Properties

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

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 5.30882254291 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.374821757\) \(a_{3}=-0.577350269\) \(a_{4}=+0.890134863\) \(a_{5}=+0.323814261\)
\(a_{6}=+0.793753711\) \(a_{7}=+0.377964473\) \(a_{8}=+0.151044981\) \(a_{9}=+0.333333333\) \(a_{10}=-0.445186891\)
\(a_{11}=+0.102336394\) \(a_{12}=-0.513919603\) \(a_{13}=-0.852433296\) \(a_{14}=-0.519633781\) \(a_{15}=-0.186954251\)
\(a_{16}=-1.097794789\) \(a_{17}=+0.936518274\) \(a_{18}=-0.458273919\) \(a_{19}=+0.410251422\) \(a_{20}=+0.288238363\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.140694301\) \(a_{23}=-0.675379289\) \(a_{24}=-0.087205860\) \(a_{25}=-0.895144325\)
\(a_{26}=+1.171943841\) \(a_{27}=-0.192450090\) \(a_{28}=+0.336439354\) \(a_{29}=+0.851958513\) \(a_{30}=+0.257028771\)
\(a_{31}=-1.834969013\) \(a_{32}=+1.358227179\) \(a_{33}=-0.059083945\) \(a_{34}=-1.287545699\) \(a_{35}=+0.122390286\)
\(a_{36}=+0.296711621\) \(a_{37}=-1.797217454\) \(a_{38}=-0.564022580\) \(a_{39}=+0.492152593\) \(a_{40}=+0.048910519\)
\(a_{41}=+0.123287559\) \(a_{42}=+0.300010703\) \(a_{43}=+1.360573390\) \(a_{44}=+0.091093192\) \(a_{45}=+0.107938087\)
\(a_{46}=+0.928526140\) \(a_{47}=-0.291244119\) \(a_{48}=+0.633812117\) \(a_{49}=+0.142857143\) \(a_{50}=+1.230663893\)
\(a_{51}=-0.540699078\) \(a_{52}=-0.758780595\) \(a_{53}=-1.178004124\) \(a_{54}=+0.264584570\) \(a_{55}=+0.033137984\)
\(a_{56}=+0.057089637\) \(a_{57}=-0.236858769\) \(a_{58}=-1.171291099\) \(a_{59}=-1.253449764\) \(a_{60}=-0.166414496\)
\(a_{61}=-1.755658570\) \(a_{62}=+2.522755322\) \(a_{63}=+0.125988158\) \(a_{64}=-0.769525488\) \(a_{65}=-0.276030057\)
\(a_{66}=+0.081229893\) \(a_{67}=+0.998300450\) \(a_{68}=+0.833627565\) \(a_{69}=+0.389930414\) \(a_{70}=-0.168264829\)
\(a_{71}=-1.184638284\) \(a_{72}=+0.050348327\) \(a_{73}=+0.301541607\) \(a_{74}=+2.470853657\) \(a_{75}=+0.516811817\)
\(a_{76}=+0.365179093\) \(a_{77}=+0.038679521\) \(a_{78}=-0.676622092\) \(a_{79}=-0.170916083\) \(a_{80}=-0.355481608\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.169498419\) \(a_{83}=+0.344606453\) \(a_{84}=-0.194243352\) \(a_{85}=+0.303257972\)
\(a_{86}=-1.870545899\) \(a_{87}=-0.491878477\) \(a_{88}=+0.015457399\) \(a_{89}=-0.413402940\) \(a_{90}=-0.148395630\)
\(a_{91}=-0.322189501\) \(a_{92}=-0.601178651\) \(a_{93}=+1.059419854\) \(a_{94}=+0.400408752\) \(a_{95}=+0.132845261\)
\(a_{96}=-0.784172828\) \(a_{97}=+1.503949960\) \(a_{98}=-0.196403108\) \(a_{99}=+0.034112131\) \(a_{100}=-0.796799171\)

Showing 100 of 198 available coefficients

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