Properties

Level $58$
Weight $0$
Character 58.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 58 = 2 \cdot 29 \)
Weight: \( 0 \)
Character: 58.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.86547774199 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.809523173\) \(a_{4}=+0.500000000\) \(a_{5}=-1.673557824\)
\(a_{6}=-1.279526106\) \(a_{7}=-0.113159340\) \(a_{8}=+0.353553391\) \(a_{9}=+2.274374114\) \(a_{10}=-1.183384086\)
\(a_{11}=+0.255490038\) \(a_{12}=-0.904761587\) \(a_{13}=-1.181594336\) \(a_{14}=-0.080015736\) \(a_{15}=+3.028341664\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.130797020\) \(a_{18}=+1.608225359\) \(a_{19}=-1.502593872\) \(a_{20}=-0.836778912\)
\(a_{21}=+0.204764447\) \(a_{22}=+0.180658738\) \(a_{23}=+0.348447734\) \(a_{24}=-0.639763053\) \(a_{25}=+1.800795791\)
\(a_{26}=-0.835513368\) \(a_{27}=-2.306009490\) \(a_{28}=-0.056579670\) \(a_{29}=+0.185695338\) \(a_{30}=+2.141360926\)
\(a_{31}=+1.360057835\) \(a_{32}=+0.176776695\) \(a_{33}=-0.462315144\) \(a_{34}=+0.799594241\) \(a_{35}=+0.189378698\)
\(a_{36}=+1.137187057\) \(a_{37}=+0.768420363\) \(a_{38}=-1.062494316\) \(a_{39}=+2.138122332\) \(a_{40}=-0.591692043\)
\(a_{41}=-0.742521111\) \(a_{42}=+0.144790329\) \(a_{43}=+0.456529339\) \(a_{44}=+0.127745019\) \(a_{45}=-3.806296593\)
\(a_{46}=+0.246389755\) \(a_{47}=+0.795498936\) \(a_{48}=-0.452380793\) \(a_{49}=-0.987194964\) \(a_{50}=+1.273354915\)
\(a_{51}=-2.046203412\) \(a_{52}=-0.590797168\) \(a_{53}=-0.835115289\) \(a_{54}=-1.630594948\) \(a_{55}=-0.427577352\)
\(a_{56}=-0.040007868\) \(a_{57}=+2.718978431\) \(a_{58}=+0.131306433\) \(a_{59}=+0.427316528\) \(a_{60}=+1.514170832\)
\(a_{61}=-0.509897288\) \(a_{62}=+0.961706118\) \(a_{63}=-0.257366673\) \(a_{64}=+0.125000000\) \(a_{65}=+1.977466446\)
\(a_{66}=-0.326906174\) \(a_{67}=+1.371859854\) \(a_{68}=+0.565398510\) \(a_{69}=-0.630524249\) \(a_{70}=+0.133910962\)
\(a_{71}=-1.759193115\) \(a_{72}=+0.804112679\) \(a_{73}=+0.318459149\) \(a_{74}=+0.543355249\) \(a_{75}=-3.258581713\)
\(a_{76}=-0.751296936\) \(a_{77}=-0.028911084\) \(a_{78}=+1.511880800\) \(a_{79}=+1.474532985\) \(a_{80}=-0.418389456\)
\(a_{81}=+1.898403496\) \(a_{82}=-0.525041713\) \(a_{83}=+1.433171101\) \(a_{84}=+0.102382224\) \(a_{85}=-1.892454200\)
\(a_{86}=+0.322814991\) \(a_{87}=-0.336020018\) \(a_{88}=+0.090329369\) \(a_{89}=-0.825412673\) \(a_{90}=-2.691458132\)
\(a_{91}=+0.133708435\) \(a_{92}=+0.174223867\) \(a_{93}=-2.461056170\) \(a_{94}=+0.562502692\) \(a_{95}=+2.514677731\)
\(a_{96}=-0.319881527\) \(a_{97}=+1.909935279\) \(a_{98}=-0.698052253\) \(a_{99}=+0.581079929\) \(a_{100}=+0.900397895\)

Showing 100 of 520 available coefficients

Rows: Cols: