Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 5.69430016396 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.058647886\) \(a_{3}=+0.737996041\) \(a_{4}=-0.996560425\) \(a_{5}=+0.825781443\)
\(a_{6}=-0.043281908\) \(a_{7}=-1.480479144\) \(a_{8}=+0.117094049\) \(a_{9}=-0.455361843\) \(a_{10}=-0.048430336\)
\(a_{11}=-1.391271021\) \(a_{12}=-0.735457649\) \(a_{13}=+0.277350098\) \(a_{14}=+0.086826972\) \(a_{15}=+0.609423436\)
\(a_{16}=+0.989693107\) \(a_{17}=-1.240787604\) \(a_{18}=+0.026706010\) \(a_{19}=+0.133953482\) \(a_{20}=-0.822941106\)
\(a_{21}=-1.092587748\) \(a_{22}=+0.081595105\) \(a_{23}=+1.245812002\) \(a_{24}=+0.086414944\) \(a_{25}=-0.318085009\)
\(a_{26}=-0.016265997\) \(a_{27}=-1.074051279\) \(a_{28}=+1.475386926\) \(a_{29}=+0.043177973\) \(a_{30}=-0.035741396\)
\(a_{31}=+1.439936583\) \(a_{32}=-0.175137457\) \(a_{33}=-1.026752506\) \(a_{34}=+0.072769570\) \(a_{35}=-1.222552203\)
\(a_{36}=+0.453795592\) \(a_{37}=-0.092065054\) \(a_{38}=-0.007856089\) \(a_{39}=+0.204683275\) \(a_{40}=+0.096694094\)
\(a_{41}=-1.298120947\) \(a_{42}=+0.064077960\) \(a_{43}=-0.323395687\) \(a_{44}=+1.386485647\) \(a_{45}=-0.376029369\)
\(a_{46}=-0.073064250\) \(a_{47}=+0.383323006\) \(a_{48}=+0.730389592\) \(a_{49}=+1.191818496\) \(a_{50}=+0.018655013\)
\(a_{51}=-0.915696340\) \(a_{52}=-0.276396132\) \(a_{53}=+0.787404328\) \(a_{54}=+0.062990837\) \(a_{55}=-1.148885791\)
\(a_{56}=-0.173355297\) \(a_{57}=+0.098857139\) \(a_{58}=-0.002532297\) \(a_{59}=+0.053397267\) \(a_{60}=-0.607327278\)
\(a_{61}=-0.706681426\) \(a_{62}=-0.084449237\) \(a_{63}=+0.674153711\) \(a_{64}=-0.979421666\) \(a_{65}=+0.229030565\)
\(a_{66}=+0.060216864\) \(a_{67}=-0.077943478\) \(a_{68}=+1.236519822\) \(a_{69}=+0.919404327\) \(a_{70}=+0.071700103\)
\(a_{71}=-0.995207474\) \(a_{72}=-0.053320162\) \(a_{73}=-0.103906905\) \(a_{74}=+0.005399420\) \(a_{75}=-0.234745476\)
\(a_{76}=-0.133492739\) \(a_{77}=+2.059747728\) \(a_{78}=-0.012004244\) \(a_{79}=-0.893884253\) \(a_{80}=+0.817270207\)
\(a_{81}=-0.337283767\) \(a_{82}=+0.076132041\) \(a_{83}=-0.371036877\) \(a_{84}=+1.088829734\) \(a_{85}=-1.024619449\)
\(a_{86}=+0.018966452\) \(a_{87}=+0.031865083\) \(a_{88}=-0.162909531\) \(a_{89}=-1.557469796\) \(a_{90}=+0.022053327\)
\(a_{91}=-0.410611036\) \(a_{92}=-1.241526938\) \(a_{93}=+1.062667498\) \(a_{94}=-0.022481082\) \(a_{95}=+0.110616299\)
\(a_{96}=-0.129250750\) \(a_{97}=-0.410238566\) \(a_{98}=-0.069897635\) \(a_{99}=+0.633531738\) \(a_{100}=+0.316990930\)

Showing 100 of 1000 available coefficients

Rows: Cols: