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: \( 14.6481407612 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.385435318\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.979650709\) \(a_{7}=+1.361667026\) \(a_{8}=+0.353553391\) \(a_{9}=+0.919431022\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.377100082\) \(a_{12}=+0.692717659\) \(a_{13}=+1.645930561\) \(a_{14}=+0.962843988\) \(a_{15}=-0.619585510\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.084704326\) \(a_{18}=+0.650135910\) \(a_{19}=+0.664141306\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.886501590\) \(a_{22}=-0.973756807\) \(a_{23}=+1.298466048\) \(a_{24}=+0.489825354\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.163848661\) \(a_{27}=-0.111623108\) \(a_{28}=+0.680833513\) \(a_{29}=-1.340710731\) \(a_{30}=-0.438113116\)
\(a_{31}=+1.002714303\) \(a_{32}=+0.176776695\) \(a_{33}=-1.907883091\) \(a_{34}=+0.059895003\) \(a_{35}=-0.608956007\)
\(a_{36}=+0.459715511\) \(a_{37}=-0.166118533\) \(a_{38}=+0.469618821\) \(a_{39}=+2.280330331\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.859026794\) \(a_{42}=+1.333958067\) \(a_{43}=+0.192022552\) \(a_{44}=-0.688550041\) \(a_{45}=-0.411182053\)
\(a_{46}=+0.918154148\) \(a_{47}=+1.101821121\) \(a_{48}=+0.346358830\) \(a_{49}=+0.854137089\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.117352365\) \(a_{52}=+0.822965280\) \(a_{53}=+0.602475366\) \(a_{54}=-0.078929457\) \(a_{55}=+0.615857879\)
\(a_{56}=+0.481421994\) \(a_{57}=+0.920124822\) \(a_{58}=-0.948025649\) \(a_{59}=-1.139019949\) \(a_{60}=-0.309792755\)
\(a_{61}=+1.514585919\) \(a_{62}=+0.709026083\) \(a_{63}=+1.251958905\) \(a_{64}=+0.125000000\) \(a_{65}=-0.736082524\)
\(a_{66}=-1.349077072\) \(a_{67}=-1.062076541\) \(a_{68}=+0.042352163\) \(a_{69}=+1.798940723\) \(a_{70}=-0.430596922\)
\(a_{71}=+0.269208853\) \(a_{72}=+0.325067955\) \(a_{73}=+1.303681389\) \(a_{74}=-0.117463541\) \(a_{75}=+0.277087064\)
\(a_{76}=+0.332070653\) \(a_{77}=-1.875151774\) \(a_{78}=+1.612437040\) \(a_{79}=+0.269640123\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.074077619\) \(a_{82}=-0.607423672\) \(a_{83}=-0.831560340\) \(a_{84}=+0.943250795\) \(a_{85}=-0.037880926\)
\(a_{86}=+0.135780449\) \(a_{87}=-1.857467998\) \(a_{88}=-0.486878403\) \(a_{89}=+0.340920580\) \(a_{90}=-0.290749618\)
\(a_{91}=+2.241209369\) \(a_{92}=+0.649233024\) \(a_{93}=+1.389195804\) \(a_{94}=+0.779105187\) \(a_{95}=-0.297013022\)
\(a_{96}=+0.244912677\) \(a_{97}=-1.338109949\) \(a_{98}=+0.603966128\) \(a_{99}=-1.266148560\) \(a_{100}=+0.099975586\)

Showing 100 of 162 available coefficients

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