Properties

Level $13$
Weight $0$
Character 13.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 6.09349565841 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.506719394\) \(a_{3}=-0.431091540\) \(a_{4}=+1.270203331\) \(a_{5}=+0.534124345\)
\(a_{6}=+0.649533983\) \(a_{7}=+0.582432841\) \(a_{8}=-0.407120600\) \(a_{9}=-0.814160084\) \(a_{10}=-0.804775510\)
\(a_{11}=+0.225876097\) \(a_{12}=-0.547573910\) \(a_{13}=+0.277350098\) \(a_{14}=-0.877562858\) \(a_{15}=-0.230256486\)
\(a_{16}=-0.656786828\) \(a_{17}=+0.184819207\) \(a_{18}=+1.226710789\) \(a_{19}=-0.353215558\) \(a_{20}=+0.678446523\)
\(a_{21}=-0.251081870\) \(a_{22}=-0.340331896\) \(a_{23}=-1.735288204\) \(a_{24}=+0.175506246\) \(a_{25}=-0.714711184\)
\(a_{26}=-0.417888772\) \(a_{27}=+0.782069064\) \(a_{28}=+0.739808136\) \(a_{29}=+1.250446597\) \(a_{30}=+0.346931914\)
\(a_{31}=-1.056278064\) \(a_{32}=+1.396714052\) \(a_{33}=-0.097373275\) \(a_{34}=-0.278470683\) \(a_{35}=+0.311091560\)
\(a_{36}=-1.034148851\) \(a_{37}=-1.605237182\) \(a_{38}=+0.532196731\) \(a_{39}=-0.119563280\) \(a_{40}=-0.217453022\)
\(a_{41}=-0.747486851\) \(a_{42}=+0.378309920\) \(a_{43}=-0.164500819\) \(a_{44}=+0.286908577\) \(a_{45}=-0.434862742\)
\(a_{46}=+2.614592384\) \(a_{47}=-0.013275596\) \(a_{48}=+0.283135240\) \(a_{49}=-0.660772090\) \(a_{50}=+1.076869247\)
\(a_{51}=-0.079673776\) \(a_{52}=+0.352291019\) \(a_{53}=-1.094994038\) \(a_{54}=-1.178358626\) \(a_{55}=+0.120645923\)
\(a_{56}=-0.237120408\) \(a_{57}=+0.152268239\) \(a_{58}=-1.884072139\) \(a_{59}=+1.356592848\) \(a_{60}=-0.292472556\)
\(a_{61}=+1.341202870\) \(a_{62}=+1.591514645\) \(a_{63}=-0.474193572\) \(a_{64}=-1.447669321\) \(a_{65}=+0.148139440\)
\(a_{66}=+0.146714202\) \(a_{67}=-1.887981985\) \(a_{68}=+0.234757971\) \(a_{69}=+0.748068064\) \(a_{70}=-0.468727686\)
\(a_{71}=+0.322511148\) \(a_{72}=+0.331461340\) \(a_{73}=-1.056476489\) \(a_{74}=+2.418641995\) \(a_{75}=+0.308105943\)
\(a_{76}=-0.448655580\) \(a_{77}=+0.131557659\) \(a_{78}=+0.180148317\) \(a_{79}=-1.255054603\) \(a_{80}=-0.350805839\)
\(a_{81}=+0.477016734\) \(a_{82}=+1.126252934\) \(a_{83}=+0.174148547\) \(a_{84}=-0.318925045\) \(a_{85}=+0.098716454\)
\(a_{86}=+0.247856630\) \(a_{87}=-0.539056987\) \(a_{88}=-0.091958834\) \(a_{89}=+0.068526916\) \(a_{90}=+0.655216112\)
\(a_{91}=+0.161537721\) \(a_{92}=-2.204169387\) \(a_{93}=+0.455352537\) \(a_{94}=+0.020002672\) \(a_{95}=-0.188661028\)
\(a_{96}=-0.602111612\) \(a_{97}=-1.753610442\) \(a_{98}=+0.995597965\) \(a_{99}=-0.183899304\) \(a_{100}=-0.907828526\)

Showing 100 of 1000 available coefficients

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