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: \( 3.25120755726 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.342525359\) \(a_{3}=+0.577350269\) \(a_{4}=+0.802374342\) \(a_{5}=+1.553203984\)
\(a_{6}=-0.775107377\) \(a_{7}=-0.377964473\) \(a_{8}=+0.265317459\) \(a_{9}=+0.333333333\) \(a_{10}=-2.085215738\)
\(a_{11}=+0.951307881\) \(a_{12}=+0.463251042\) \(a_{13}=+1.236665569\) \(a_{14}=+0.507426890\) \(a_{15}=+0.896742738\)
\(a_{16}=-1.158569758\) \(a_{17}=-0.639400343\) \(a_{18}=-0.447508453\) \(a_{19}=-0.147443903\) \(a_{20}=+1.246251024\)
\(a_{21}=-0.218217890\) \(a_{22}=-1.277154956\) \(a_{23}=+0.436474647\) \(a_{24}=+0.153181104\) \(a_{25}=+1.412442621\)
\(a_{26}=-1.660254885\) \(a_{27}=+0.192450089\) \(a_{28}=-0.303269000\) \(a_{29}=+0.974061214\) \(a_{30}=-1.203899860\)
\(a_{31}=-1.250359896\) \(a_{32}=+1.290091807\) \(a_{33}=+0.549237850\) \(a_{34}=+0.858411189\) \(a_{35}=-0.587055901\)
\(a_{36}=+0.267458104\) \(a_{37}=-1.388325460\) \(a_{38}=+0.197947188\) \(a_{39}=+0.713989261\) \(a_{40}=+0.412092150\)
\(a_{41}=+0.627415355\) \(a_{42}=+0.292962992\) \(a_{43}=+0.436546664\) \(a_{44}=+0.763305194\) \(a_{45}=+0.517734535\)
\(a_{46}=-0.585978504\) \(a_{47}=-1.276842936\) \(a_{48}=-0.668900482\) \(a_{49}=+0.142857156\) \(a_{50}=-1.896240175\)
\(a_{51}=-0.369158041\) \(a_{52}=+0.992268866\) \(a_{53}=-1.193938182\) \(a_{54}=-0.258369237\) \(a_{55}=+1.477574942\)
\(a_{56}=-0.100280654\) \(a_{57}=-0.085126456\) \(a_{58}=-1.307701913\) \(a_{59}=-0.405953963\) \(a_{60}=+0.719523271\)
\(a_{61}=+0.611235267\) \(a_{62}=+1.678639850\) \(a_{63}=-0.125988144\) \(a_{64}=-0.573411202\) \(a_{65}=+1.920793915\)
\(a_{66}=-0.737365733\) \(a_{67}=-1.195248194\) \(a_{68}=-0.513038456\) \(a_{69}=+0.251998628\) \(a_{70}=+0.788137342\)
\(a_{71}=+1.076842552\) \(a_{72}=+0.088439227\) \(a_{73}=+0.144976153\) \(a_{74}=+1.863862120\) \(a_{75}=+0.815474073\)
\(a_{76}=-0.118305186\) \(a_{77}=-0.359560489\) \(a_{78}=-0.958548623\) \(a_{79}=-0.639564411\) \(a_{80}=-1.799495281\)
\(a_{81}=+0.111111127\) \(a_{82}=-0.842321072\) \(a_{83}=-1.452011886\) \(a_{84}=-0.175092478\) \(a_{85}=-0.993119041\)
\(a_{86}=-0.586074522\) \(a_{87}=+0.562374560\) \(a_{88}=+0.252398222\) \(a_{89}=+1.928798918\) \(a_{90}=-0.695071857\)
\(a_{91}=-0.467415562\) \(a_{92}=+0.350216004\) \(a_{93}=-0.721895810\) \(a_{94}=+1.714194151\) \(a_{95}=-0.229010299\)
\(a_{96}=+0.744834879\) \(a_{97}=+0.486296917\) \(a_{98}=-0.191789305\) \(a_{99}=+0.317102665\) \(a_{100}=+1.133307726\)

Showing 100 of 1500 available coefficients

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