Properties

Level $58$
Weight $0$
Character 58.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 58 = 2 \cdot 29 \)
Weight: \( 0 \)
Character: 58.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.84949888878 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.429393137\) \(a_{4}=+0.500000000\) \(a_{5}=+1.235249949\)
\(a_{6}=-1.010733580\) \(a_{7}=+1.073807707\) \(a_{8}=+0.353553391\) \(a_{9}=+1.043164739\) \(a_{10}=+0.873453615\)
\(a_{11}=+1.411721396\) \(a_{12}=-0.714696568\) \(a_{13}=-1.446337101\) \(a_{14}=+0.759296711\) \(a_{15}=-1.765657799\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.387293112\) \(a_{18}=+0.737628861\) \(a_{19}=+0.076716327\) \(a_{20}=+0.617624974\)
\(a_{21}=-1.534893366\) \(a_{22}=+0.998237773\) \(a_{23}=+1.054794806\) \(a_{24}=-0.505366790\) \(a_{25}=+0.525842436\)
\(a_{26}=-1.022714772\) \(a_{27}=-0.061699382\) \(a_{28}=+0.536903853\) \(a_{29}=-0.185695338\) \(a_{30}=-1.248508603\)
\(a_{31}=-1.065824871\) \(a_{32}=+0.176776695\) \(a_{33}=-2.017904875\) \(a_{34}=+0.980964367\) \(a_{35}=+1.326420914\)
\(a_{36}=+0.521582370\) \(a_{37}=-1.189076449\) \(a_{38}=+0.054246635\) \(a_{39}=+2.067384326\) \(a_{40}=+0.436726808\)
\(a_{41}=+0.254477013\) \(a_{42}=-1.085333507\) \(a_{43}=+1.523479736\) \(a_{44}=+0.705860698\) \(a_{45}=+1.288569191\)
\(a_{46}=+0.745852560\) \(a_{47}=-0.449484539\) \(a_{48}=-0.357348284\) \(a_{49}=+0.153062991\) \(a_{50}=+0.371826752\)
\(a_{51}=-1.982987253\) \(a_{52}=-0.723168551\) \(a_{53}=-1.060574086\) \(a_{54}=-0.043628052\) \(a_{55}=+1.743828782\)
\(a_{56}=+0.379648355\) \(a_{57}=-0.109657791\) \(a_{58}=-0.131306433\) \(a_{59}=+0.927867069\) \(a_{60}=-0.882828899\)
\(a_{61}=-1.177673241\) \(a_{62}=-0.753651994\) \(a_{63}=+1.120158336\) \(a_{64}=+0.125000000\) \(a_{65}=-1.786587830\)
\(a_{66}=-1.426874221\) \(a_{67}=+0.262697567\) \(a_{68}=+0.693646556\) \(a_{69}=-1.507716456\) \(a_{70}=+0.937921223\)
\(a_{71}=-1.193156893\) \(a_{72}=+0.368814431\) \(a_{73}=+0.046124133\) \(a_{74}=-0.840804020\) \(a_{75}=-0.751635569\)
\(a_{76}=+0.038358163\) \(a_{77}=+1.515917315\) \(a_{78}=+1.461861476\) \(a_{79}=+0.478627472\) \(a_{80}=+0.308812487\)
\(a_{81}=-0.954972066\) \(a_{82}=+0.179942422\) \(a_{83}=-0.790995819\) \(a_{84}=-0.767446683\) \(a_{85}=+1.713653745\)
\(a_{86}=+1.077262852\) \(a_{87}=+0.265431642\) \(a_{88}=+0.499118886\) \(a_{89}=+0.913002834\) \(a_{90}=+0.911156013\)
\(a_{91}=-1.553087926\) \(a_{92}=+0.527397403\) \(a_{93}=+1.523482756\) \(a_{94}=-0.317833565\) \(a_{95}=+0.094763839\)
\(a_{96}=-0.252683395\) \(a_{97}=-0.734200054\) \(a_{98}=+0.108231879\) \(a_{99}=+1.472657983\) \(a_{100}=+0.262921218\)

Showing 100 of 522 available coefficients

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