) \(a_{5}=-1.217417470\)
\(a_{6}=-0.996155965\) \(a_{7}=-0.377964473\) \(a_{8}=-1.685674404\) \(a_{9}=+0.333333333\) \(a_{10}=+2.100523267\)
\(a_{11}=-1.072470677\) \(a_{12}=+1.141410003\) \(a_{13}=-0.716733990\) \(a_{14}=+0.652137159\) \(a_{15}=-0.702876304\)
\(a_{16}=+0.931470267\) \(a_{17}=+1.161437847\) \(a_{18}=-0.575130914\) \(a_{19}=-1.116793810\) \(a_{20}=-2.406810132\)
\(a_{21}=-0.218217890\) \(a_{22}=+1.850433123\) \(a_{23}=+0.495702363\) \(a_{24}=-0.973224571\) \(a_{25}=+0.482105295\)
\(a_{26}=+1.236647624\) \(a_{27}=+0.192450090\) \(a_{28}=-0.747228247\) \(a_{29}=-1.150467535\) \(a_{30}=+1.212737672\)
\(a_{31}=-0.257754772\) \(a_{32}=+0.078522369\) \(a_{33}=-0.619191230\) \(a_{34}=-2.003936435\) \(a_{35}=+0.460140543\)
\(a_{36}=+0.658993371\) \(a_{37}=+0.256288014\) \(a_{38}=+1.926907946\) \(a_{39}=-0.413806582\) \(a_{40}=+2.052169439\)
\(a_{41}=-0.137836861\) \(a_{42}=+0.376511625\) \(a_{43}=+0.883175400\) \(a_{44}=-2.120253300\) \(a_{45}=-0.405805887\)
\(a_{46}=-0.855281256\) \(a_{47}=-1.071667897\) \(a_{48}=+0.537784601\) \(a_{49}=+0.142857144\) \(a_{50}=-0.831820965\)
\(a_{51}=+0.670556458\) \(a_{52}=-1.416968859\) \(a_{53}=-0.695791168\) \(a_{54}=-0.332051983\) \(a_{55}=+1.305644563\)
\(a_{56}=+0.637125038\) \(a_{57}=-0.644781225\) \(a_{58}=+1.985008311\) \(a_{59}=+0.195735215\) \(a_{60}=-1.389572445\)
\(a_{61}=-1.307456326\) \(a_{62}=+0.444728126\) \(a_{63}=-0.125988242\) \(a_{64}=-1.066951896\) \(a_{65}=+0.872564689\)
\(a_{66}=+1.068347774\) \(a_{67}=+1.728245781\) \(a_{68}=+2.296139719\) \(a_{69}=+0.286193407\) \(a_{70}=-0.793920472\)
\(a_{71}=+1.129288399\) \(a_{72}=-0.561883764\) \(a_{73}=-0.468685840\) \(a_{74}=-0.442189014\) \(a_{75}=+0.278343620\)
\(a_{76}=-2.207858105\) \(a_{77}=+0.405343138\) \(a_{78}=+0.713920513\) \(a_{79}=-0.297350304\) \(a_{80}=-1.134002562\)
\(a_{81}=+0.111036640\) \(a_{82}=+0.237906587\) \(a_{83}=-1.570665702\) \(a_{84}=-0.431412483\) \(a_{85}=-1.413954781\)
\(a_{86}=-1.523824415\) \(a_{87}=-0.664222793\) \(a_{88}=+1.807836178\) \(a_{89}=-0.078569807\) \(a_{90}=+0.700174636\)
\(a_{91}=+0.270899389\) \(a_{92}=+0.979994880\) \(a_{93}=-0.148814839\) \(a_{94}=+1.849049892\) \(a_{95}=+1.359605904\)
\(a_{96}=+0.045334584\) \(a_{97}=-0.578328936\) \(a_{98}=-0.246482351\) \(a_{99}=-0.357487294\) \(a_{100}=+0.953115260\)

Showing 100 of 1500 available coefficients

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