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: \( 14.1093933296 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.990361883\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.700291603\) \(a_{7}=-0.161149652\) \(a_{8}=-0.353553391\) \(a_{9}=-0.019183341\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.576634757\) \(a_{12}=-0.495180941\) \(a_{13}=+0.484844600\) \(a_{14}=+0.113950012\) \(a_{15}=+0.442903298\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.901292023\) \(a_{18}=+0.013564671\) \(a_{19}=+0.285655031\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.159596473\) \(a_{22}=+0.407742347\) \(a_{23}=+0.456302290\) \(a_{24}=+0.350145802\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.342836905\) \(a_{27}=+1.009360333\) \(a_{28}=-0.080574826\) \(a_{29}=+1.170925985\) \(a_{30}=-0.313179926\)
\(a_{31}=+1.420821777\) \(a_{32}=-0.176776695\) \(a_{33}=+0.571077083\) \(a_{34}=-0.637309702\) \(a_{35}=+0.072068315\)
\(a_{36}=-0.009591671\) \(a_{37}=-1.747754769\) \(a_{38}=-0.201988610\) \(a_{39}=-0.480171611\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.126581898\) \(a_{42}=-0.112851748\) \(a_{43}=-1.065407340\) \(a_{44}=-0.288317378\) \(a_{45}=+0.008579051\)
\(a_{46}=-0.322654443\) \(a_{47}=-0.134651703\) \(a_{48}=-0.247590471\) \(a_{49}=-0.974030790\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.892605265\) \(a_{52}=+0.242422300\) \(a_{53}=-1.164431770\) \(a_{54}=-0.713725536\) \(a_{55}=+0.257878903\)
\(a_{56}=+0.056975006\) \(a_{57}=-0.282901855\) \(a_{58}=-0.827969704\) \(a_{59}=+1.798171036\) \(a_{60}=+0.221451649\)
\(a_{61}=+1.004263619\) \(a_{62}=-1.004672714\) \(a_{63}=+0.003091389\) \(a_{64}=+0.125000000\) \(a_{65}=-0.216829097\)
\(a_{66}=-0.403812478\) \(a_{67}=-1.825105263\) \(a_{68}=+0.450646012\) \(a_{69}=-0.451904395\) \(a_{70}=-0.050959994\)
\(a_{71}=-1.179871006\) \(a_{72}=+0.006782335\) \(a_{73}=+1.300843022\) \(a_{74}=+1.235849249\) \(a_{75}=-0.198072377\)
\(a_{76}=+0.142827516\) \(a_{77}=+0.092924490\) \(a_{78}=+0.339532602\) \(a_{79}=+0.424887423\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.980448661\) \(a_{82}=+0.089506918\) \(a_{83}=-0.468147663\) \(a_{84}=+0.079798236\) \(a_{85}=-0.403070046\)
\(a_{86}=+0.753356755\) \(a_{87}=-1.159640454\) \(a_{88}=+0.203871173\) \(a_{89}=+1.382183208\) \(a_{90}=-0.006066305\)
\(a_{91}=-0.078132553\) \(a_{92}=+0.228151145\) \(a_{93}=-1.407127776\) \(a_{94}=+0.095213133\) \(a_{95}=-0.127748814\)
\(a_{96}=+0.175072901\) \(a_{97}=-1.387738714\) \(a_{98}=+0.688743776\) \(a_{99}=+0.011061846\) \(a_{100}=+0.099975586\)

Showing 100 of 156 available coefficients

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