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: \( 27.6452063226 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.828141789\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.585584675\) \(a_{7}=+1.190939245\) \(a_{8}=+0.353553391\) \(a_{9}=-0.314181177\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.500172511\) \(a_{12}=-0.414070895\) \(a_{13}=-0.342006044\) \(a_{14}=+0.842121216\) \(a_{15}=+0.370356267\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.694324681\) \(a_{18}=-0.222159640\) \(a_{19}=-0.353942081\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.986266558\) \(a_{22}=+1.060782155\) \(a_{23}=+1.477201853\) \(a_{24}=-0.292792338\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.241834793\) \(a_{27}=+1.088328351\) \(a_{28}=+0.595469623\) \(a_{29}=-0.526441868\) \(a_{30}=+0.261881428\)
\(a_{31}=+0.034666595\) \(a_{32}=+0.176776695\) \(a_{33}=-1.242355548\) \(a_{34}=+0.490961691\) \(a_{35}=-0.532604222\)
\(a_{36}=-0.157090588\) \(a_{37}=-1.274735874\) \(a_{38}=-0.250274846\) \(a_{39}=+0.283229497\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.549835656\) \(a_{42}=-0.697395771\) \(a_{43}=-0.481774005\) \(a_{44}=+0.750086255\) \(a_{45}=+0.140506094\)
\(a_{46}=+1.044539447\) \(a_{47}=+0.295748609\) \(a_{48}=-0.207035447\) \(a_{49}=+0.418336286\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.574999284\) \(a_{52}=-0.171003022\) \(a_{53}=-0.787621664\) \(a_{54}=+0.769564357\) \(a_{55}=-0.670897542\)
\(a_{56}=+0.421060608\) \(a_{57}=+0.293114229\) \(a_{58}=-0.372250615\) \(a_{59}=-1.824015219\) \(a_{60}=+0.185178134\)
\(a_{61}=+1.088164782\) \(a_{62}=+0.024512985\) \(a_{63}=-0.374170693\) \(a_{64}=+0.125000000\) \(a_{65}=+0.152949753\)
\(a_{66}=-0.878478032\) \(a_{67}=-1.210686262\) \(a_{68}=+0.347162341\) \(a_{69}=-1.223332586\) \(a_{70}=-0.376608057\)
\(a_{71}=-0.927452579\) \(a_{72}=-0.111079820\) \(a_{73}=+0.182713436\) \(a_{74}=-0.901374380\) \(a_{75}=-0.165628358\)
\(a_{76}=-0.176971041\) \(a_{77}=+1.786614318\) \(a_{78}=+0.200273498\) \(a_{79}=+1.446165810\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.587109012\) \(a_{82}=+1.095899302\) \(a_{83}=+0.412109573\) \(a_{84}=-0.493133279\) \(a_{85}=-0.310511437\)
\(a_{86}=-0.340665666\) \(a_{87}=+0.435968510\) \(a_{88}=+0.530391078\) \(a_{89}=+1.304005099\) \(a_{90}=+0.099352812\)
\(a_{91}=-0.407308420\) \(a_{92}=+0.738600926\) \(a_{93}=-0.028708856\) \(a_{94}=+0.209125847\) \(a_{95}=+0.158287711\)
\(a_{96}=-0.146396169\) \(a_{97}=-0.777137769\) \(a_{98}=+0.295808425\) \(a_{99}=-0.471325965\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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