Properties

Level $57$
Weight $0$
Character 57.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 57 = 3 \cdot 19 \)
Weight: \( 0 \)
Character: 57.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.48946607452 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.379188261\) \(a_{3}=-0.577350269\) \(a_{4}=+0.902160260\) \(a_{5}=-0.408006035\)
\(a_{6}=-0.796274714\) \(a_{7}=-0.146250833\) \(a_{8}=-0.134939421\) \(a_{9}=+0.333333333\) \(a_{10}=-0.562717135\)
\(a_{11}=+0.045354045\) \(a_{12}=-0.520862469\) \(a_{13}=-0.232755057\) \(a_{14}=-0.201707432\) \(a_{15}=+0.235562394\)
\(a_{16}=-1.088267125\) \(a_{17}=+1.669442093\) \(a_{18}=+0.459729420\) \(a_{19}=+0.229415734\) \(a_{20}=-0.368086831\)
\(a_{21}=+0.084437958\) \(a_{22}=+0.062551767\) \(a_{23}=+1.000898323\) \(a_{24}=+0.077907311\) \(a_{25}=-0.833531075\)
\(a_{26}=-0.321013043\) \(a_{27}=-0.192450090\) \(a_{28}=-0.131941690\) \(a_{29}=-0.959449894\) \(a_{30}=+0.324884889\)
\(a_{31}=+0.381441328\) \(a_{32}=-1.365985824\) \(a_{33}=-0.026185170\) \(a_{34}=+2.302474937\) \(a_{35}=+0.059671223\)
\(a_{36}=+0.300720087\) \(a_{37}=-0.039252926\) \(a_{38}=+0.316407487\) \(a_{39}=+0.134381195\) \(a_{40}=+0.055056098\)
\(a_{41}=+0.308155797\) \(a_{42}=+0.116455840\) \(a_{43}=+1.379436544\) \(a_{44}=+0.040916617\) \(a_{45}=-0.136002012\)
\(a_{46}=+1.380427217\) \(a_{47}=-1.419929852\) \(a_{48}=+0.628311318\) \(a_{49}=-0.978610694\) \(a_{50}=-1.149596274\)
\(a_{51}=-0.963852842\) \(a_{52}=-0.209982363\) \(a_{53}=-0.325529258\) \(a_{54}=-0.265424905\) \(a_{55}=-0.018504724\)
\(a_{56}=+0.019735003\) \(a_{57}=-0.132453236\) \(a_{58}=-1.323262032\) \(a_{59}=-0.819921489\) \(a_{60}=+0.212515031\)
\(a_{61}=-1.134662620\) \(a_{62}=+0.526079402\) \(a_{63}=-0.048750278\) \(a_{64}=-0.795684488\) \(a_{65}=+0.094965468\)
\(a_{66}=-0.036114279\) \(a_{67}=-0.211686624\) \(a_{68}=+1.506104313\) \(a_{69}=-0.577868916\) \(a_{70}=+0.082297850\)
\(a_{71}=+1.221549489\) \(a_{72}=-0.044979807\) \(a_{73}=+1.110370967\) \(a_{74}=-0.054137174\) \(a_{75}=+0.481239391\)
\(a_{76}=+0.206969758\) \(a_{77}=-0.006633067\) \(a_{78}=+0.185336967\) \(a_{79}=-0.087864072\) \(a_{80}=+0.444019555\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.425004858\) \(a_{83}=+0.135791055\) \(a_{84}=+0.076176570\) \(a_{85}=-0.681142450\)
\(a_{86}=+1.902502688\) \(a_{87}=+0.553938655\) \(a_{88}=-0.006120049\) \(a_{89}=+0.275404040\) \(a_{90}=-0.187572378\)
\(a_{91}=+0.034040621\) \(a_{92}=+0.902970691\) \(a_{93}=-0.220225253\) \(a_{94}=-1.958350584\) \(a_{95}=-0.093603004\)
\(a_{96}=+0.788652283\) \(a_{97}=+1.541523321\) \(a_{98}=-1.349688381\) \(a_{99}=+0.015118015\) \(a_{100}=-0.751978612\)

Showing 100 of 432 available coefficients

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