Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 19.3345983161 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.567876663\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.108656220\) \(a_{7}=-1.779966850\) \(a_{8}=+0.353553391\) \(a_{9}=+1.458237230\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.191442021\) \(a_{12}=-0.783938331\) \(a_{13}=-0.442808244\) \(a_{14}=-1.258626630\) \(a_{15}=-0.701175760\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.460146644\) \(a_{18}=+1.031129434\) \(a_{19}=-0.475906164\) \(a_{20}=+0.223606798\)
\(a_{21}=+2.790768485\) \(a_{22}=+0.135369951\) \(a_{23}=-0.541289448\) \(a_{24}=-0.554328110\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.313112712\) \(a_{27}=-0.718459458\) \(a_{28}=-0.889983425\) \(a_{29}=-1.975061720\) \(a_{30}=-0.495806134\)
\(a_{31}=+1.033149673\) \(a_{32}=+0.176776695\) \(a_{33}=-0.300157476\) \(a_{34}=-1.032479594\) \(a_{35}=-0.796025375\)
\(a_{36}=+0.729118615\) \(a_{37}=-1.413586842\) \(a_{38}=-0.336516476\) \(a_{39}=+0.694268712\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.476999757\) \(a_{42}=+1.973371320\) \(a_{43}=+0.645526773\) \(a_{44}=+0.095721010\) \(a_{45}=+0.652143515\)
\(a_{46}=-0.382749439\) \(a_{47}=-1.048096000\) \(a_{48}=-0.391969166\) \(a_{49}=+2.168281987\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.289329847\) \(a_{52}=-0.221404122\) \(a_{53}=-0.860976049\) \(a_{54}=-0.508027555\) \(a_{55}=+0.085615474\)
\(a_{56}=-0.629313315\) \(a_{57}=+0.746162169\) \(a_{58}=-1.396579536\) \(a_{59}=+0.169572527\) \(a_{60}=-0.350587880\)
\(a_{61}=-0.073373694\) \(a_{62}=+0.730547140\) \(a_{63}=-2.595613928\) \(a_{64}=+0.125000000\) \(a_{65}=-0.198029867\)
\(a_{66}=-0.212243387\) \(a_{67}=+1.588870249\) \(a_{68}=-0.730073322\) \(a_{69}=+0.848675094\) \(a_{70}=-0.562874941\)
\(a_{71}=+1.001943627\) \(a_{72}=+0.515564717\) \(a_{73}=+1.277939322\) \(a_{74}=-0.999556842\) \(a_{75}=-0.313575333\)
\(a_{76}=-0.237953082\) \(a_{77}=-0.340760450\) \(a_{78}=+0.490922114\) \(a_{79}=+1.691028364\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.331781412\) \(a_{82}=-0.337289763\) \(a_{83}=+0.736645004\) \(a_{84}=+1.395384242\) \(a_{85}=-0.652997431\)
\(a_{86}=+0.456456359\) \(a_{87}=+3.096653179\) \(a_{88}=+0.067684975\) \(a_{89}=+0.814658254\) \(a_{90}=+0.461135101\)
\(a_{91}=+0.788183995\) \(a_{92}=-0.270644724\) \(a_{93}=-1.619851261\) \(a_{94}=-0.741115789\) \(a_{95}=-0.212831707\)
\(a_{96}=-0.277164055\) \(a_{97}=+0.669044478\) \(a_{98}=+1.533206897\) \(a_{99}=+0.279167882\) \(a_{100}=+0.099975586\)

Showing 100 of 190 available coefficients

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