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: \( 29.1014092651 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.301266971\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.920134699\) \(a_{7}=-1.636531802\) \(a_{8}=+0.353553391\) \(a_{9}=+0.693295729\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.466206728\) \(a_{12}=-0.650633485\) \(a_{13}=+0.894819423\) \(a_{14}=-1.157202735\) \(a_{15}=+0.581944281\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.227975012\) \(a_{18}=+0.490234111\) \(a_{19}=-1.027244911\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.129564781\) \(a_{22}=+1.036764720\) \(a_{23}=-0.307436672\) \(a_{24}=-0.460067350\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.632732882\) \(a_{27}=+0.399104138\) \(a_{28}=-0.818265901\) \(a_{29}=-1.828248920\) \(a_{30}=+0.411496747\)
\(a_{31}=-1.078942679\) \(a_{32}=+0.176776695\) \(a_{33}=-1.907926387\) \(a_{34}=+0.161202677\) \(a_{35}=+0.731879272\)
\(a_{36}=+0.346647864\) \(a_{37}=-0.832903188\) \(a_{38}=-0.726371842\) \(a_{39}=-1.164398960\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.388677739\) \(a_{42}=+1.505829697\) \(a_{43}=-1.655305293\) \(a_{44}=+0.733103364\) \(a_{45}=-0.310051276\)
\(a_{46}=-0.217390555\) \(a_{47}=+0.786892128\) \(a_{48}=-0.325316743\) \(a_{49}=+1.678236340\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.296656353\) \(a_{52}=+0.447409711\) \(a_{53}=+0.961863951\) \(a_{54}=+0.282209242\) \(a_{55}=-0.655707582\)
\(a_{56}=-0.578601368\) \(a_{57}=+1.336719873\) \(a_{58}=-1.292767209\) \(a_{59}=+0.451290410\) \(a_{60}=+0.290972140\)
\(a_{61}=-0.104159461\) \(a_{62}=-0.762927685\) \(a_{63}=-1.134600508\) \(a_{64}=+0.125000000\) \(a_{65}=-0.400175411\)
\(a_{66}=-1.349107686\) \(a_{67}=-1.085033293\) \(a_{68}=+0.113987506\) \(a_{69}=+0.400057187\) \(a_{70}=+0.517516796\)
\(a_{71}=+0.643871060\) \(a_{72}=+0.245117056\) \(a_{73}=-1.064796091\) \(a_{74}=-0.588951492\) \(a_{75}=-0.260253394\)
\(a_{76}=-0.513622455\) \(a_{77}=-2.399493939\) \(a_{78}=-0.823354400\) \(a_{79}=+1.333920718\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.212636761\) \(a_{82}=-0.981943446\) \(a_{83}=+0.218297052\) \(a_{84}=+1.064782390\) \(a_{85}=-0.101953525\)
\(a_{86}=-1.170477598\) \(a_{87}=+2.379039934\) \(a_{88}=+0.518382360\) \(a_{89}=-0.133586195\) \(a_{90}=-0.219239359\)
\(a_{91}=-1.464400443\) \(a_{92}=-0.153718336\) \(a_{93}=+1.403992472\) \(a_{94}=+0.556416760\) \(a_{95}=+0.459397890\)
\(a_{96}=-0.230033675\) \(a_{97}=+1.011094523\) \(a_{98}=+1.186692297\) \(a_{99}=+1.016514862\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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