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: \( 2.04509705725 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.338097230\) \(a_{3}=+0.577350267\) \(a_{4}=-0.885690260\) \(a_{5}=+1.339623349\)
\(a_{6}=-0.195200528\) \(a_{7}=+0.377964473\) \(a_{8}=+0.637546659\) \(a_{9}=+0.333333333\) \(a_{10}=-0.452922951\)
\(a_{11}=-0.698244285\) \(a_{12}=-0.511353508\) \(a_{13}=-1.275675616\) \(a_{14}=-0.127788738\) \(a_{15}=+0.773431902\)
\(a_{16}=+0.670137510\) \(a_{17}=+0.921613936\) \(a_{18}=-0.112699085\) \(a_{19}=+0.337271318\) \(a_{20}=-1.186491350\)
\(a_{21}=+0.218217897\) \(a_{22}=+0.236074458\) \(a_{23}=-0.427433883\) \(a_{24}=+0.368087745\) \(a_{25}=+0.794590763\)
\(a_{26}=+0.431302320\) \(a_{27}=+0.192450045\) \(a_{28}=-0.334759557\) \(a_{29}=+0.746711100\) \(a_{30}=-0.261495122\)
\(a_{31}=-1.572749799\) \(a_{32}=-0.864118167\) \(a_{33}=-0.403131471\) \(a_{34}=-0.311595186\) \(a_{35}=+0.506329840\)
\(a_{36}=-0.295230001\) \(a_{37}=+0.785254493\) \(a_{38}=-0.114030474\) \(a_{39}=-0.736511745\) \(a_{40}=+0.854072611\)
\(a_{41}=+0.882948151\) \(a_{42}=-0.073778393\) \(a_{43}=-1.475566008\) \(a_{44}=+0.618428114\) \(a_{45}=+0.446540613\)
\(a_{46}=+0.144514593\) \(a_{47}=+0.031204467\) \(a_{48}=+0.386903664\) \(a_{49}=+0.142857111\) \(a_{50}=-0.268649039\)
\(a_{51}=+0.532094617\) \(a_{52}=+1.129852985\) \(a_{53}=+0.262177483\) \(a_{54}=-0.065066870\) \(a_{55}=-0.935383847\)
\(a_{56}=+0.240968858\) \(a_{57}=+0.194723698\) \(a_{58}=-0.252460514\) \(a_{59}=-1.495040710\) \(a_{60}=-0.685020657\)
\(a_{61}=+0.526372633\) \(a_{62}=+0.531742381\) \(a_{63}=+0.125987297\) \(a_{64}=-0.377981071\) \(a_{65}=-1.708924357\)
\(a_{66}=+0.136297791\) \(a_{67}=+1.156333543\) \(a_{68}=-0.816264472\) \(a_{69}=-0.246779281\) \(a_{70}=-0.171188854\)
\(a_{71}=+0.843994580\) \(a_{72}=+0.212515700\) \(a_{73}=-0.758012082\) \(a_{74}=-0.265492694\) \(a_{75}=+0.458757247\)
\(a_{76}=-0.298717823\) \(a_{77}=-0.263911635\) \(a_{78}=+0.249012483\) \(a_{79}=+1.243947267\) \(a_{80}=+0.897731785\)
\(a_{81}=+0.111111188\) \(a_{82}=-0.298522467\) \(a_{83}=-0.146919951\) \(a_{84}=-0.193273339\) \(a_{85}=+1.234615498\)
\(a_{86}=+0.498884873\) \(a_{87}=+0.431113638\) \(a_{88}=-0.445163370\) \(a_{89}=+0.273667302\) \(a_{90}=-0.150974334\)
\(a_{91}=-0.482160140\) \(a_{92}=+0.378574062\) \(a_{93}=-0.908027714\) \(a_{94}=-0.010549760\) \(a_{95}=+0.451816829\)
\(a_{96}=-0.498898917\) \(a_{97}=-0.384784561\) \(a_{98}=-0.048299600\) \(a_{99}=-0.232748278\) \(a_{100}=-0.703761169\)

Showing 100 of 1500 available coefficients

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