Properties

Label 3.83
Level $3$
Weight $0$
Character 3.1
Symmetry odd
\(R\) 24.95264
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(24.9526483935992719814873254245 \pm 8 \cdot 10^{-3}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= +1.91954949 \pm 156 \) \(a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.68467023 \pm 284 \) \(a_{5}= -1.02176265 \pm 215 \) \(a_{6}= \pm1.10825241 \pm 90. \)
\(a_{7}= -0.59259233 \pm 177 \) \(a_{8}= +3.23380787 \pm 191 \) \(a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8} \)
\(a_{10}= -1.96132397 \pm 124 \) \(a_{11}= -0.49177126 \pm 197 \) \(a_{12}= \pm1.54999508 \pm 164 \)
\(a_{13}= -0.50356810 \pm 192 \) \(a_{14}= -1.13751030 \pm 121 \) \(a_{15}= \pm0.58991494 \pm 124 \)
\(a_{16}= +3.52278401 \pm 230 \) \(a_{17}= -1.41516468 \pm 144 \) \(a_{18}= \pm0.63984983 \pm 52. \)
\(a_{19}= -0.54189440 \pm 117 \) \(a_{20}= -2.74309577 \pm 201 \) \(a_{21}= \pm0.34213334 \pm 102 \)
\(a_{22}= -0.94397926 \pm 99. \) \(a_{23}= -0.64574953 \pm 432 \) \(a_{24}= \pm1.86703985 \pm 110 \)
\(a_{25}= +0.04399891 \pm 178 \) \(a_{26}= -0.96662388 \pm 67. \) \(a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8} \)
\(a_{28}= -1.59091499 \pm 117 \) \(a_{29}= +0.24748147 \pm 408 \) \(a_{30}= \pm1.13237092 \pm 71. \)
\(a_{31}= -1.48959388 \pm 182 \) \(a_{32}= +3.52835037 \pm 255 \) \(a_{33}= \pm0.28392427 \pm 113 \)
\(a_{34}= -2.71647863 \pm 174 \) \(a_{35}= +0.60548871 \pm 78. \) \(a_{36}= \pm0.89489008 \pm 94. \)
\(a_{37}= +1.07311652 \pm 219 \) \(a_{38}= -1.04019311 \pm 53. \) \(a_{39}= \pm0.29073518 \pm 110 \)
\(a_{40}= -3.30418410 \pm 118 \) \(a_{41}= -0.60926677 \pm 416 \) \(a_{42}= \pm0.65674188 \pm 70. \)
\(a_{43}= +0.10499168 \pm 276 \) \(a_{44}= -1.32024365 \pm 173 \) \(a_{45}= \pm0.34058755 \pm 71. \)
\(a_{46}= -1.23954818 \pm 125 \) \(a_{47}= +1.07601420 \pm 344 \) \(a_{48}= \pm2.03388030 \pm 133 \)
\(a_{49}= -0.64883433 \pm 300 \) \(a_{50}= +0.08445809 \pm 87. \) \(a_{51}= \pm0.81704571 \pm 83. \)
\(a_{52}= -1.35191428 \pm 175 \) \(a_{53}= +0.83602499 \pm 172 \) \(a_{54}= \pm0.36941747 \pm 30. \)
\(a_{55}= +0.50247350 \pm 137 \) \(a_{56}= -1.91632974 \pm 170 \) \(a_{57}= \pm0.31286288 \pm 67. \)
\(a_{58}= +0.47505293 \pm 169 \) \(a_{59}= +0.07865940 \pm 276 \) \(a_{60}= \pm1.58372708 \pm 116 \)

Displaying $a_n$ with $n$ up to: 60 180 1000