Properties

Level $29$
Weight $0$
Character 29.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.34983686267 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.583380038\) \(a_{3}=+0.667545952\) \(a_{4}=+1.507092346\) \(a_{5}=+1.522431838\)
\(a_{6}=-1.056978935\) \(a_{7}=+0.474372973\) \(a_{8}=-0.802919898\) \(a_{9}=-0.554382402\) \(a_{10}=-2.410588182\)
\(a_{11}=+1.607106696\) \(a_{12}=+1.006053395\) \(a_{13}=-0.053767975\) \(a_{14}=-0.751112697\) \(a_{15}=+1.016293211\)
\(a_{16}=-0.235765007\) \(a_{17}=+0.602907388\) \(a_{18}=+0.877798029\) \(a_{19}=-0.220091794\) \(a_{20}=+2.294445370\)
\(a_{21}=+0.316665758\) \(a_{22}=-2.544660661\) \(a_{23}=-1.838374294\) \(a_{24}=-0.535985928\) \(a_{25}=+1.317798702\)
\(a_{26}=+0.085135139\) \(a_{27}=-1.037621680\) \(a_{28}=+0.714923877\) \(a_{29}=+0.185695338\) \(a_{30}=-1.609178384\)
\(a_{31}=+0.454671663\) \(a_{32}=+1.176225505\) \(a_{33}=+1.072817569\) \(a_{34}=-0.954631524\) \(a_{35}=+0.722200517\)
\(a_{36}=-0.835505476\) \(a_{37}=-0.145869935\) \(a_{38}=+0.348488956\) \(a_{39}=-0.035892594\) \(a_{40}=-1.222390819\)
\(a_{41}=+0.969044872\) \(a_{42}=-0.501402238\) \(a_{43}=-1.811928546\) \(a_{44}=+2.422058203\) \(a_{45}=-0.844009420\)
\(a_{46}=+2.910845148\) \(a_{47}=-0.599541226\) \(a_{48}=-0.157383965\) \(a_{49}=-0.774970259\) \(a_{50}=-2.086576159\)
\(a_{51}=+0.402468357\) \(a_{52}=-0.081033286\) \(a_{53}=-0.363570932\) \(a_{54}=+1.642949481\) \(a_{55}=+2.446710364\)
\(a_{56}=-0.380883531\) \(a_{57}=-0.146921385\) \(a_{58}=-0.294026281\) \(a_{59}=+0.456274979\) \(a_{60}=+1.531647691\)
\(a_{61}=+0.266614218\) \(a_{62}=-0.719918096\) \(a_{63}=-0.262983981\) \(a_{64}=-1.626646995\) \(a_{65}=-0.081858112\)
\(a_{66}=-1.698677847\) \(a_{67}=-1.750236986\) \(a_{68}=+0.908637198\) \(a_{69}=-1.227199273\) \(a_{70}=-1.143517940\)
\(a_{71}=+0.351609027\) \(a_{72}=+0.445124638\) \(a_{73}=+0.795059152\) \(a_{74}=+0.230967517\) \(a_{75}=+0.879691290\)
\(a_{76}=-0.331698633\) \(a_{77}=+0.762367988\) \(a_{78}=+0.056831642\) \(a_{79}=+0.194327031\) \(a_{80}=-0.358936098\)
\(a_{81}=-0.138277762\) \(a_{82}=-1.534366332\) \(a_{83}=-0.221629343\) \(a_{84}=+0.477244534\) \(a_{85}=+0.917885474\)
\(a_{86}=+2.868971412\) \(a_{87}=+0.123960247\) \(a_{88}=-1.290377969\) \(a_{89}=+0.174095940\) \(a_{90}=+1.336387607\)
\(a_{91}=-0.025505994\) \(a_{92}=-2.770599843\) \(a_{93}=+0.303514160\) \(a_{94}=+0.949301666\) \(a_{95}=-0.335074720\)
\(a_{96}=+0.785184629\) \(a_{97}=+0.838842641\) \(a_{98}=+1.227072485\) \(a_{99}=-0.890951726\) \(a_{100}=+1.986044281\)

Showing 100 of 1500 available coefficients

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