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: \( 15.5019918437 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.579648465\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.116980142\) \(a_{7}=-0.442116438\) \(a_{8}=+0.353553391\) \(a_{9}=+1.495289274\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.085189792\) \(a_{12}=-0.789824233\) \(a_{13}=+0.484488102\) \(a_{14}=-0.312623531\) \(a_{15}=-0.706440270\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.788909495\) \(a_{18}=+1.057329186\) \(a_{19}=+1.769729765\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.698388553\) \(a_{22}=-0.767345061\) \(a_{23}=+0.384147629\) \(a_{24}=-0.558490071\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.342584822\) \(a_{27}=-0.782382942\) \(a_{28}=-0.221058219\) \(a_{29}=-1.651728897\) \(a_{30}=-0.499528705\)
\(a_{31}=-0.544474500\) \(a_{32}=+0.176776695\) \(a_{33}=+1.714218390\) \(a_{34}=+0.557843254\) \(a_{35}=-0.197720482\)
\(a_{36}=+0.747644637\) \(a_{37}=-1.338215348\) \(a_{38}=+1.251387918\) \(a_{39}=-0.765320886\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.860534634\) \(a_{42}=+0.493835282\) \(a_{43}=-1.600655543\) \(a_{44}=-0.542594896\) \(a_{45}=+0.668713693\)
\(a_{46}=+0.271633393\) \(a_{47}=-1.418267494\) \(a_{48}=-0.394912116\) \(a_{49}=-0.804533055\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.246199674\) \(a_{52}=+0.242244051\) \(a_{53}=+1.495574481\) \(a_{54}=-0.553228284\) \(a_{55}=-0.485311629\)
\(a_{56}=-0.156311766\) \(a_{57}=-2.795550908\) \(a_{58}=-1.167948704\) \(a_{59}=-0.055764568\) \(a_{60}=-0.353220135\)
\(a_{61}=+0.804408273\) \(a_{62}=-0.385001611\) \(a_{63}=-0.661091968\) \(a_{64}=+0.125000000\) \(a_{65}=+0.216669666\)
\(a_{66}=+1.212135448\) \(a_{67}=-0.648872563\) \(a_{68}=+0.394454748\) \(a_{69}=-0.606818212\) \(a_{70}=-0.139809493\)
\(a_{71}=-1.761539892\) \(a_{72}=+0.528664593\) \(a_{73}=+0.510785818\) \(a_{74}=-0.946261147\) \(a_{75}=-0.315929693\)
\(a_{76}=+0.884864883\) \(a_{77}=+0.479780245\) \(a_{78}=-0.541163588\) \(a_{79}=-1.559316486\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.259399260\) \(a_{82}=+0.608489875\) \(a_{83}=-0.205954939\) \(a_{84}=+0.349194276\) \(a_{85}=+0.352811052\)
\(a_{86}=-1.131834389\) \(a_{87}=+2.609151018\) \(a_{88}=-0.383672530\) \(a_{89}=-0.966971895\) \(a_{90}=+0.472851987\)
\(a_{91}=-0.214200154\) \(a_{92}=+0.192073814\) \(a_{93}=+0.860078309\) \(a_{94}=-1.002866562\) \(a_{95}=+0.791447211\)
\(a_{96}=-0.279245035\) \(a_{97}=+0.113335374\) \(a_{98}=-0.568890779\) \(a_{99}=-1.622672659\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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