Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 49.6835200753 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.336387405\) \(a_{3}=+1.570653320\) \(a_{4}=+0.785931297\) \(a_{5}=+1.009222072\)
\(a_{6}=+2.099001315\) \(a_{7}=+1.027333424\) \(a_{8}=-0.286078719\) \(a_{9}=+1.466951852\) \(a_{10}=+1.348711665\)
\(a_{11}=+1.315634232\) \(a_{12}=+1.234425601\) \(a_{13}=-0.749573343\) \(a_{14}=+1.372915449\) \(a_{15}=+1.585137998\)
\(a_{16}=-1.168243294\) \(a_{17}=-0.669573789\) \(a_{18}=+1.960415980\) \(a_{19}=+0.332704519\) \(a_{20}=+0.793179213\)
\(a_{21}=+1.613584646\) \(a_{22}=+1.758197078\) \(a_{23}=-0.863361160\) \(a_{24}=-0.449330490\) \(a_{25}=+0.018529190\)
\(a_{26}=-1.001720374\) \(a_{27}=+0.733419477\) \(a_{28}=+0.807413490\) \(a_{29}=+1.356440269\) \(a_{30}=+2.118358455\)
\(a_{31}=+0.715037170\) \(a_{32}=-1.275146905\) \(a_{33}=+2.066405275\) \(a_{34}=-0.894809978\) \(a_{35}=+1.036807567\)
\(a_{36}=+1.152923372\) \(a_{37}=-0.997157215\) \(a_{38}=+0.444622129\) \(a_{39}=-1.177319859\) \(a_{40}=-0.288716957\)
\(a_{41}=-0.349403233\) \(a_{42}=+2.156374209\) \(a_{43}=-1.374860769\) \(a_{44}=+1.033998118\) \(a_{45}=+1.480480187\)
\(a_{46}=-1.153784981\) \(a_{47}=+0.232910652\) \(a_{48}=-1.834905208\) \(a_{49}=+0.055413965\) \(a_{50}=+0.024762176\)
\(a_{51}=-1.051668295\) \(a_{52}=-0.589113149\) \(a_{53}=+0.209451910\) \(a_{54}=+0.980132552\) \(a_{55}=+1.327767105\)
\(a_{56}=-0.293898230\) \(a_{57}=+0.522563457\) \(a_{58}=+1.812729692\) \(a_{59}=+0.729608536\) \(a_{60}=+1.245809562\)
\(a_{61}=-0.198269297\) \(a_{62}=+0.955566670\) \(a_{63}=+1.507048670\) \(a_{64}=-0.535846972\) \(a_{65}=-0.756485955\)
\(a_{66}=+2.761517971\) \(a_{67}=-0.034300399\) \(a_{68}=-0.526238964\) \(a_{69}=-1.356041189\) \(a_{70}=+1.385576781\)
\(a_{71}=+0.937993949\) \(a_{72}=-0.419663707\) \(a_{73}=+0.587401203\) \(a_{74}=-1.332588343\) \(a_{75}=+0.029102933\)
\(a_{76}=+0.261482894\) \(a_{77}=+1.351595021\) \(a_{78}=-1.573355432\) \(a_{79}=+1.720003603\) \(a_{80}=-1.179016917\)
\(a_{81}=-0.315004115\) \(a_{82}=-0.466938080\) \(a_{83}=+0.774494367\) \(a_{84}=+1.268166680\) \(a_{85}=-0.675748646\)
\(a_{86}=-1.837346616\) \(a_{87}=+2.130497413\) \(a_{88}=-0.376374956\) \(a_{89}=-1.654302078\) \(a_{90}=+1.978495076\)
\(a_{91}=-0.770061749\) \(a_{92}=-0.678542556\) \(a_{93}=+1.123075506\) \(a_{94}=+0.311258862\) \(a_{95}=+0.335772743\)
\(a_{96}=-2.002813720\) \(a_{97}=-0.131517722\) \(a_{98}=+0.074054524\) \(a_{99}=+1.929972074\) \(a_{100}=+0.014562671\)

Showing 100 of 5000 available coefficients

Rows: Cols: