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: \( 31.6329465687 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.791478895\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.559660094\) \(a_{7}=-1.544537227\) \(a_{8}=+0.353553391\) \(a_{9}=-0.373561159\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.797593805\) \(a_{12}=-0.395739447\) \(a_{13}=-0.951467773\) \(a_{14}=-1.092152747\) \(a_{15}=-0.353960122\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.256696949\) \(a_{18}=-0.264147629\) \(a_{19}=+1.019652918\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.222468617\) \(a_{22}=-0.563983988\) \(a_{23}=+1.302198801\) \(a_{24}=-0.279830047\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.672789314\) \(a_{27}=+1.087144668\) \(a_{28}=-0.772268613\) \(a_{29}=-1.042648146\) \(a_{30}=-0.250287603\)
\(a_{31}=+1.568470127\) \(a_{32}=+0.176776695\) \(a_{33}=+0.631278663\) \(a_{34}=+0.888618934\) \(a_{35}=-0.690738047\)
\(a_{36}=-0.186780580\) \(a_{37}=+1.570932295\) \(a_{38}=+0.721003492\) \(a_{39}=+0.753066661\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.540267524\) \(a_{42}=+0.864415849\) \(a_{43}=-1.801550388\) \(a_{44}=-0.398796902\) \(a_{45}=-0.167061629\)
\(a_{46}=+0.920793602\) \(a_{47}=-0.473923387\) \(a_{48}=-0.197869724\) \(a_{49}=+1.385595245\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.994649112\) \(a_{52}=-0.475733886\) \(a_{53}=+0.948048602\) \(a_{54}=+0.768727367\) \(a_{55}=-0.356694793\)
\(a_{56}=-0.546076373\) \(a_{57}=-0.807033764\) \(a_{58}=-0.737263575\) \(a_{59}=-1.500355904\) \(a_{60}=-0.176980061\)
\(a_{61}=-1.092327580\) \(a_{62}=+1.109075863\) \(a_{63}=+0.576979117\) \(a_{64}=+0.125000000\) \(a_{65}=-0.425509324\)
\(a_{66}=+0.446381423\) \(a_{67}=-0.253388277\) \(a_{68}=+0.628348474\) \(a_{69}=-1.030662867\) \(a_{70}=-0.488425557\)
\(a_{71}=+1.180242283\) \(a_{72}=-0.132073814\) \(a_{73}=-1.823843914\) \(a_{74}=+1.110816879\) \(a_{75}=-0.158295779\)
\(a_{76}=+0.509826459\) \(a_{77}=+1.231913324\) \(a_{78}=+0.532498543\) \(a_{79}=+0.396038495\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.486890901\) \(a_{82}=+0.382026830\) \(a_{83}=-0.216785094\) \(a_{84}=+0.611234309\) \(a_{85}=+0.562011961\)
\(a_{86}=-1.273888496\) \(a_{87}=+0.825234002\) \(a_{88}=-0.281991994\) \(a_{89}=+0.540906851\) \(a_{90}=-0.118130411\)
\(a_{91}=+1.469577395\) \(a_{92}=+0.651099400\) \(a_{93}=-1.241411002\) \(a_{94}=-0.335114440\) \(a_{95}=+0.456002647\)
\(a_{96}=-0.139915023\) \(a_{97}=+0.722069812\) \(a_{98}=+0.979763794\) \(a_{99}=+0.297950066\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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