Properties

Level $93$
Weight $0$
Character 93.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 93 = 3 \cdot 31 \)
Weight: \( 0 \)
Character: 93.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.83443562497 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.662514071\) \(a_{3}=+0.577350269\) \(a_{4}=-0.561075105\) \(a_{5}=+0.981693125\)
\(a_{6}=-0.382502677\) \(a_{7}=-0.441490299\) \(a_{8}=+1.034234224\) \(a_{9}=+0.333333333\) \(a_{10}=-0.650385509\)
\(a_{11}=-0.255255028\) \(a_{12}=-0.323936863\) \(a_{13}=-0.858745151\) \(a_{14}=+0.292493536\) \(a_{15}=+0.566780790\)
\(a_{16}=-0.124119621\) \(a_{17}=-1.933285456\) \(a_{18}=-0.220838024\) \(a_{19}=-0.887023011\) \(a_{20}=-0.550803573\)
\(a_{21}=-0.254894543\) \(a_{22}=+0.169110048\) \(a_{23}=-0.571661989\) \(a_{24}=+0.597115407\) \(a_{25}=-0.036278609\)
\(a_{26}=+0.568930746\) \(a_{27}=+0.192450090\) \(a_{28}=+0.247709216\) \(a_{29}=+0.253564915\) \(a_{30}=-0.375500249\)
\(a_{31}=+0.179605302\) \(a_{32}=-0.952003228\) \(a_{33}=-0.147371559\) \(a_{34}=+1.280828819\) \(a_{35}=-0.433407991\)
\(a_{36}=-0.187025035\) \(a_{37}=+0.493424649\) \(a_{38}=+0.587665226\) \(a_{39}=-0.495796744\) \(a_{40}=+1.015300627\)
\(a_{41}=+0.987745059\) \(a_{42}=+0.168871221\) \(a_{43}=+0.126487565\) \(a_{44}=+0.143217242\) \(a_{45}=+0.327231042\)
\(a_{46}=+0.378734112\) \(a_{47}=-1.216046324\) \(a_{48}=-0.071660496\) \(a_{49}=-0.805086316\) \(a_{50}=+0.024035089\)
\(a_{51}=-1.116182879\) \(a_{52}=+0.481820526\) \(a_{53}=-0.528102830\) \(a_{54}=-0.127500892\) \(a_{55}=-0.250582106\)
\(a_{56}=-0.456604377\) \(a_{57}=-0.512122974\) \(a_{58}=-0.167990324\) \(a_{59}=-0.781254752\) \(a_{60}=-0.318006591\)
\(a_{61}=-0.998789196\) \(a_{62}=-0.118991040\) \(a_{63}=-0.147163433\) \(a_{64}=+0.754835155\) \(a_{65}=-0.843024210\)
\(a_{66}=+0.097635732\) \(a_{67}=-0.668011163\) \(a_{68}=+1.084718341\) \(a_{69}=-0.330049203\) \(a_{70}=+0.287138893\)
\(a_{71}=+0.672823580\) \(a_{72}=+0.344744741\) \(a_{73}=+1.777988267\) \(a_{74}=-0.326900773\) \(a_{75}=-0.020945465\)
\(a_{76}=+0.497686529\) \(a_{77}=+0.112692619\) \(a_{78}=+0.328472319\) \(a_{79}=+0.480384197\) \(a_{80}=-0.121847378\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.654395000\) \(a_{83}=+1.570309661\) \(a_{84}=+0.143014983\) \(a_{85}=-1.897893041\)
\(a_{86}=-0.083799792\) \(a_{87}=+0.146395772\) \(a_{88}=-0.263993485\) \(a_{89}=-1.857490554\) \(a_{90}=-0.216795170\)
\(a_{91}=+0.379127653\) \(a_{92}=+0.320745311\) \(a_{93}=+0.103695169\) \(a_{94}=+0.805647801\) \(a_{95}=-0.870784391\)
\(a_{96}=-0.549639320\) \(a_{97}=+0.411089189\) \(a_{98}=+0.533381013\) \(a_{99}=-0.085085009\) \(a_{100}=+0.020355024\)

Showing 100 of 822 available coefficients

Rows: Cols: