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: \( 22.2244552093 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.515513973\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.364523426\) \(a_{7}=+0.464791793\) \(a_{8}=+0.353553391\) \(a_{9}=-0.734245343\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.266056211\) \(a_{12}=+0.257756987\) \(a_{13}=-1.565078532\) \(a_{14}=+0.328657429\) \(a_{15}=-0.230544858\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.852956134\) \(a_{18}=-0.519189861\) \(a_{19}=-0.366003925\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.239606664\) \(a_{22}=-0.895236932\) \(a_{23}=+1.496962896\) \(a_{24}=+0.182261713\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.106677643\) \(a_{27}=-0.894027708\) \(a_{28}=+0.232395897\) \(a_{29}=+0.212689549\) \(a_{30}=-0.163019832\)
\(a_{31}=+1.545811061\) \(a_{32}=+0.176776695\) \(a_{33}=-0.652669668\) \(a_{34}=+1.310237848\) \(a_{35}=-0.207861209\)
\(a_{36}=-0.367122672\) \(a_{37}=+1.641302973\) \(a_{38}=-0.258803857\) \(a_{39}=-0.806819853\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.197985578\) \(a_{42}=+0.169427497\) \(a_{43}=-0.698803372\) \(a_{44}=-0.633028106\) \(a_{45}=+0.328364500\)
\(a_{46}=+1.058512615\) \(a_{47}=+1.780599055\) \(a_{48}=+0.128878493\) \(a_{49}=-0.783968589\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.955224779\) \(a_{52}=-0.782539266\) \(a_{53}=-0.373704059\) \(a_{54}=-0.632173055\) \(a_{55}=+0.566197550\)
\(a_{56}=+0.164328714\) \(a_{57}=-0.188680138\) \(a_{58}=+0.150394222\) \(a_{59}=+1.181524183\) \(a_{60}=-0.115272429\)
\(a_{61}=+0.981770779\) \(a_{62}=+1.093053483\) \(a_{63}=-0.341271210\) \(a_{64}=+0.125000000\) \(a_{65}=+0.699924398\)
\(a_{66}=-0.461507148\) \(a_{67}=-0.634324606\) \(a_{68}=+0.926478067\) \(a_{69}=+0.771705291\) \(a_{70}=-0.146980070\)
\(a_{71}=+1.210225151\) \(a_{72}=-0.259594931\) \(a_{73}=-0.772045107\) \(a_{74}=+1.160576462\) \(a_{75}=+0.103102795\)
\(a_{76}=-0.183001962\) \(a_{77}=-0.588452537\) \(a_{78}=-0.570507789\) \(a_{79}=-0.801526242\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.273361567\) \(a_{82}=+0.139996945\) \(a_{83}=-0.540242559\) \(a_{84}=+0.119803332\) \(a_{85}=-0.828667175\)
\(a_{86}=-0.494128603\) \(a_{87}=+0.109644434\) \(a_{88}=-0.447618466\) \(a_{89}=-1.256035722\) \(a_{90}=+0.232188765\)
\(a_{91}=-0.727435658\) \(a_{92}=+0.748481448\) \(a_{93}=+0.796887202\) \(a_{94}=+1.259073666\) \(a_{95}=+0.163681931\)
\(a_{96}=+0.091130857\) \(a_{97}=-0.671793635\) \(a_{98}=-0.554349505\) \(a_{99}=+0.929595877\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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