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: \( 27.0839397618 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.931785803\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.658872060\) \(a_{7}=-0.767954458\) \(a_{8}=-0.353553391\) \(a_{9}=-0.131775217\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.420698044\) \(a_{12}=+0.465892901\) \(a_{13}=-1.600299419\) \(a_{14}=+0.543025805\) \(a_{15}=-0.416707279\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.843049615\) \(a_{18}=+0.093179150\) \(a_{19}=+1.188317395\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.715569062\) \(a_{22}=+0.297478440\) \(a_{23}=-1.417689107\) \(a_{24}=-0.329436030\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.131582571\) \(a_{27}=-1.054572080\) \(a_{28}=-0.383977229\) \(a_{29}=-0.884869556\) \(a_{30}=+0.294656543\)
\(a_{31}=-1.816611985\) \(a_{32}=-0.176776695\) \(a_{33}=-0.392000465\) \(a_{34}=+0.596126100\) \(a_{35}=+0.343439675\)
\(a_{36}=-0.065887609\) \(a_{37}=+0.756304294\) \(a_{38}=-0.840267288\) \(a_{39}=-1.491136279\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.044617823\) \(a_{42}=+0.505983736\) \(a_{43}=+0.509000349\) \(a_{44}=-0.210349022\) \(a_{45}=+0.058931669\)
\(a_{46}=+1.002457581\) \(a_{47}=-0.167604655\) \(a_{48}=+0.232946451\) \(a_{49}=-0.410245950\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.785541663\) \(a_{52}=-0.800149710\) \(a_{53}=+1.829110788\) \(a_{54}=+0.745695069\) \(a_{55}=+0.188141885\)
\(a_{56}=+0.271512903\) \(a_{57}=+1.107257278\) \(a_{58}=+0.625697263\) \(a_{59}=-0.821179339\) \(a_{60}=-0.208353640\)
\(a_{61}=+0.365725397\) \(a_{62}=+1.284538653\) \(a_{63}=+0.101197366\) \(a_{64}=+0.125000000\) \(a_{65}=+0.715675657\)
\(a_{66}=+0.277186187\) \(a_{67}=+1.384731334\) \(a_{68}=-0.421524808\) \(a_{69}=-1.320982583\) \(a_{70}=-0.242848523\)
\(a_{71}=+0.479873526\) \(a_{72}=+0.046589575\) \(a_{73}=-0.276131706\) \(a_{74}=-0.534787895\) \(a_{75}=+0.186357161\)
\(a_{76}=+0.594158698\) \(a_{77}=+0.323076939\) \(a_{78}=+1.054392575\) \(a_{79}=+0.464399491\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.850860075\) \(a_{82}=+0.031549565\) \(a_{83}=-1.826755557\) \(a_{84}=-0.357784531\) \(a_{85}=+0.377023250\)
\(a_{86}=-0.359917598\) \(a_{87}=-0.824508890\) \(a_{88}=+0.148739220\) \(a_{89}=-1.579492017\) \(a_{90}=-0.041670983\)
\(a_{91}=+1.228957074\) \(a_{92}=-0.708844554\) \(a_{93}=-1.692693257\) \(a_{94}=+0.118514388\) \(a_{95}=-0.531431695\)
\(a_{96}=-0.164718015\) \(a_{97}=-0.070015254\) \(a_{98}=+0.290087693\) \(a_{99}=+0.055437576\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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