Properties

Level $27$
Weight $0$
Character 27.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 27 = 3^{3} \)
Weight: \( 0 \)
Character: 27.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.2456545638 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.794165531\) \(a_{3}=+0.000000000\) \(a_{4}=-0.369301107\) \(a_{5}=+1.358137957\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.488253125\) \(a_{8}=-1.087451736\) \(a_{9}=+0.000000000\) \(a_{10}=+1.078586354\)
\(a_{11}=+0.792013125\) \(a_{12}=+0.000000000\) \(a_{13}=-0.898935896\) \(a_{14}=+0.387753799\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.494315584\) \(a_{17}=-0.220323792\) \(a_{18}=+0.000000000\) \(a_{19}=-0.931893681\) \(a_{20}=-0.501561851\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.628989524\) \(a_{23}=+0.412443551\) \(a_{24}=+0.000000000\) \(a_{25}=+0.844538728\)
\(a_{26}=-0.713903901\) \(a_{27}=+0.000000000\) \(a_{28}=-0.180312411\) \(a_{29}=+0.417312667\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.281993078\) \(a_{32}=+0.694883355\) \(a_{33}=+0.000000000\) \(a_{34}=-0.174973549\) \(a_{35}=+0.663115110\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.087919995\) \(a_{38}=-0.740077802\) \(a_{39}=+0.000000000\) \(a_{40}=-1.476909483\)
\(a_{41}=-1.501166668\) \(a_{42}=+0.000000000\) \(a_{43}=-0.654306706\) \(a_{44}=-0.292491357\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.327548396\) \(a_{47}=+1.507831801\) \(a_{48}=+0.000000000\) \(a_{49}=-0.761608877\) \(a_{50}=+0.670703556\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.331978038\) \(a_{53}=-0.508994419\) \(a_{54}=+0.000000000\) \(a_{55}=+1.075663160\)
\(a_{56}=-0.530951795\) \(a_{57}=+0.000000000\) \(a_{58}=+0.331415307\) \(a_{59}=+0.336172267\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.113320485\) \(a_{62}=+1.018114724\) \(a_{63}=+0.000000000\) \(a_{64}=+1.046168003\) \(a_{65}=-1.220878924\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.333617742\) \(a_{68}=+0.081365870\) \(a_{69}=+0.000000000\) \(a_{70}=+0.526623132\)
\(a_{71}=-0.655356487\) \(a_{72}=+0.000000000\) \(a_{73}=-1.721525846\) \(a_{74}=-0.069823082\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.344149361\) \(a_{77}=+0.386702920\) \(a_{78}=+0.000000000\) \(a_{79}=-0.218830851\) \(a_{80}=-0.671348780\)
\(a_{81}=+0.000000000\) \(a_{82}=-1.192174802\) \(a_{83}=+1.806518054\) \(a_{84}=+0.000000000\) \(a_{85}=-0.299230136\)
\(a_{86}=-0.519627962\) \(a_{87}=+0.000000000\) \(a_{88}=-0.861276026\) \(a_{89}=+1.352315749\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.438908097\) \(a_{92}=-0.152315711\) \(a_{93}=+0.000000000\) \(a_{94}=+1.197468108\) \(a_{95}=-1.265640094\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.248113944\) \(a_{98}=-0.604843486\) \(a_{99}=+0.000000000\) \(a_{100}=-0.311889076\)

Showing 100 of 2000 available coefficients

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