Properties

Level 10
Weight 0
Character 10.1
Symmetry odd
Fricke sign +1

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: \(+1\)
Spectral parameter: \( 15.9987139994 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.370920476\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.969387165\) \(a_{7}=-0.756361486\) \(a_{8}=-0.353553391\) \(a_{9}=+0.879422950\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.360267654\) \(a_{12}=-0.685460238\) \(a_{13}=-0.944252376\) \(a_{14}=+0.534828336\) \(a_{15}=+0.613094275\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.666750944\) \(a_{18}=-0.621845932\) \(a_{19}=+1.658655115\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.036911449\) \(a_{22}=+0.254747701\) \(a_{23}=+0.325038395\) \(a_{24}=+0.484693582\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.667687258\) \(a_{27}=+0.165301546\) \(a_{28}=-0.378180743\) \(a_{29}=+1.645532530\) \(a_{30}=-0.433523119\)
\(a_{31}=-0.936099936\) \(a_{32}=-0.176776695\) \(a_{33}=+0.493898303\) \(a_{34}=+0.471464114\) \(a_{35}=+0.338255140\)
\(a_{36}=+0.439711475\) \(a_{37}=+1.363758648\) \(a_{38}=-1.172846279\) \(a_{39}=+1.294494916\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.733449779\) \(a_{42}=-0.733207117\) \(a_{43}=+0.070910745\) \(a_{44}=-0.180133827\) \(a_{45}=-0.393289900\)
\(a_{46}=-0.229836854\) \(a_{47}=-0.653027513\) \(a_{48}=-0.342730119\) \(a_{49}=-0.427917302\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.914062522\) \(a_{52}=-0.472126188\) \(a_{53}=-0.198510946\) \(a_{54}=-0.116885844\) \(a_{55}=+0.161116593\)
\(a_{56}=+0.267414168\) \(a_{57}=-2.273884259\) \(a_{58}=-1.163567210\) \(a_{59}=-1.587314088\) \(a_{60}=+0.306547138\)
\(a_{61}=-1.109267835\) \(a_{62}=+0.661922612\) \(a_{63}=-0.665161650\) \(a_{64}=+0.125000000\) \(a_{65}=+0.422282500\)
\(a_{66}=-0.349238839\) \(a_{67}=+1.047569669\) \(a_{68}=-0.333375472\) \(a_{69}=-0.445601792\) \(a_{70}=-0.239182503\)
\(a_{71}=-0.241537717\) \(a_{72}=-0.310922966\) \(a_{73}=-1.073197975\) \(a_{74}=-0.964322988\) \(a_{75}=-0.274184095\)
\(a_{76}=+0.829327557\) \(a_{77}=+0.272492578\) \(a_{78}=-0.915346133\) \(a_{79}=+1.983387071\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.106038225\) \(a_{82}=-1.225734094\) \(a_{83}=+0.564964834\) \(a_{84}=+0.518455724\) \(a_{85}=+0.298180087\)
\(a_{86}=-0.050141469\) \(a_{87}=-2.255894237\) \(a_{88}=+0.127373850\) \(a_{89}=+0.667463578\) \(a_{90}=+0.278097955\)
\(a_{91}=+0.714196129\) \(a_{92}=+0.162519198\) \(a_{93}=+1.283318565\) \(a_{94}=+0.461760183\) \(a_{95}=-0.741773118\)
\(a_{96}=+0.242346791\) \(a_{97}=-1.424198442\) \(a_{98}=+0.302583226\) \(a_{99}=-0.316827632\) \(a_{100}=+0.099975586\)

Showing 100 of 166 available coefficients

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