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: \( 15.7532336885 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.120442985\) \(a_{3}=+0.577350269\) \(a_{4}=-0.985493487\) \(a_{5}=+0.476527640\)
\(a_{6}=-0.069537790\) \(a_{7}=+0.037618734\) \(a_{8}=+0.239138763\) \(a_{9}=+0.333333333\) \(a_{10}=-0.057394411\)
\(a_{11}=-1.183663158\) \(a_{12}=-0.568974930\) \(a_{13}=+1.035331658\) \(a_{14}=-0.004530913\) \(a_{15}=+0.275123361\)
\(a_{16}=+0.956690901\) \(a_{17}=+1.338042117\) \(a_{18}=-0.040147662\) \(a_{19}=+1.396317859\) \(a_{20}=-0.469614885\)
\(a_{21}=+0.021719186\) \(a_{22}=+0.142563924\) \(a_{23}=+1.285615513\) \(a_{24}=+0.138066829\) \(a_{25}=-0.772921409\)
\(a_{26}=-0.124698435\) \(a_{27}=+0.192450090\) \(a_{28}=-0.037073018\) \(a_{29}=+0.136596712\) \(a_{30}=-0.033136679\)
\(a_{31}=+0.985731081\) \(a_{32}=-0.354365471\) \(a_{33}=-0.683388243\) \(a_{34}=-0.161157787\) \(a_{35}=+0.017926367\)
\(a_{36}=-0.328497829\) \(a_{37}=+0.866231135\) \(a_{38}=-0.168176691\) \(a_{39}=+0.597749011\) \(a_{40}=+0.113956230\)
\(a_{41}=-0.475920559\) \(a_{42}=-0.002615924\) \(a_{43}=-1.744601577\) \(a_{44}=+1.166492333\) \(a_{45}=+0.158842547\)
\(a_{46}=-0.154843370\) \(a_{47}=+0.718506910\) \(a_{48}=+0.552345749\) \(a_{49}=-0.998584831\) \(a_{50}=+0.093092962\)
\(a_{51}=+0.772518976\) \(a_{52}=-1.020312606\) \(a_{53}=-0.070344174\) \(a_{54}=-0.023179263\) \(a_{55}=-0.564048210\)
\(a_{56}=+0.008996098\) \(a_{57}=+0.806164492\) \(a_{58}=-0.016452116\) \(a_{59}=+1.426929435\) \(a_{60}=-0.271132280\)
\(a_{61}=-0.919139567\) \(a_{62}=-0.118724394\) \(a_{63}=+0.012539578\) \(a_{64}=-0.914010066\) \(a_{65}=+0.493364151\)
\(a_{66}=+0.082309320\) \(a_{67}=+0.514278768\) \(a_{68}=-1.318631792\) \(a_{69}=+0.742250462\) \(a_{70}=-0.002159105\)
\(a_{71}=+0.855936676\) \(a_{72}=+0.079712921\) \(a_{73}=+0.636923865\) \(a_{74}=-0.104331464\) \(a_{75}=-0.446246383\)
\(a_{76}=-1.376062156\) \(a_{77}=-0.044527910\) \(a_{78}=-0.071994675\) \(a_{79}=-0.050129616\) \(a_{80}=+0.455889657\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.057321293\) \(a_{83}=+0.275927308\) \(a_{84}=-0.021404117\) \(a_{85}=+0.637614051\)
\(a_{86}=+0.210125022\) \(a_{87}=+0.078864148\) \(a_{88}=-0.283059743\) \(a_{89}=-0.618516422\) \(a_{90}=-0.019131470\)
\(a_{91}=+0.038947867\) \(a_{92}=-1.266965715\) \(a_{93}=+0.569112105\) \(a_{94}=-0.086539117\) \(a_{95}=+0.665384053\)
\(a_{96}=-0.204593000\) \(a_{97}=-0.116825311\) \(a_{98}=+0.120272538\) \(a_{99}=-0.394554386\) \(a_{100}=+0.761709015\)

Showing 100 of 1228 available coefficients

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