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: \( 27.4132128948 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.318945764\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.932635494\) \(a_{7}=-1.453956586\) \(a_{8}=+0.353553391\) \(a_{9}=+0.739617928\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.055540280\) \(a_{12}=+0.659472882\) \(a_{13}=+0.111212711\) \(a_{14}=-1.028102561\) \(a_{15}=+0.589850477\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.782973606\) \(a_{18}=+0.522988852\) \(a_{19}=-1.980258687\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.917689879\) \(a_{22}=+0.746379690\) \(a_{23}=+1.373571026\) \(a_{24}=+0.466317747\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.078639262\) \(a_{27}=-0.343429831\) \(a_{28}=-0.726978293\) \(a_{29}=+0.469194527\) \(a_{30}=+0.417087272\)
\(a_{31}=-0.855312126\) \(a_{32}=+0.176776695\) \(a_{33}=+1.392200381\) \(a_{34}=-1.260752727\) \(a_{35}=-0.650229152\)
\(a_{36}=+0.369808964\) \(a_{37}=-0.988309629\) \(a_{38}=-1.400254346\) \(a_{39}=+0.146683534\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.284620369\) \(a_{42}=-1.356011518\) \(a_{43}=-0.533513739\) \(a_{44}=+0.527770140\) \(a_{45}=+0.330767193\)
\(a_{46}=+0.971261387\) \(a_{47}=-1.122973853\) \(a_{48}=+0.329736441\) \(a_{49}=+1.113989753\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.351645484\) \(a_{52}=+0.055606355\) \(a_{53}=-0.356362353\) \(a_{54}=-0.242841563\) \(a_{55}=+0.472051964\)
\(a_{56}=-0.514051281\) \(a_{57}=-2.611853806\) \(a_{58}=+0.331770632\) \(a_{59}=-0.506122991\) \(a_{60}=+0.294925239\)
\(a_{61}=-1.714092642\) \(a_{62}=-0.604797005\) \(a_{63}=-1.075372357\) \(a_{64}=+0.125000000\) \(a_{65}=+0.049735836\)
\(a_{66}=+0.984434330\) \(a_{67}=+1.007720686\) \(a_{68}=-0.891486803\) \(a_{69}=+1.811665686\) \(a_{70}=-0.459781443\)
\(a_{71}=-0.290993811\) \(a_{72}=+0.261494426\) \(a_{73}=-0.255657760\) \(a_{74}=-0.698840441\) \(a_{75}=+0.263789153\)
\(a_{76}=-0.990129344\) \(a_{77}=-1.534709742\) \(a_{78}=+0.103720921\) \(a_{79}=+0.849684245\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.192583249\) \(a_{82}=+0.908363774\) \(a_{83}=-1.238557546\) \(a_{84}=-0.958844940\) \(a_{85}=-0.797370037\)
\(a_{86}=-0.377251183\) \(a_{87}=+0.618842134\) \(a_{88}=+0.373189845\) \(a_{89}=-0.019806189\) \(a_{90}=+0.233887725\)
\(a_{91}=-0.161698453\) \(a_{92}=+0.686785513\) \(a_{93}=-1.128110306\) \(a_{94}=-0.794062427\) \(a_{95}=-0.885598607\)
\(a_{96}=+0.233158873\) \(a_{97}=+0.404781160\) \(a_{98}=+0.787709708\) \(a_{99}=+0.780696514\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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