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: \( 1.37929245765 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.042745121\) \(a_{3}=+1.121763278\) \(a_{4}=-0.998172854\) \(a_{5}=+0.790189273\)
\(a_{6}=+0.047949906\) \(a_{7}=-1.037946894\) \(a_{8}=-0.085412140\) \(a_{9}=+0.258352853\) \(a_{10}=+0.033776736\)
\(a_{11}=-0.892775628\) \(a_{12}=-1.119713653\) \(a_{13}=+1.555987888\) \(a_{14}=-0.044367166\) \(a_{15}=+0.886405310\)
\(a_{16}=+0.994521901\) \(a_{17}=+1.436718356\) \(a_{18}=+0.011043328\) \(a_{19}=-0.887362055\) \(a_{20}=-0.788745482\)
\(a_{21}=-1.164330719\) \(a_{22}=-0.038161804\) \(a_{23}=+0.470896142\) \(a_{24}=-0.095812202\) \(a_{25}=-0.375600905\)
\(a_{26}=+0.066510876\) \(a_{27}=-0.831952615\) \(a_{28}=+1.036050368\) \(a_{29}=+0.185695350\) \(a_{30}=+0.037889502\)
\(a_{31}=+0.127631055\) \(a_{32}=+0.127923118\) \(a_{33}=-1.001482879\) \(a_{34}=+0.061412667\) \(a_{35}=-0.820174501\)
\(a_{36}=-0.257880836\) \(a_{37}=-0.879950825\) \(a_{38}=-0.037930377\) \(a_{39}=+1.745450083\) \(a_{40}=-0.067491750\)
\(a_{41}=+0.269881907\) \(a_{42}=-0.049769477\) \(a_{43}=+0.290915171\) \(a_{44}=+0.891144398\) \(a_{45}=+0.204147918\)
\(a_{46}=+0.020128654\) \(a_{47}=+0.398923215\) \(a_{48}=+1.115618220\) \(a_{49}=+0.077333705\) \(a_{50}=-0.016055093\)
\(a_{51}=+1.611657949\) \(a_{52}=-1.553144888\) \(a_{53}=-1.131517938\) \(a_{54}=-0.035561886\) \(a_{55}=-0.705461712\)
\(a_{56}=+0.088653283\) \(a_{57}=-0.995410205\) \(a_{58}=+0.007937579\) \(a_{59}=-0.545917741\) \(a_{60}=-0.884785717\)
\(a_{61}=+1.533855922\) \(a_{62}=+0.005455572\) \(a_{63}=-0.268156648\) \(a_{64}=-0.989053843\) \(a_{65}=+1.229524935\)
\(a_{66}=-0.042808423\) \(a_{67}=-0.120002817\) \(a_{68}=-1.434093180\) \(a_{69}=+0.528233888\) \(a_{70}=-0.035058458\)
\(a_{71}=+0.825761133\) \(a_{72}=-0.022066469\) \(a_{73}=-0.940204770\) \(a_{74}=-0.037613599\) \(a_{75}=-0.421335276\)
\(a_{76}=+0.885740711\) \(a_{77}=+0.926653706\) \(a_{78}=+0.074609455\) \(a_{79}=-0.838953478\) \(a_{80}=+0.785860405\)
\(a_{81}=-1.191606686\) \(a_{82}=+0.011536199\) \(a_{83}=+0.120729893\) \(a_{84}=+1.162203480\) \(a_{85}=+1.135279312\)
\(a_{86}=+0.012435266\) \(a_{87}=+0.208306265\) \(a_{88}=+0.076253803\) \(a_{89}=+0.972275859\) \(a_{90}=+0.008726344\)
\(a_{91}=-1.615032844\) \(a_{92}=-0.470035726\) \(a_{93}=+0.143171852\) \(a_{94}=+0.017052036\) \(a_{95}=-0.701183966\)
\(a_{96}=+0.143499473\) \(a_{97}=+1.101789793\) \(a_{98}=+0.003305592\) \(a_{99}=-0.230651068\) \(a_{100}=+0.374914598\)

Showing 100 of 1500 available coefficients

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