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: \( 30.3643867787 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.081293610\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.057483263\) \(a_{7}=+0.936726973\) \(a_{8}=-0.353553391\) \(a_{9}=-0.993391349\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.756335189\) \(a_{12}=-0.040646805\) \(a_{13}=-0.945167686\) \(a_{14}=-0.662365995\) \(a_{15}=+0.036355608\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.847468088\) \(a_{18}=+0.702433759\) \(a_{19}=+0.710974751\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.076149917\) \(a_{22}=+1.241916523\) \(a_{23}=+1.078127594\) \(a_{24}=+0.028741631\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.668334480\) \(a_{27}=+0.162049979\) \(a_{28}=+0.468363487\) \(a_{29}=-0.304557281\) \(a_{30}=-0.025707297\)
\(a_{31}=-0.586339068\) \(a_{32}=-0.176776695\) \(a_{33}=+0.142778828\) \(a_{34}=-0.599250432\) \(a_{35}=-0.418917038\)
\(a_{36}=-0.496695674\) \(a_{37}=+0.304550345\) \(a_{38}=-0.502735068\) \(a_{39}=+0.076836093\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.035042333\) \(a_{42}=+0.053846123\) \(a_{43}=+0.962020451\) \(a_{44}=-0.878167595\) \(a_{45}=+0.444258117\)
\(a_{46}=-0.762351333\) \(a_{47}=+0.837479419\) \(a_{48}=-0.020323403\) \(a_{49}=-0.122542578\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.068893740\) \(a_{52}=-0.472583843\) \(a_{53}=-0.037759908\) \(a_{54}=-0.114586639\) \(a_{55}=+0.785456975\)
\(a_{56}=-0.331182997\) \(a_{57}=-0.057797704\) \(a_{58}=+0.215354519\) \(a_{59}=-0.521397743\) \(a_{60}=+0.018177804\)
\(a_{61}=-1.705560803\) \(a_{62}=+0.414604331\) \(a_{63}=-0.930536472\) \(a_{64}=+0.125000000\) \(a_{65}=+0.422691839\)
\(a_{66}=-0.100959878\) \(a_{67}=+0.318161598\) \(a_{68}=+0.423734044\) \(a_{69}=-0.087644884\) \(a_{70}=+0.296219078\)
\(a_{71}=+0.372372847\) \(a_{72}=+0.351216880\) \(a_{73}=+1.363615927\) \(a_{74}=-0.215349614\) \(a_{75}=-0.016258722\)
\(a_{76}=+0.355487375\) \(a_{77}=-1.645206546\) \(a_{78}=-0.054331323\) \(a_{79}=-1.246486037\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.980217721\) \(a_{82}=-0.731885452\) \(a_{83}=-0.270462303\) \(a_{84}=-0.038074959\) \(a_{85}=-0.378999251\)
\(a_{86}=-0.680251185\) \(a_{87}=+0.024758561\) \(a_{88}=+0.620958261\) \(a_{89}=+1.914753647\) \(a_{90}=-0.314137927\)
\(a_{91}=-0.885364065\) \(a_{92}=+0.539063797\) \(a_{93}=+0.047665620\) \(a_{94}=-0.592187376\) \(a_{95}=-0.317957575\)
\(a_{96}=+0.014370816\) \(a_{97}=+0.816341908\) \(a_{98}=+0.086650688\) \(a_{99}=+1.744728183\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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