Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 29.0279908058 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.518489607\) \(a_{3}=-0.577350269\) \(a_{4}=-0.731168527\) \(a_{5}=-0.421910029\)
\(a_{6}=-0.299350114\) \(a_{7}=+0.942166918\) \(a_{8}=-0.897592890\) \(a_{9}=+0.333333333\) \(a_{10}=-0.218755965\)
\(a_{11}=-0.080913987\) \(a_{12}=+0.422140346\) \(a_{13}=+0.316458394\) \(a_{14}=+0.488503756\) \(a_{15}=+0.243589869\)
\(a_{16}=+0.265775942\) \(a_{17}=+0.201684406\) \(a_{18}=+0.172829869\) \(a_{19}=+0.887087863\) \(a_{20}=+0.308487334\)
\(a_{21}=-0.543960324\) \(a_{22}=-0.041953061\) \(a_{23}=+1.721530425\) \(a_{24}=+0.518225497\) \(a_{25}=-0.821991928\)
\(a_{26}=+0.164080388\) \(a_{27}=-0.192450090\) \(a_{28}=-0.688882798\) \(a_{29}=-0.958981743\) \(a_{30}=+0.126298815\)
\(a_{31}=-0.607848692\) \(a_{32}=+1.035394954\) \(a_{33}=+0.046715712\) \(a_{34}=+0.104571268\) \(a_{35}=-0.397509671\)
\(a_{36}=-0.243722842\) \(a_{37}=-1.680273523\) \(a_{38}=+0.459945838\) \(a_{39}=-0.182707339\) \(a_{40}=+0.378703442\)
\(a_{41}=-0.799503093\) \(a_{42}=-0.282037775\) \(a_{43}=+1.430395627\) \(a_{44}=+0.059161760\) \(a_{45}=-0.140636676\)
\(a_{46}=+0.892595634\) \(a_{47}=+1.362049693\) \(a_{48}=-0.153445812\) \(a_{49}=-0.112321498\) \(a_{50}=-0.426194272\)
\(a_{51}=-0.116442546\) \(a_{52}=-0.231384418\) \(a_{53}=-0.941423132\) \(a_{54}=-0.099783371\) \(a_{55}=+0.034138422\)
\(a_{56}=-0.845682327\) \(a_{57}=-0.512160417\) \(a_{58}=-0.497222067\) \(a_{59}=-1.393310913\) \(a_{60}=-0.178105245\)
\(a_{61}=-1.780760724\) \(a_{62}=-0.315163230\) \(a_{63}=+0.314055639\) \(a_{64}=+0.271065581\) \(a_{65}=-0.133516970\)
\(a_{66}=+0.024221611\) \(a_{67}=-1.587229160\) \(a_{68}=-0.147465290\) \(a_{69}=-0.993926054\) \(a_{70}=-0.206104634\)
\(a_{71}=+0.244807603\) \(a_{72}=-0.299197630\) \(a_{73}=+1.350531568\) \(a_{74}=-0.871204359\) \(a_{75}=+0.474577261\)
\(a_{76}=-0.648610726\) \(a_{77}=-0.076234482\) \(a_{78}=-0.094731856\) \(a_{79}=-0.109938022\) \(a_{80}=-0.112133535\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.414534045\) \(a_{83}=-0.400324798\) \(a_{84}=+0.397726669\) \(a_{85}=-0.085092673\)
\(a_{86}=+0.741645267\) \(a_{87}=+0.553668367\) \(a_{88}=+0.072627819\) \(a_{89}=-0.858959118\) \(a_{90}=-0.072918655\)
\(a_{91}=+0.298156630\) \(a_{92}=-1.258728865\) \(a_{93}=+0.350941606\) \(a_{94}=+0.706208611\) \(a_{95}=-0.374271266\)
\(a_{96}=-0.597785555\) \(a_{97}=+0.734300935\) \(a_{98}=-0.058237530\) \(a_{99}=-0.026971329\) \(a_{100}=+0.601014627\)

Showing 100 of 1228 available coefficients

Rows: Cols: