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: \( 3.104912482 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.581630211\) \(a_{3}=+0.577350269\) \(a_{4}=-0.661706298\) \(a_{5}=-0.741194488\)
\(a_{6}=+0.335804359\) \(a_{7}=-0.922678360\) \(a_{8}=-0.966498585\) \(a_{9}=+0.333333333\) \(a_{10}=-0.431101107\)
\(a_{11}=-0.496832270\) \(a_{12}=-0.382036309\) \(a_{13}=+1.475453600\) \(a_{14}=-0.536657609\) \(a_{15}=-0.427928837\)
\(a_{16}=+0.099561522\) \(a_{17}=-0.242535625\) \(a_{18}=+0.193876737\) \(a_{19}=-1.580780051\) \(a_{20}=+0.490453061\)
\(a_{21}=-0.532708600\) \(a_{22}=-0.288972658\) \(a_{23}=-0.765917857\) \(a_{24}=-0.558008218\) \(a_{25}=-0.450630730\)
\(a_{26}=+0.858168388\) \(a_{27}=+0.192450090\) \(a_{28}=+0.610542082\) \(a_{29}=+0.657896447\) \(a_{30}=-0.248896340\)
\(a_{31}=-0.643265713\) \(a_{32}=+1.024406574\) \(a_{33}=-0.286846245\) \(a_{34}=-0.141066047\) \(a_{35}=+0.683884115\)
\(a_{36}=-0.220568766\) \(a_{37}=-1.475503422\) \(a_{38}=-0.919429435\) \(a_{39}=+0.851853533\) \(a_{40}=+0.716363424\)
\(a_{41}=+1.556162287\) \(a_{42}=-0.309839415\) \(a_{43}=+1.280652927\) \(a_{44}=+0.328757042\) \(a_{45}=-0.247064829\)
\(a_{46}=-0.445480965\) \(a_{47}=-0.378430084\) \(a_{48}=+0.057481872\) \(a_{49}=-0.148664644\) \(a_{50}=-0.262100447\)
\(a_{51}=-0.140028008\) \(a_{52}=-0.976316939\) \(a_{53}=-0.178994546\) \(a_{54}=+0.111934786\) \(a_{55}=+0.368249340\)
\(a_{56}=+0.891767329\) \(a_{57}=-0.912663788\) \(a_{58}=+0.382652449\) \(a_{59}=-1.061374673\) \(a_{60}=+0.283163207\)
\(a_{61}=-0.781803314\) \(a_{62}=-0.374142772\) \(a_{63}=-0.307559453\) \(a_{64}=+0.496264290\) \(a_{65}=-1.093598076\)
\(a_{66}=-0.166838442\) \(a_{67}=+0.419187871\) \(a_{68}=+0.160487350\) \(a_{69}=-0.442202881\) \(a_{70}=+0.397767662\)
\(a_{71}=+0.342144894\) \(a_{72}=-0.322166195\) \(a_{73}=-0.131860405\) \(a_{74}=-0.858197367\) \(a_{75}=-0.260171773\)
\(a_{76}=+1.046012115\) \(a_{77}=+0.458416384\) \(a_{78}=+0.495463750\) \(a_{79}=-0.387238057\) \(a_{80}=-0.073794451\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.905111000\) \(a_{83}=+0.354904106\) \(a_{84}=+0.352496635\) \(a_{85}=+0.179766069\)
\(a_{86}=+0.744866432\) \(a_{87}=+0.379836691\) \(a_{88}=+0.480187686\) \(a_{89}=+1.718398871\) \(a_{90}=-0.143700369\)
\(a_{91}=-1.361369108\) \(a_{92}=+0.506812669\) \(a_{93}=-0.371389632\) \(a_{94}=-0.220106370\) \(a_{95}=+1.171665461\)
\(a_{96}=+0.591441411\) \(a_{97}=-1.733210723\) \(a_{98}=-0.086467848\) \(a_{99}=-0.165610757\) \(a_{100}=+0.298185192\)

Showing 100 of 438 available coefficients

Rows: Cols: