Properties

Level $40$
Weight $0$
Character 40.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 40 = 2^{3} \cdot 5 \)
Weight: \( 0 \)
Character: 40.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.86274827851 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.711467477\) \(a_{4}=+0.000000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.275356335\) \(a_{8}=+0.000000000\) \(a_{9}=-0.493814029\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.164921205\) \(a_{12}=+0.000000000\) \(a_{13}=-0.118783334\) \(a_{14}=+0.000000000\) \(a_{15}=-0.318177928\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.826418801\) \(a_{18}=+0.000000000\) \(a_{19}=+0.234822779\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.195907077\) \(a_{22}=+0.000000000\) \(a_{23}=+0.911540466\) \(a_{24}=+0.000000000\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.062800098\) \(a_{28}=+0.000000000\) \(a_{29}=-0.131864639\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.526355531\) \(a_{32}=+0.000000000\) \(a_{33}=-0.828803550\) \(a_{34}=+0.000000000\) \(a_{35}=-0.123143096\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.197278495\) \(a_{38}=+0.000000000\) \(a_{39}=-0.084510479\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.317611138\) \(a_{42}=+0.000000000\) \(a_{43}=+0.171817326\) \(a_{44}=+0.000000000\) \(a_{45}=+0.220840348\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.712354194\) \(a_{48}=+0.000000000\) \(a_{49}=-0.924178889\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.299437576\) \(a_{52}=+0.000000000\) \(a_{53}=+0.006648473\) \(a_{54}=+0.000000000\) \(a_{55}=+0.520968600\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.167068770\) \(a_{58}=+0.000000000\) \(a_{59}=+0.085299920\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.080947644\) \(a_{62}=+0.000000000\) \(a_{63}=-0.135974821\) \(a_{64}=+0.000000000\) \(a_{65}=+0.053121522\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.107386125\) \(a_{68}=+0.000000000\) \(a_{69}=+0.648531396\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.508144398\) \(a_{72}=+0.000000000\) \(a_{73}=+0.823744070\) \(a_{74}=+0.000000000\) \(a_{75}=+0.142293495\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.320768433\) \(a_{78}=+0.000000000\) \(a_{79}=-1.264783800\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.262333675\) \(a_{82}=+0.000000000\) \(a_{83}=-1.568167100\) \(a_{84}=+0.000000000\) \(a_{85}=-0.816799319\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.093817402\) \(a_{88}=+0.000000000\) \(a_{89}=+0.699754400\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.032707743\) \(a_{92}=+0.000000000\) \(a_{93}=+0.374484841\) \(a_{94}=+0.000000000\) \(a_{95}=-0.105015939\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.412125970\) \(a_{98}=+0.000000000\) \(a_{99}=+0.575254434\) \(a_{100}=+0.000000000\)

Showing 100 of 222 available coefficients

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