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: \( 14.9238928466 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.580788631\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.117786361\) \(a_{7}=-0.798040638\) \(a_{8}=-0.353553391\) \(a_{9}=+1.498892697\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.993303430\) \(a_{12}=-0.790394316\) \(a_{13}=+0.221361958\) \(a_{14}=+0.564299947\) \(a_{15}=-0.706950168\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.651028375\) \(a_{18}=-1.059877190\) \(a_{19}=-1.579774565\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.261533569\) \(a_{22}=-1.409478373\) \(a_{23}=-1.255200880\) \(a_{24}=+0.558893180\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.156526542\) \(a_{27}=-0.788643904\) \(a_{28}=-0.399020319\) \(a_{29}=+0.188115279\) \(a_{30}=+0.499889257\)
\(a_{31}=-0.411069173\) \(a_{32}=-0.176776695\) \(a_{33}=-3.150991402\) \(a_{34}=+0.460346578\) \(a_{35}=-0.356894623\)
\(a_{36}=+0.749446349\) \(a_{37}=-0.929530286\) \(a_{38}=+1.117069308\) \(a_{39}=-0.349926467\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.573215209\) \(a_{42}=-0.892038941\) \(a_{43}=-0.021057423\) \(a_{44}=+0.996651715\) \(a_{45}=+0.670325192\)
\(a_{46}=+0.887561054\) \(a_{47}=+0.372508352\) \(a_{48}=-0.395197158\) \(a_{49}=-0.363131139\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.029138253\) \(a_{52}=+0.110680979\) \(a_{53}=+0.846911549\) \(a_{54}=+0.557655452\) \(a_{55}=+0.891432394\)
\(a_{56}=+0.282149974\) \(a_{57}=+2.497289673\) \(a_{58}=-0.133017589\) \(a_{59}=-0.300331418\) \(a_{60}=-0.353475084\)
\(a_{61}=-1.239738902\) \(a_{62}=+0.290669800\) \(a_{63}=-1.196177285\) \(a_{64}=+0.125000000\) \(a_{65}=+0.098996077\)
\(a_{66}=+2.228087388\) \(a_{67}=-1.406856105\) \(a_{68}=-0.325514187\) \(a_{69}=+1.984207280\) \(a_{70}=+0.252362608\)
\(a_{71}=+0.256726083\) \(a_{72}=-0.529938595\) \(a_{73}=+1.186360610\) \(a_{74}=+0.657277169\) \(a_{75}=-0.316157726\)
\(a_{76}=-0.789887283\) \(a_{77}=-1.590737142\) \(a_{78}=+0.247435378\) \(a_{79}=+0.342871471\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.252213380\) \(a_{82}=-1.112431143\) \(a_{83}=+1.807519093\) \(a_{84}=+0.630766784\) \(a_{85}=-0.291148740\)
\(a_{86}=+0.014889846\) \(a_{87}=-0.297370494\) \(a_{88}=-0.704739186\) \(a_{89}=+0.845439207\) \(a_{90}=-0.473991489\)
\(a_{91}=-0.176655839\) \(a_{92}=-0.627600440\) \(a_{93}=+0.649813475\) \(a_{94}=-0.263403181\) \(a_{95}=-0.706496663\)
\(a_{96}=+0.279446590\) \(a_{97}=+0.380548250\) \(a_{98}=+0.256772491\) \(a_{99}=+2.987747955\) \(a_{100}=+0.099975586\)

Showing 100 of 172 available coefficients

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