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: \( 13.1075094406 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.885463899\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.333224309\) \(a_{7}=+1.370716696\) \(a_{8}=-0.353553391\) \(a_{9}=+2.554974114\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.877469477\) \(a_{12}=-0.942731949\) \(a_{13}=-0.036915655\) \(a_{14}=-0.969243071\) \(a_{15}=-0.843205089\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.165242880\) \(a_{18}=-1.806639522\) \(a_{19}=+1.383897946\) \(a_{20}=+0.223606798\)
\(a_{21}=-2.584436845\) \(a_{22}=+0.620464618\) \(a_{23}=-1.452079368\) \(a_{24}=+0.666612154\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.026103310\) \(a_{27}=-2.931847555\) \(a_{28}=+0.685358348\) \(a_{29}=+0.465405180\) \(a_{30}=+0.596236037\)
\(a_{31}=-0.121934193\) \(a_{32}=-0.176776695\) \(a_{33}=+1.654437022\) \(a_{34}=+0.116844361\) \(a_{35}=+0.613003142\)
\(a_{36}=+1.277487057\) \(a_{37}=+0.420036566\) \(a_{38}=-0.978563622\) \(a_{39}=+0.069603135\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.008795935\) \(a_{42}=+1.827472819\) \(a_{43}=+0.662281700\) \(a_{44}=-0.438734739\) \(a_{45}=+1.142619160\)
\(a_{46}=+1.026775168\) \(a_{47}=-0.953140607\) \(a_{48}=-0.471365975\) \(a_{49}=+0.878864260\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.311559484\) \(a_{52}=-0.018457828\) \(a_{53}=+0.211814200\) \(a_{54}=+2.073129288\) \(a_{55}=-0.392416280\)
\(a_{56}=-0.484621535\) \(a_{57}=-2.609289616\) \(a_{58}=-0.329091159\) \(a_{59}=+0.356789888\) \(a_{60}=-0.421602545\)
\(a_{61}=+0.507811895\) \(a_{62}=+0.086220495\) \(a_{63}=+3.502145675\) \(a_{64}=+0.125000000\) \(a_{65}=-0.016509183\)
\(a_{66}=-1.169863637\) \(a_{67}=-0.839072128\) \(a_{68}=-0.082621440\) \(a_{69}=+2.737843227\) \(a_{70}=-0.433458679\)
\(a_{71}=-0.869019174\) \(a_{72}=-0.903319761\) \(a_{73}=-1.530483873\) \(a_{74}=-0.297010704\) \(a_{75}=-0.377092780\)
\(a_{76}=+0.691948973\) \(a_{77}=-1.202762058\) \(a_{78}=-0.049216849\) \(a_{79}=+1.523376681\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.972918620\) \(a_{82}=-0.006219666\) \(a_{83}=-0.052538350\) \(a_{84}=-1.292218423\) \(a_{85}=-0.073898862\)
\(a_{86}=-0.468303881\) \(a_{87}=-0.877504636\) \(a_{88}=+0.310232309\) \(a_{89}=+1.084013343\) \(a_{90}=-0.807953756\)
\(a_{91}=-0.050600849\) \(a_{92}=-0.726039684\) \(a_{93}=+0.229902496\) \(a_{94}=+0.673972187\) \(a_{95}=+0.618897976\)
\(a_{96}=+0.333306077\) \(a_{97}=+0.735518612\) \(a_{98}=-0.621450878\) \(a_{99}=-2.241912037\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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