Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 17.8206758792 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.504842283\) \(a_{3}=-0.577350269\) \(a_{4}=+1.264550297\) \(a_{5}=-0.767609818\)
\(a_{6}=-0.868821097\) \(a_{7}=+0.929690136\) \(a_{8}=+0.398106474\) \(a_{9}=+0.333333333\) \(a_{10}=-1.155131712\)
\(a_{11}=-1.595781981\) \(a_{12}=-0.730088455\) \(a_{13}=-1.413158494\) \(a_{14}=+1.399037027\) \(a_{15}=+0.443179735\)
\(a_{16}=-0.665462843\) \(a_{17}=+0.037072005\) \(a_{18}=+0.501614095\) \(a_{19}=-0.875368862\) \(a_{20}=-0.970681224\)
\(a_{21}=-0.536756850\) \(a_{22}=-2.401400200\) \(a_{23}=+1.415220246\) \(a_{24}=-0.229846880\) \(a_{25}=-0.410775167\)
\(a_{26}=-2.126580655\) \(a_{27}=-0.192450090\) \(a_{28}=+1.175639938\) \(a_{29}=-0.575812142\) \(a_{30}=+0.666915605\)
\(a_{31}=-0.303685874\) \(a_{32}=-1.399523097\) \(a_{33}=+0.921325156\) \(a_{34}=+0.055787520\) \(a_{35}=-0.713639277\)
\(a_{36}=+0.421516766\) \(a_{37}=+0.784676750\) \(a_{38}=-1.317292076\) \(a_{39}=+0.815887437\) \(a_{40}=-0.305590438\)
\(a_{41}=+0.987550280\) \(a_{42}=-0.807734404\) \(a_{43}=+0.468278656\) \(a_{44}=-2.017946579\) \(a_{45}=-0.255869940\)
\(a_{46}=+2.129683266\) \(a_{47}=+0.253628621\) \(a_{48}=+0.384205151\) \(a_{49}=-0.135676251\) \(a_{50}=-0.618151840\)
\(a_{51}=-0.021403532\) \(a_{52}=-1.787009994\) \(a_{53}=+0.696598376\) \(a_{54}=-0.289607033\) \(a_{55}=+1.224937917\)
\(a_{56}=+0.370115662\) \(a_{57}=+0.505394448\) \(a_{58}=-0.866506459\) \(a_{59}=+0.431361398\) \(a_{60}=+0.560423066\)
\(a_{61}=-1.348490722\) \(a_{62}=-0.456999344\) \(a_{63}=+0.309896712\) \(a_{64}=-1.440598690\) \(a_{65}=+1.084754335\)
\(a_{66}=+1.386449052\) \(a_{67}=+0.337513823\) \(a_{68}=+0.046879414\) \(a_{69}=-0.817077790\) \(a_{70}=-1.073914558\)
\(a_{71}=+0.697689451\) \(a_{72}=+0.132702158\) \(a_{73}=-0.223120817\) \(a_{74}=+1.180814753\) \(a_{75}=+0.237161153\)
\(a_{76}=-1.106947954\) \(a_{77}=-1.483582767\) \(a_{78}=+1.227781914\) \(a_{79}=-1.099204824\) \(a_{80}=+0.510815812\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.486107418\) \(a_{83}=+0.291710047\) \(a_{84}=-0.678756035\) \(a_{85}=-0.028456835\)
\(a_{86}=+0.704685521\) \(a_{87}=+0.332445295\) \(a_{88}=-0.635291137\) \(a_{89}=-1.777297170\) \(a_{90}=-0.385043904\)
\(a_{91}=-1.313799513\) \(a_{92}=+1.789617183\) \(a_{93}=+0.175333121\) \(a_{94}=+0.381671073\) \(a_{95}=+0.671941733\)
\(a_{96}=+0.808015037\) \(a_{97}=+0.583021764\) \(a_{98}=-0.204171359\) \(a_{99}=-0.531927327\) \(a_{100}=-0.519445859\)

Showing 100 of 1228 available coefficients

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