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: \( 31.1496545383 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.597639621\) \(a_{3}=+0.577350269\) \(a_{4}=-0.642826883\) \(a_{5}=-1.424943641\)
\(a_{6}=-0.345047396\) \(a_{7}=+0.348614636\) \(a_{8}=+0.981818436\) \(a_{9}=+0.333333333\) \(a_{10}=+0.851602778\)
\(a_{11}=+0.275947047\) \(a_{12}=-0.371136274\) \(a_{13}=-1.142728487\) \(a_{14}=-0.208345919\) \(a_{15}=-0.822691594\)
\(a_{16}=+0.056053285\) \(a_{17}=-1.661620039\) \(a_{18}=-0.199213207\) \(a_{19}=-0.662254822\) \(a_{20}=+0.915992079\)
\(a_{21}=+0.201272754\) \(a_{22}=-0.164916889\) \(a_{23}=-0.704716094\) \(a_{24}=+0.566853138\) \(a_{25}=+1.030464379\)
\(a_{26}=+0.682939820\) \(a_{27}=+0.192450090\) \(a_{28}=-0.224098860\) \(a_{29}=-0.396504595\) \(a_{30}=+0.491673093\)
\(a_{31}=-0.507899132\) \(a_{32}=-1.015318100\) \(a_{33}=+0.159318102\) \(a_{34}=+0.993049971\) \(a_{35}=-0.496756208\)
\(a_{36}=-0.214275628\) \(a_{37}=-1.835527761\) \(a_{38}=+0.395789721\) \(a_{39}=-0.659754599\) \(a_{40}=-1.399035937\)
\(a_{41}=+1.554512934\) \(a_{42}=-0.120288572\) \(a_{43}=+0.537129129\) \(a_{44}=-0.177386180\) \(a_{45}=-0.474981214\)
\(a_{46}=+0.421166259\) \(a_{47}=+1.772441797\) \(a_{48}=+0.032362379\) \(a_{49}=-0.878467836\) \(a_{50}=-0.615846341\)
\(a_{51}=-0.959336777\) \(a_{52}=+0.734576591\) \(a_{53}=-1.538256527\) \(a_{54}=-0.115015799\) \(a_{55}=-0.393208990\)
\(a_{56}=+0.342276277\) \(a_{57}=-0.382353000\) \(a_{58}=+0.236966856\) \(a_{59}=-0.463230594\) \(a_{60}=+0.528848273\)
\(a_{61}=+0.400606355\) \(a_{62}=+0.303540645\) \(a_{63}=+0.116204879\) \(a_{64}=+0.550741040\) \(a_{65}=+1.628323690\)
\(a_{66}=-0.095214810\) \(a_{67}=+1.502776530\) \(a_{68}=+1.068134031\) \(a_{69}=-0.406868027\) \(a_{70}=+0.296881192\)
\(a_{71}=-0.141183368\) \(a_{72}=+0.327272812\) \(a_{73}=+0.915389584\) \(a_{74}=+1.096984116\) \(a_{75}=+0.594938887\)
\(a_{76}=+0.425715203\) \(a_{77}=+0.096199179\) \(a_{78}=+0.394295489\) \(a_{79}=+0.001623342\) \(a_{80}=-0.079872772\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.929038521\) \(a_{83}=+0.283293463\) \(a_{84}=-0.129383537\) \(a_{85}=+2.367714908\)
\(a_{86}=-0.321009649\) \(a_{87}=-0.228922035\) \(a_{88}=+0.270929898\) \(a_{89}=-0.563299499\) \(a_{90}=+0.283867593\)
\(a_{91}=-0.398371875\) \(a_{92}=+0.453010450\) \(a_{93}=-0.293235700\) \(a_{94}=-1.059281444\) \(a_{95}=+0.943675797\)
\(a_{96}=-0.586194178\) \(a_{97}=+0.682344800\) \(a_{98}=+0.525007185\) \(a_{99}=+0.091982349\) \(a_{100}=-0.662410205\)

Showing 100 of 1228 available coefficients

Rows: Cols: