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: \( 18.2615112082 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.322936496\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.935457368\) \(a_{7}=-0.071639054\) \(a_{8}=+0.353553391\) \(a_{9}=+0.750160973\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.245063035\) \(a_{12}=+0.661468248\) \(a_{13}=+0.888726585\) \(a_{14}=-0.050656461\) \(a_{15}=-0.591635187\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.777583963\) \(a_{18}=+0.530443911\) \(a_{19}=+0.300389457\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.094773920\) \(a_{22}=+0.173285734\) \(a_{23}=+1.718464713\) \(a_{24}=+0.467728684\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.628424595\) \(a_{27}=-0.330521167\) \(a_{28}=-0.035819527\) \(a_{29}=+1.734057032\) \(a_{30}=-0.418349253\)
\(a_{31}=+0.090204249\) \(a_{32}=+0.176776695\) \(a_{33}=+0.324202833\) \(a_{34}=-0.549834893\) \(a_{35}=+0.032037959\)
\(a_{36}=+0.375080486\) \(a_{37}=+1.054974158\) \(a_{38}=+0.212407422\) \(a_{39}=+1.175728834\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.843227271\) \(a_{42}=-0.067015281\) \(a_{43}=+1.189140876\) \(a_{44}=+0.122531517\) \(a_{45}=-0.335482186\)
\(a_{46}=+1.215138052\) \(a_{47}=-0.987216415\) \(a_{48}=+0.330734124\) \(a_{49}=-0.994867846\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.028694203\) \(a_{52}=+0.444363293\) \(a_{53}=-0.987731436\) \(a_{54}=-0.233713759\) \(a_{55}=-0.109595521\)
\(a_{56}=-0.025328231\) \(a_{57}=+0.397396176\) \(a_{58}=+1.226163486\) \(a_{59}=+0.333680521\) \(a_{60}=-0.295817594\)
\(a_{61}=-1.520477443\) \(a_{62}=+0.063784036\) \(a_{63}=-0.053740823\) \(a_{64}=+0.125000000\) \(a_{65}=-0.397450612\)
\(a_{66}=+0.229246022\) \(a_{67}=+0.792038419\) \(a_{68}=-0.388791981\) \(a_{69}=+2.273419686\) \(a_{70}=+0.022654258\)
\(a_{71}=+1.152613151\) \(a_{72}=+0.265221955\) \(a_{73}=+0.872914085\) \(a_{74}=+0.745979381\) \(a_{75}=+0.264587299\)
\(a_{76}=+0.150194729\) \(a_{77}=-0.017556084\) \(a_{78}=+0.831365832\) \(a_{79}=-0.728991050\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.187419488\) \(a_{82}=+0.596251721\) \(a_{83}=+1.035335460\) \(a_{84}=-0.047386960\) \(a_{85}=+0.347746120\)
\(a_{86}=+0.840849577\) \(a_{87}=+2.294047335\) \(a_{88}=+0.086642867\) \(a_{89}=-0.306359351\) \(a_{90}=-0.237221729\)
\(a_{91}=-0.063667532\) \(a_{92}=+0.859232357\) \(a_{93}=+0.119334493\) \(a_{94}=-0.698067421\) \(a_{95}=-0.134338249\)
\(a_{96}=+0.233864342\) \(a_{97}=+0.657099325\) \(a_{98}=-0.703477800\) \(a_{99}=+0.183836726\) \(a_{100}=+0.099975586\)

Showing 100 of 180 available coefficients

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