Properties

Level $49$
Weight $0$
Character 49.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 49 = 7^{2} \)
Weight: \( 0 \)
Character: 49.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.91732822 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.778363000\) \(a_{3}=+0.337769002\) \(a_{4}=+2.162574960\) \(a_{5}=+0.539421998\)
\(a_{6}=-0.600675892\) \(a_{7}=+0.000000000\) \(a_{8}=-2.067480293\) \(a_{9}=-0.885912103\) \(a_{10}=-0.959288126\)
\(a_{11}=+0.373796999\) \(a_{12}=+0.730450782\) \(a_{13}=-0.903329998\) \(a_{14}=+0.000000000\) \(a_{15}=+0.182200030\)
\(a_{16}=+1.514155497\) \(a_{17}=+0.338530999\) \(a_{18}=+1.575473305\) \(a_{19}=-1.695850000\) \(a_{20}=+1.166540510\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.664746754\) \(a_{23}=-0.852803400\) \(a_{24}=-0.698330751\) \(a_{25}=-0.709023906\)
\(a_{26}=+1.606448649\) \(a_{27}=-0.637002645\) \(a_{28}=+0.000000000\) \(a_{29}=+0.861859977\) \(a_{30}=-0.324017791\)
\(a_{31}=-1.266240001\) \(a_{32}=-0.625237819\) \(a_{33}=+0.126257039\) \(a_{34}=-0.602031005\) \(a_{35}=+0.000000000\)
\(a_{36}=-1.915851330\) \(a_{37}=+0.315199852\) \(a_{38}=+3.015836894\) \(a_{39}=-0.305116871\) \(a_{40}=-1.115244355\)
\(a_{41}=-0.467900008\) \(a_{42}=+0.000000000\) \(a_{43}=+0.719400406\) \(a_{44}=+0.808364032\) \(a_{45}=-0.477880478\)
\(a_{46}=+1.516594013\) \(a_{47}=+0.161499977\) \(a_{48}=+0.511434788\) \(a_{49}=+0.000000000\) \(a_{50}=+1.260901880\)
\(a_{51}=+0.114345277\) \(a_{52}=-1.953518838\) \(a_{53}=-0.664600015\) \(a_{54}=+1.132821935\) \(a_{55}=+0.201634325\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.572805559\) \(a_{58}=-1.532699935\) \(a_{59}=-0.170800000\) \(a_{60}=+0.394021222\)
\(a_{61}=-1.600700021\) \(a_{62}=+2.251834365\) \(a_{63}=+0.000000000\) \(a_{64}=-0.402255694\) \(a_{65}=-0.487276075\)
\(a_{66}=-0.224530846\) \(a_{67}=+0.033100009\) \(a_{68}=+0.732098664\) \(a_{69}=-0.288050552\) \(a_{70}=+0.000000000\)

Showing all 70 available coefficients

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