Properties

Level $51$
Weight $0$
Character 51.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 51 = 3 \cdot 17 \)
Weight: \( 0 \)
Character: 51.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.64594761554 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.691634850\) \(a_{3}=-0.577350269\) \(a_{4}=-0.521641235\) \(a_{5}=+1.594744171\)
\(a_{6}=-0.399315567\) \(a_{7}=+0.534640687\) \(a_{8}=-1.052420107\) \(a_{9}=+0.333333333\) \(a_{10}=+1.102980645\)
\(a_{11}=+0.793961201\) \(a_{12}=+0.301169707\) \(a_{13}=+1.096967951\) \(a_{14}=+0.369776131\) \(a_{15}=-0.920725976\)
\(a_{16}=-0.206249188\) \(a_{17}=-0.242535625\) \(a_{18}=+0.230544950\) \(a_{19}=+1.220553697\) \(a_{20}=-0.831884318\)
\(a_{21}=-0.308674945\) \(a_{22}=+0.549131236\) \(a_{23}=-0.013170881\) \(a_{24}=+0.607615032\) \(a_{25}=+1.543208970\)
\(a_{26}=+0.758701264\) \(a_{27}=-0.192450090\) \(a_{28}=-0.278890628\) \(a_{29}=+0.263443749\) \(a_{30}=-0.636806172\)
\(a_{31}=+0.448537401\) \(a_{32}=+0.909770981\) \(a_{33}=-0.458393713\) \(a_{34}=-0.167746091\) \(a_{35}=+0.852615119\)
\(a_{36}=-0.173880412\) \(a_{37}=-1.990438342\) \(a_{38}=+0.844177473\) \(a_{39}=-0.633334742\) \(a_{40}=-1.678340830\)
\(a_{41}=+0.571573222\) \(a_{42}=-0.213490349\) \(a_{43}=+0.690936965\) \(a_{44}=-0.414162901\) \(a_{45}=+0.531581390\)
\(a_{46}=-0.009109440\) \(a_{47}=-0.015212213\) \(a_{48}=+0.119078024\) \(a_{49}=-0.714159336\) \(a_{50}=+1.067337104\)
\(a_{51}=+0.140028008\) \(a_{52}=-0.572223716\) \(a_{53}=-1.915511961\) \(a_{54}=-0.133105189\) \(a_{55}=+1.266164998\)
\(a_{56}=-0.562666609\) \(a_{57}=-0.704687005\) \(a_{58}=+0.182206878\) \(a_{59}=+1.505090377\) \(a_{60}=+0.480288635\)
\(a_{61}=+0.443753664\) \(a_{62}=+0.310224098\) \(a_{63}=+0.178213562\) \(a_{64}=+0.835478503\) \(a_{65}=+1.749383245\)
\(a_{66}=-0.317041067\) \(a_{67}=+0.596201840\) \(a_{68}=+0.126516583\) \(a_{69}=+0.007604212\) \(a_{70}=+0.589698330\)
\(a_{71}=-0.292594348\) \(a_{72}=-0.350806702\) \(a_{73}=+0.734095185\) \(a_{74}=-1.376656524\) \(a_{75}=-0.890972114\)
\(a_{76}=-0.636691137\) \(a_{77}=+0.424483962\) \(a_{78}=-0.438036379\) \(a_{79}=-1.898540352\) \(a_{80}=-0.328914690\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.395319960\) \(a_{83}=-0.577882692\) \(a_{84}=+0.161017579\) \(a_{85}=-0.386782274\)
\(a_{86}=+0.477876084\) \(a_{87}=-0.152099319\) \(a_{88}=-0.835580732\) \(a_{89}=-0.014663117\) \(a_{90}=+0.367660215\)
\(a_{91}=+0.586483699\) \(a_{92}=+0.006870475\) \(a_{93}=-0.258963189\) \(a_{94}=-0.010521297\) \(a_{95}=+1.946470893\)
\(a_{96}=-0.525256521\) \(a_{97}=+0.761300369\) \(a_{98}=-0.493937485\) \(a_{99}=+0.264653734\) \(a_{100}=-0.805001433\)

Showing 100 of 486 available coefficients

Rows: Cols: