Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.42669715561 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.442440107\) \(a_{3}=-1.463594003\) \(a_{4}=+1.080633461\) \(a_{5}=+1.240481865\)
\(a_{6}=-2.111146689\) \(a_{7}=-0.047909727\) \(a_{8}=+0.116308938\) \(a_{9}=+1.142107404\) \(a_{10}=+1.789320795\)
\(a_{11}=-0.554318214\) \(a_{12}=-1.581608654\) \(a_{13}=+0.277350098\) \(a_{14}=-0.069106911\) \(a_{15}=-1.815561819\)
\(a_{16}=-0.912864787\) \(a_{17}=+1.125292889\) \(a_{18}=+1.647421533\) \(a_{19}=-0.008179321\) \(a_{20}=+1.340506200\)
\(a_{21}=+0.070120418\) \(a_{22}=-0.799570807\) \(a_{23}=-0.702543415\) \(a_{24}=-0.170229077\) \(a_{25}=+0.538795258\)
\(a_{26}=+0.400060905\) \(a_{27}=-0.207987544\) \(a_{28}=-0.051772855\) \(a_{29}=-0.021055322\) \(a_{30}=-2.618839184\)
\(a_{31}=+0.993703105\) \(a_{32}=-1.433061712\) \(a_{33}=+0.811296813\) \(a_{34}=+1.623167589\) \(a_{35}=-0.059431153\)
\(a_{36}=+1.234199483\) \(a_{37}=-0.319914791\) \(a_{38}=-0.011798178\) \(a_{39}=-0.405927957\) \(a_{40}=+0.144279128\)
\(a_{41}=-1.431345161\) \(a_{42}=+0.101144478\) \(a_{43}=+1.526150281\) \(a_{44}=-0.599014833\) \(a_{45}=+1.416763537\)
\(a_{46}=-1.013376598\) \(a_{47}=-0.634535946\) \(a_{48}=+1.336063425\) \(a_{49}=-0.997704652\) \(a_{50}=+0.777179887\)
\(a_{51}=-1.646971920\) \(a_{52}=+0.299713793\) \(a_{53}=+0.882312639\) \(a_{54}=-0.300009587\) \(a_{55}=-0.687621675\)
\(a_{56}=-0.005572328\) \(a_{57}=+0.011971183\) \(a_{58}=-0.030371024\) \(a_{59}=+0.091965679\) \(a_{60}=-1.961956871\)
\(a_{61}=-0.184614181\) \(a_{62}=+1.433356979\) \(a_{63}=-0.054717868\) \(a_{64}=-1.154241010\) \(a_{65}=+0.344047878\)
\(a_{66}=+1.170248115\) \(a_{67}=+1.820678309\) \(a_{68}=+1.216029193\) \(a_{69}=+1.028238216\) \(a_{70}=-0.085725849\)
\(a_{71}=-1.114514114\) \(a_{72}=+0.132837402\) \(a_{73}=+0.450630019\) \(a_{74}=-0.461457634\) \(a_{75}=-0.788577414\)
\(a_{76}=-0.008838908\) \(a_{77}=+0.026556884\) \(a_{78}=-0.585527357\) \(a_{79}=-0.973394548\) \(a_{80}=-1.132392112\)
\(a_{81}=-0.837698560\) \(a_{82}=-2.064629654\) \(a_{83}=-0.675809831\) \(a_{84}=+0.075774583\) \(a_{85}=+1.395905477\)
\(a_{86}=+2.201380380\) \(a_{87}=+0.030816552\) \(a_{88}=-0.064472367\) \(a_{89}=+1.784038182\) \(a_{90}=+2.043596528\)
\(a_{91}=-0.013287750\) \(a_{92}=-0.759191861\) \(a_{93}=-1.454377911\) \(a_{94}=-0.915280123\) \(a_{95}=-0.010146292\)
\(a_{96}=+2.097420567\) \(a_{97}=+0.422296540\) \(a_{98}=-1.439129134\) \(a_{99}=-0.633090977\) \(a_{100}=+0.582240202\)

Showing 100 of 1000 available coefficients

Rows: Cols: