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: \( 3.27272100042 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.205416822\) \(a_{3}=+0.577350269\) \(a_{4}=-0.957803929\) \(a_{5}=-1.664126630\)
\(a_{6}=-0.118597458\) \(a_{7}=+0.377964473\) \(a_{8}=+0.402165862\) \(a_{9}=+0.333333333\) \(a_{10}=+0.341839604\)
\(a_{11}=-0.882398558\) \(a_{12}=-0.552988356\) \(a_{13}=+0.367438860\) \(a_{14}=-0.077640261\) \(a_{15}=-0.960783958\)
\(a_{16}=+0.875192296\) \(a_{17}=-0.703523624\) \(a_{18}=-0.068472274\) \(a_{19}=-0.946098324\) \(a_{20}=+1.593907025\)
\(a_{21}=+0.218217890\) \(a_{22}=+0.181259508\) \(a_{23}=-1.575754205\) \(a_{24}=+0.232190568\) \(a_{25}=+1.769317440\)
\(a_{26}=-0.075478123\) \(a_{27}=+0.192450090\) \(a_{28}=-0.362015857\) \(a_{29}=-0.131492336\) \(a_{30}=+0.197361187\)
\(a_{31}=+1.013855867\) \(a_{32}=-0.581945081\) \(a_{33}=-0.509453045\) \(a_{34}=+0.144515586\) \(a_{35}=-0.628980746\)
\(a_{36}=-0.319267975\) \(a_{37}=-1.484763623\) \(a_{38}=+0.194344510\) \(a_{39}=+0.212140920\) \(a_{40}=-0.669254921\)
\(a_{41}=+0.782132041\) \(a_{42}=-0.044825618\) \(a_{43}=+0.435301503\) \(a_{44}=+0.845164787\) \(a_{45}=-0.554708870\)
\(a_{46}=+0.323686458\) \(a_{47}=+0.270215871\) \(a_{48}=+0.505292454\) \(a_{49}=+0.142857094\) \(a_{50}=-0.363447507\)
\(a_{51}=-0.406179435\) \(a_{52}=-0.351934408\) \(a_{53}=+0.304762583\) \(a_{54}=-0.039532577\) \(a_{55}=+1.468423253\)
\(a_{56}=+0.152004407\) \(a_{57}=-0.546230123\) \(a_{58}=+0.027010739\) \(a_{59}=+0.220306381\) \(a_{60}=+0.920242650\)
\(a_{61}=-0.600031802\) \(a_{62}=-0.208263053\) \(a_{63}=+0.125988161\) \(a_{64}=-0.755650981\) \(a_{65}=-0.611464792\)
\(a_{66}=+0.104650215\) \(a_{67}=-1.640404285\) \(a_{68}=+0.673837703\) \(a_{69}=-0.909762106\) \(a_{70}=+0.129203214\)
\(a_{71}=-1.734465615\) \(a_{72}=+0.134055280\) \(a_{73}=+1.229450514\) \(a_{74}=+0.304995424\) \(a_{75}=+1.021515826\)
\(a_{76}=+0.906176775\) \(a_{77}=-0.333515228\) \(a_{78}=-0.043577311\) \(a_{79}=+0.644581316\) \(a_{80}=-1.456430942\)
\(a_{81}=+0.111110019\) \(a_{82}=-0.160662953\) \(a_{83}=+0.682536954\) \(a_{84}=-0.209010851\) \(a_{85}=+1.170748377\)
\(a_{86}=-0.089419150\) \(a_{87}=-0.075920910\) \(a_{88}=-0.354856517\) \(a_{89}=-0.563248709\) \(a_{90}=+0.113941829\)
\(a_{91}=+0.138885832\) \(a_{92}=+1.509275683\) \(a_{93}=+0.585326943\) \(a_{94}=-0.055468806\) \(a_{95}=+1.574427415\)
\(a_{96}=-0.335986154\) \(a_{97}=-0.615884411\) \(a_{98}=-0.029345307\) \(a_{99}=-0.294132797\) \(a_{100}=-1.694659174\)

Showing 100 of 1500 available coefficients

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