Properties

Level $63$
Weight $0$
Character 63.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 63 = 3^{2} \cdot 7 \)
Weight: \( 0 \)
Character: 63.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.85926308826 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.391672172\) \(a_{3}=+0.000000000\) \(a_{4}=+0.936751434\) \(a_{5}=+1.287187759\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.377964473\) \(a_{8}=-0.088021269\) \(a_{9}=+0.000000000\) \(a_{10}=+1.791343384\)
\(a_{11}=-0.911179490\) \(a_{12}=+0.000000000\) \(a_{13}=-1.677568914\) \(a_{14}=+0.526002639\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.059248185\) \(a_{17}=+0.811715551\) \(a_{18}=+0.000000000\) \(a_{19}=+0.520814573\) \(a_{20}=+1.205774979\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.268063140\) \(a_{23}=+1.030328573\) \(a_{24}=+0.000000000\) \(a_{25}=+0.656852327\)
\(a_{26}=-2.334625975\) \(a_{27}=+0.000000000\) \(a_{28}=+0.354058762\) \(a_{29}=-0.094806584\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.574927892\) \(a_{32}=-1.386104953\) \(a_{33}=+0.000000000\) \(a_{34}=+1.129641944\) \(a_{35}=+0.486511243\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.416045550\) \(a_{38}=+0.724803148\) \(a_{39}=+0.000000000\) \(a_{40}=-0.113299900\)
\(a_{41}=+0.371836250\) \(a_{42}=+0.000000000\) \(a_{43}=+1.702703895\) \(a_{44}=-0.853548694\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.433879603\) \(a_{47}=+1.309061676\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.914123105\)
\(a_{51}=+0.000000000\) \(a_{52}=-1.571465087\) \(a_{53}=-0.758863870\) \(a_{54}=+0.000000000\) \(a_{55}=-1.172859086\)
\(a_{56}=-0.033268912\) \(a_{57}=+0.000000000\) \(a_{58}=-0.131939684\) \(a_{59}=+0.493733999\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.144899291\) \(a_{62}=+0.800111148\) \(a_{63}=+0.000000000\) \(a_{64}=-0.869755506\) \(a_{65}=-2.159346171\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.047747316\) \(a_{68}=+0.760375707\) \(a_{69}=+0.000000000\) \(a_{70}=+0.677064158\)
\(a_{71}=+0.211684261\) \(a_{72}=+0.000000000\) \(a_{73}=-0.653790735\) \(a_{74}=-1.970671186\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.487873798\) \(a_{77}=-0.344393476\) \(a_{78}=+0.000000000\) \(a_{79}=-0.135663453\) \(a_{80}=-1.363451297\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.517474161\) \(a_{83}=+0.400385911\) \(a_{84}=+0.000000000\) \(a_{85}=+1.044830321\)
\(a_{86}=+2.369605628\) \(a_{87}=+0.000000000\) \(a_{88}=+0.080203175\) \(a_{89}=-0.197926918\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.634061451\) \(a_{92}=+0.965161768\) \(a_{93}=+0.000000000\) \(a_{94}=+1.821784705\) \(a_{95}=+0.670386143\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.476670640\) \(a_{98}=+0.198810310\) \(a_{99}=+0.000000000\) \(a_{100}=+0.615307359\)

Showing 100 of 486 available coefficients

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