Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.53504130312 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.764725254\) \(a_{3}=-0.577350269\) \(a_{4}=+2.114255223\) \(a_{5}=+1.291616916\)
\(a_{6}=-1.018864601\) \(a_{7}=+0.377964473\) \(a_{8}=+1.966354330\) \(a_{9}=+0.333333333\) \(a_{10}=+2.279348990\)
\(a_{11}=+0.534618333\) \(a_{12}=-1.220665822\) \(a_{13}=-1.900831859\) \(a_{14}=+0.667003451\) \(a_{15}=-0.745715374\)
\(a_{16}=+1.355819925\) \(a_{17}=+0.149396949\) \(a_{18}=+0.588241752\) \(a_{19}=-0.887192570\) \(a_{20}=+2.730807810\)
\(a_{21}=-0.218217890\) \(a_{22}=+0.943454475\) \(a_{23}=-0.075830220\) \(a_{24}=-1.135275203\) \(a_{25}=+0.668274257\)
\(a_{26}=-3.354445986\) \(a_{27}=-0.192450089\) \(a_{28}=+0.799113361\) \(a_{29}=+1.420106735\) \(a_{30}=-1.315982754\)
\(a_{31}=-0.391616629\) \(a_{32}=+0.426295332\) \(a_{33}=-0.308662040\) \(a_{34}=+0.263644566\) \(a_{35}=+0.488185307\)
\(a_{36}=+0.704751745\) \(a_{37}=-0.022705574\) \(a_{38}=-1.565651136\) \(a_{39}=+1.097445779\) \(a_{40}=+2.539776519\)
\(a_{41}=-0.862030894\) \(a_{42}=-0.385094618\) \(a_{43}=-0.417148519\) \(a_{44}=+1.130319596\) \(a_{45}=+0.430538991\)
\(a_{46}=-0.133819492\) \(a_{47}=-1.557763585\) \(a_{48}=-0.782783044\) \(a_{49}=+0.142857142\) \(a_{50}=+1.179320502\)
\(a_{51}=-0.086254339\) \(a_{52}=-4.018843730\) \(a_{53}=+0.582479623\) \(a_{54}=-0.339621465\) \(a_{55}=+0.690522214\)
\(a_{56}=+0.743212048\) \(a_{57}=+0.512220549\) \(a_{58}=+2.506098127\) \(a_{59}=+0.862235053\) \(a_{60}=-1.576632616\)
\(a_{61}=+1.424324214\) \(a_{62}=-0.691095747\) \(a_{63}=+0.125988186\) \(a_{64}=-0.603525791\) \(a_{65}=-2.455146598\)
\(a_{66}=-0.544703713\) \(a_{67}=-0.984746967\) \(a_{68}=+0.315863298\) \(a_{69}=+0.043780581\) \(a_{70}=+0.861512943\)
\(a_{71}=+0.623864256\) \(a_{72}=+0.655451451\) \(a_{73}=+1.549139723\) \(a_{74}=-0.040069124\) \(a_{75}=-0.385828352\)
\(a_{76}=-1.875751541\) \(a_{77}=+0.202066730\) \(a_{78}=+1.936690357\) \(a_{79}=+0.621534867\) \(a_{80}=+1.751199945\)
\(a_{81}=+0.111111105\) \(a_{82}=-1.521247711\) \(a_{83}=-0.858493217\) \(a_{84}=-0.461368303\) \(a_{85}=+0.192963597\)
\(a_{86}=-0.736152584\) \(a_{87}=-0.819899019\) \(a_{88}=+1.051249076\) \(a_{89}=+0.954116895\) \(a_{90}=+0.759782996\)
\(a_{91}=-0.718446867\) \(a_{92}=-0.160324448\) \(a_{93}=+0.226099950\) \(a_{94}=-2.749024752\) \(a_{95}=-1.145912930\)
\(a_{96}=-0.246121666\) \(a_{97}=+0.911134218\) \(a_{98}=+0.252103547\) \(a_{99}=+0.178206143\) \(a_{100}=+1.412902412\)

Showing 100 of 1500 available coefficients

Rows: Cols: