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: \( 20.3173037027 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.088513170\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.062588263\) \(a_{7}=+0.719162774\) \(a_{8}=-0.353553391\) \(a_{9}=-0.992165419\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.482375743\) \(a_{12}=-0.044256585\) \(a_{13}=+0.780145181\) \(a_{14}=-0.508524874\) \(a_{15}=-0.039584293\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.158277451\) \(a_{18}=+0.701566896\) \(a_{19}=-0.700316730\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.063655377\) \(a_{22}=+1.048197940\) \(a_{23}=+0.889052318\) \(a_{24}=+0.031294131\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.551645948\) \(a_{27}=+0.176332877\) \(a_{28}=+0.359581387\) \(a_{29}=-1.305984833\) \(a_{30}=+0.027990322\)
\(a_{31}=+1.351445993\) \(a_{32}=-0.176776695\) \(a_{33}=+0.131209776\) \(a_{34}=-0.111919059\) \(a_{35}=+0.321619370\)
\(a_{36}=-0.496082709\) \(a_{37}=+1.448288462\) \(a_{38}=+0.495198709\) \(a_{39}=-0.069053123\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.263708331\) \(a_{42}=+0.045011149\) \(a_{43}=-1.124711982\) \(a_{44}=-0.741187871\) \(a_{45}=-0.443709864\)
\(a_{46}=-0.628654923\) \(a_{47}=+0.616698413\) \(a_{48}=-0.022128293\) \(a_{49}=-0.482804904\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.014009639\) \(a_{52}=+0.390072590\) \(a_{53}=+0.911767387\) \(a_{54}=-0.124686173\) \(a_{55}=-0.662938586\)
\(a_{56}=-0.254262437\) \(a_{57}=+0.061987254\) \(a_{58}=+0.923470731\) \(a_{59}=-0.777386955\) \(a_{60}=-0.019792147\)
\(a_{61}=-0.112669624\) \(a_{62}=-0.955616626\) \(a_{63}=-0.713528435\) \(a_{64}=+0.125000000\) \(a_{65}=+0.348891531\)
\(a_{66}=-0.092779323\) \(a_{67}=-0.642292333\) \(a_{68}=+0.079138725\) \(a_{69}=-0.078692839\) \(a_{70}=-0.227419238\)
\(a_{71}=-1.705230041\) \(a_{72}=+0.350783448\) \(a_{73}=+1.191383525\) \(a_{74}=-1.024094592\) \(a_{75}=-0.017702634\)
\(a_{76}=-0.350158365\) \(a_{77}=-1.066069452\) \(a_{78}=+0.048827932\) \(a_{79}=+0.659860770\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.976557637\) \(a_{82}=+0.893576730\) \(a_{83}=+0.599333182\) \(a_{84}=-0.031827689\) \(a_{85}=+0.070783828\)
\(a_{86}=+0.795291469\) \(a_{87}=+0.115596858\) \(a_{88}=+0.524098970\) \(a_{89}=+0.635647291\) \(a_{90}=+0.313750254\)
\(a_{91}=+0.561051372\) \(a_{92}=+0.444526159\) \(a_{93}=-0.119620769\) \(a_{94}=-0.436071630\) \(a_{95}=-0.313191163\)
\(a_{96}=+0.015647066\) \(a_{97}=+0.374471014\) \(a_{98}=+0.341394622\) \(a_{99}=+1.470761950\) \(a_{100}=+0.099975586\)

Showing 100 of 192 available coefficients

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