Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 30.5862790482 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.010612718\) \(a_{3}=+0.577350269\) \(a_{4}=-0.999887370\) \(a_{5}=-0.182474037\)
\(a_{6}=+0.006127256\) \(a_{7}=-0.630660599\) \(a_{8}=-0.021224240\) \(a_{9}=+0.333333333\) \(a_{10}=-0.001936545\)
\(a_{11}=+0.807667779\) \(a_{12}=-0.577285242\) \(a_{13}=+0.133443027\) \(a_{14}=-0.006693023\) \(a_{15}=-0.105351434\)
\(a_{16}=+0.999662123\) \(a_{17}=+1.450356568\) \(a_{18}=+0.003537573\) \(a_{19}=-0.157096574\) \(a_{20}=+0.182453485\)
\(a_{21}=-0.364112066\) \(a_{22}=+0.008571550\) \(a_{23}=-0.462265881\) \(a_{24}=-0.012253821\) \(a_{25}=-0.966703226\)
\(a_{26}=+0.001416193\) \(a_{27}=+0.192450090\) \(a_{28}=+0.630589567\) \(a_{29}=+0.281568001\) \(a_{30}=-0.001118065\)
\(a_{31}=-1.588492411\) \(a_{32}=+0.031833372\) \(a_{33}=+0.466307210\) \(a_{34}=+0.015392225\) \(a_{35}=+0.115079185\)
\(a_{36}=-0.333295790\) \(a_{37}=+1.152122107\) \(a_{38}=-0.001667222\) \(a_{39}=+0.077043368\) \(a_{40}=+0.003872873\)
\(a_{41}=-0.501420897\) \(a_{42}=-0.003864219\) \(a_{43}=-0.975842436\) \(a_{44}=-0.807576812\) \(a_{45}=-0.060824679\)
\(a_{46}=-0.004905897\) \(a_{47}=+1.332983125\) \(a_{48}=+0.577155196\) \(a_{49}=-0.602267209\) \(a_{50}=-0.010259349\)
\(a_{51}=+0.837363755\) \(a_{52}=-0.133427998\) \(a_{53}=+1.670290014\) \(a_{54}=+0.002042419\) \(a_{55}=-0.147378400\)
\(a_{56}=+0.013385292\) \(a_{57}=-0.090699749\) \(a_{58}=+0.002988202\) \(a_{59}=-1.569334104\) \(a_{60}=+0.105339569\)
\(a_{61}=-1.219524176\) \(a_{62}=-0.016858222\) \(a_{63}=-0.210220200\) \(a_{64}=-0.999324285\) \(a_{65}=-0.024349888\)
\(a_{66}=+0.004948787\) \(a_{67}=-1.543139786\) \(a_{68}=-1.450193214\) \(a_{69}=-0.266889331\) \(a_{70}=+0.001221303\)
\(a_{71}=-0.885553955\) \(a_{72}=-0.007074747\) \(a_{73}=+0.060480623\) \(a_{74}=+0.012227147\) \(a_{75}=-0.558126368\)
\(a_{76}=+0.157078880\) \(a_{77}=-0.509364245\) \(a_{78}=+0.000817640\) \(a_{79}=-1.323267444\) \(a_{80}=-0.182412383\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.005321439\) \(a_{83}=+0.431513321\) \(a_{84}=+0.364071057\) \(a_{85}=-0.264652418\)
\(a_{86}=-0.010356340\) \(a_{87}=+0.162563361\) \(a_{88}=-0.017142135\) \(a_{89}=-0.729784125\) \(a_{90}=-0.000645515\)
\(a_{91}=-0.084157260\) \(a_{92}=+0.462213816\) \(a_{93}=-0.917116521\) \(a_{94}=+0.014146574\) \(a_{95}=+0.028666046\)
\(a_{96}=+0.018379006\) \(a_{97}=+0.973059892\) \(a_{98}=-0.006391692\) \(a_{99}=+0.269222593\) \(a_{100}=+0.966594346\)

Showing 100 of 1228 available coefficients

Rows: Cols: