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: \( 28.1082072398 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.210630707\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.856045182\) \(a_{7}=+1.931135781\) \(a_{8}=-0.353553391\) \(a_{9}=+0.465626709\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.107920935\) \(a_{12}=-0.605315353\) \(a_{13}=+0.249271773\) \(a_{14}=-1.365519206\) \(a_{15}=-0.541410511\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.363848669\) \(a_{18}=-0.329247803\) \(a_{19}=+0.567650880\) \(a_{20}=+0.223606798\)
\(a_{21}=-2.337892275\) \(a_{22}=+0.076311625\) \(a_{23}=+1.370926499\) \(a_{24}=+0.428022591\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.176261761\) \(a_{27}=+0.646928715\) \(a_{28}=+0.965567890\) \(a_{29}=+0.934026322\) \(a_{30}=+0.382835044\)
\(a_{31}=+1.169981414\) \(a_{32}=-0.176776695\) \(a_{33}=+0.130652398\) \(a_{34}=+0.257279861\) \(a_{35}=+0.863630176\)
\(a_{36}=+0.232813354\) \(a_{37}=+0.861168602\) \(a_{38}=-0.401389787\) \(a_{39}=-0.301776063\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.352654813\) \(a_{42}=+1.653139482\) \(a_{43}=+0.741941014\) \(a_{44}=-0.053960468\) \(a_{45}=+0.208234595\)
\(a_{46}=-0.969391424\) \(a_{47}=+1.720816090\) \(a_{48}=-0.302657677\) \(a_{49}=+2.729285403\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.440486371\) \(a_{52}=+0.124635886\) \(a_{53}=-0.423778065\) \(a_{54}=-0.457447682\) \(a_{55}=-0.048263709\)
\(a_{56}=-0.682759603\) \(a_{57}=-0.687215586\) \(a_{58}=-0.660456346\) \(a_{59}=-1.297818266\) \(a_{60}=-0.270705256\)
\(a_{61}=-0.751875663\) \(a_{62}=-0.827301792\) \(a_{63}=+0.899188398\) \(a_{64}=+0.125000000\) \(a_{65}=+0.111477726\)
\(a_{66}=-0.092385197\) \(a_{67}=+0.693389793\) \(a_{68}=-0.181924334\) \(a_{69}=-1.659685717\) \(a_{70}=-0.610678754\)
\(a_{71}=+1.674291975\) \(a_{72}=-0.164623902\) \(a_{73}=-1.140557321\) \(a_{74}=-0.608938158\) \(a_{75}=-0.242126141\)
\(a_{76}=+0.283825440\) \(a_{77}=-0.208409979\) \(a_{78}=+0.213387900\) \(a_{79}=+0.480225565\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.248818477\) \(a_{82}=+0.956471391\) \(a_{83}=+1.103789940\) \(a_{84}=-1.168946138\) \(a_{85}=-0.162718071\)
\(a_{86}=-0.524631522\) \(a_{87}=-1.130760947\) \(a_{88}=+0.038155813\) \(a_{89}=+0.550455717\) \(a_{90}=-0.147244094\)
\(a_{91}=+0.481377640\) \(a_{92}=+0.685463250\) \(a_{93}=-1.416415426\) \(a_{94}=-1.216800727\) \(a_{95}=+0.253861191\)
\(a_{96}=+0.214011296\) \(a_{97}=-0.401295693\) \(a_{98}=-1.929896217\) \(a_{99}=-0.050250870\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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