Properties

Level $70$
Weight $0$
Character 70.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( 0 \)
Character: 70.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.5917045883 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.249188246\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.176202699\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.937905218\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.468087429\) \(a_{12}=-0.124594123\) \(a_{13}=+0.143339127\) \(a_{14}=+0.267261242\) \(a_{15}=-0.111440371\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.686982128\) \(a_{18}=-0.663199140\) \(a_{19}=+0.281273707\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.094184304\) \(a_{22}=-1.038094576\) \(a_{23}=+1.704815302\) \(a_{24}=-0.088101349\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.101356069\) \(a_{27}=+0.482903202\) \(a_{28}=+0.188982237\) \(a_{29}=-0.348506302\) \(a_{30}=-0.078800242\)
\(a_{31}=-0.590091663\) \(a_{32}=+0.176776695\) \(a_{33}=+0.365830132\) \(a_{34}=-0.485769721\) \(a_{35}=+0.169030851\)
\(a_{36}=-0.468952609\) \(a_{37}=+0.601001753\) \(a_{38}=+0.198890546\) \(a_{39}=-0.035718426\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.907412085\) \(a_{42}=-0.066598360\) \(a_{43}=-0.072310399\) \(a_{44}=-0.734043714\) \(a_{45}=-0.419443965\)
\(a_{46}=+1.205486461\) \(a_{47}=+1.071823027\) \(a_{48}=-0.062297062\) \(a_{49}=+0.142857143\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.171187871\) \(a_{52}=+0.071669564\) \(a_{53}=-0.257628848\) \(a_{54}=+0.341464129\) \(a_{55}=-0.656548658\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.070090102\) \(a_{58}=-0.246431169\) \(a_{59}=-0.013732115\) \(a_{60}=-0.055720186\)
\(a_{61}=-1.493392485\) \(a_{62}=-0.417257817\) \(a_{63}=-0.354494851\) \(a_{64}=+0.125000000\) \(a_{65}=+0.064103206\)
\(a_{66}=+0.258680967\) \(a_{67}=-0.351136506\) \(a_{68}=-0.343491064\) \(a_{69}=-0.424819935\) \(a_{70}=+0.119522861\)
\(a_{71}=+0.191700848\) \(a_{72}=-0.331599570\) \(a_{73}=-1.174120529\) \(a_{74}=+0.424972415\) \(a_{75}=-0.049837649\)
\(a_{76}=+0.140636853\) \(a_{77}=-0.554884891\) \(a_{78}=-0.025256741\) \(a_{79}=-0.094114040\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.817571416\) \(a_{82}=+0.641637239\) \(a_{83}=-1.423734541\) \(a_{84}=-0.047092152\) \(a_{85}=-0.307227747\)
\(a_{86}=-0.051131173\) \(a_{87}=+0.086843674\) \(a_{88}=-0.519047288\) \(a_{89}=+0.533385060\) \(a_{90}=-0.296591672\)
\(a_{91}=+0.054177098\) \(a_{92}=+0.852407651\) \(a_{93}=+0.147043907\) \(a_{94}=+0.757893330\) \(a_{95}=+0.125789426\)
\(a_{96}=-0.044050675\) \(a_{97}=+1.353491600\) \(a_{98}=+0.101015254\) \(a_{99}=+1.376926860\) \(a_{100}=+0.099975586\)

Showing 100 of 796 available coefficients

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