Properties

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

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 6.85909810894 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.207559609\) \(a_{3}=-0.577350269\) \(a_{4}=+0.458200209\) \(a_{5}=+0.724184803\)
\(a_{6}=-0.697184865\) \(a_{7}=-0.377964473\) \(a_{8}=-0.654255544\) \(a_{9}=+0.333333333\) \(a_{10}=+0.874496317\)
\(a_{11}=+0.093599311\) \(a_{12}=-0.264542014\) \(a_{13}=-1.274772431\) \(a_{14}=-0.456414631\) \(a_{15}=-0.418108291\)
\(a_{16}=-1.248252777\) \(a_{17}=-0.662538883\) \(a_{18}=+0.402519870\) \(a_{19}=-0.499393647\) \(a_{20}=+0.331821628\)
\(a_{21}=+0.218217890\) \(a_{22}=+0.113026747\) \(a_{23}=-1.573964388\) \(a_{24}=+0.377734614\) \(a_{25}=-0.475556371\)
\(a_{26}=-1.539363698\) \(a_{27}=-0.192450090\) \(a_{28}=-0.173183401\) \(a_{29}=-0.227941197\) \(a_{30}=-0.504890684\)
\(a_{31}=+1.402900678\) \(a_{32}=-0.853084092\) \(a_{33}=-0.054039587\) \(a_{34}=-0.800055195\) \(a_{35}=-0.273716127\)
\(a_{36}=+0.152733403\) \(a_{37}=+1.613801354\) \(a_{38}=-0.603047597\) \(a_{39}=+0.735990206\) \(a_{40}=-0.473801922\)
\(a_{41}=-0.289874407\) \(a_{42}=+0.263511110\) \(a_{43}=+0.487703734\) \(a_{44}=+0.042887224\) \(a_{45}=+0.241394934\)
\(a_{46}=-1.900655820\) \(a_{47}=-0.506654102\) \(a_{48}=+0.720679077\) \(a_{49}=+0.142857143\) \(a_{50}=-0.574262666\)
\(a_{51}=+0.382517003\) \(a_{52}=-0.584100994\) \(a_{53}=+0.999612827\) \(a_{54}=-0.232394955\) \(a_{55}=+0.067783198\)
\(a_{56}=+0.247285352\) \(a_{57}=+0.288325056\) \(a_{58}=-0.275252583\) \(a_{59}=-0.764703302\) \(a_{60}=-0.191577306\)
\(a_{61}=-1.281593856\) \(a_{62}=+1.694086194\) \(a_{63}=-0.125988158\) \(a_{64}=+0.218102885\) \(a_{65}=-0.923170822\)
\(a_{66}=-0.065256023\) \(a_{67}=+0.915150660\) \(a_{68}=-0.303575455\) \(a_{69}=+0.908728763\) \(a_{70}=-0.330528540\)
\(a_{71}=+1.394021251\) \(a_{72}=-0.218085181\) \(a_{73}=-1.758910937\) \(a_{74}=+1.948761332\) \(a_{75}=+0.274562599\)
\(a_{76}=-0.228822273\) \(a_{77}=-0.035377214\) \(a_{78}=+0.888752046\) \(a_{79}=-0.840935271\) \(a_{80}=-0.903965691\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.350040625\) \(a_{83}=-0.544291880\) \(a_{84}=+0.099987483\) \(a_{85}=-0.479800590\)
\(a_{86}=+0.588931330\) \(a_{87}=+0.131601912\) \(a_{88}=-0.061237868\) \(a_{89}=-1.528180594\) \(a_{90}=+0.291498772\)
\(a_{91}=+0.481818690\) \(a_{92}=-0.721190811\) \(a_{93}=-0.809965084\) \(a_{94}=-0.611815029\) \(a_{95}=-0.361653290\)
\(a_{96}=+0.492528330\) \(a_{97}=+1.159719668\) \(a_{98}=+0.172508516\) \(a_{99}=+0.031199770\) \(a_{100}=-0.217900029\)

Showing 100 of 312 available coefficients

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