Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 7.22295707842 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.402900957\) \(a_{4}=+0.500000000\) \(a_{5}=+1.273130591\)
\(a_{6}=+0.284893999\) \(a_{7}=-0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.837670819\) \(a_{10}=+0.900239274\)
\(a_{11}=+1.665442378\) \(a_{12}=+0.201450478\) \(a_{13}=+0.175239241\) \(a_{14}=-0.267261242\) \(a_{15}=+0.512945533\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.863809947\) \(a_{18}=-0.592322717\) \(a_{19}=+1.649468124\) \(a_{20}=+0.636565295\)
\(a_{21}=-0.152282248\) \(a_{22}=+1.177645599\) \(a_{23}=-1.422477220\) \(a_{24}=+0.142446999\) \(a_{25}=+0.620861501\)
\(a_{26}=+0.123912856\) \(a_{27}=-0.740399331\) \(a_{28}=-0.188982237\) \(a_{29}=+0.144200997\) \(a_{30}=+0.362707265\)
\(a_{31}=-0.344979355\) \(a_{32}=+0.176776695\) \(a_{33}=+0.671008328\) \(a_{34}=+0.610805871\) \(a_{35}=-0.481198133\)
\(a_{36}=-0.418835409\) \(a_{37}=-1.020145883\) \(a_{38}=+1.166350096\) \(a_{39}=+0.070604058\) \(a_{40}=+0.450119637\)
\(a_{41}=+0.288227391\) \(a_{42}=-0.107679810\) \(a_{43}=+0.582078456\) \(a_{44}=+0.832721189\) \(a_{45}=-1.066464345\)
\(a_{46}=-1.005843288\) \(a_{47}=-1.796403890\) \(a_{48}=+0.100725239\) \(a_{49}=+0.142857143\) \(a_{50}=+0.439015377\)
\(a_{51}=+0.348029854\) \(a_{52}=+0.087619620\) \(a_{53}=-0.515108199\) \(a_{54}=-0.523541388\) \(a_{55}=+2.120325638\)
\(a_{56}=-0.133630621\) \(a_{57}=+0.664572285\) \(a_{58}=+0.101965503\) \(a_{59}=-0.375359829\) \(a_{60}=+0.256472767\)
\(a_{61}=-0.448097993\) \(a_{62}=-0.243937241\) \(a_{63}=+0.316609810\) \(a_{64}=+0.125000000\) \(a_{65}=+0.223102438\)
\(a_{66}=+0.474474539\) \(a_{67}=-0.418768030\) \(a_{68}=+0.431904974\) \(a_{69}=-0.573117433\) \(a_{70}=-0.340258463\)
\(a_{71}=-1.181731129\) \(a_{72}=-0.296161358\) \(a_{73}=-0.764499556\) \(a_{74}=-0.721352072\) \(a_{75}=+0.250145693\)
\(a_{76}=+0.824734062\) \(a_{77}=-0.629478051\) \(a_{78}=+0.049924608\) \(a_{79}=+1.615646175\) \(a_{80}=+0.318282648\)
\(a_{81}=+0.539363220\) \(a_{82}=+0.203807542\) \(a_{83}=-0.973363857\) \(a_{84}=-0.076141124\) \(a_{85}=+1.099742868\)
\(a_{86}=+0.411591624\) \(a_{87}=+0.058098720\) \(a_{88}=+0.588822800\) \(a_{89}=+0.100984284\) \(a_{90}=-0.754104170\)
\(a_{91}=-0.066234207\) \(a_{92}=-0.711238610\) \(a_{93}=-0.138992512\) \(a_{94}=-1.270249372\) \(a_{95}=+2.099988327\)
\(a_{96}=+0.071223500\) \(a_{97}=-0.238015970\) \(a_{98}=+0.101015254\) \(a_{99}=-1.395092481\) \(a_{100}=+0.310430750\)

Showing 100 of 210 available coefficients

Rows: Cols: