Properties

Level $57$
Weight $0$
Character 57.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 57 = 3 \cdot 19 \)
Weight: \( 0 \)
Character: 57.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.53318440291 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.942150272\) \(a_{3}=+0.577350269\) \(a_{4}=+2.771947677\) \(a_{5}=-0.139722003\)
\(a_{6}=+1.121300982\) \(a_{7}=+0.166743978\) \(a_{8}=+3.441388663\) \(a_{9}=+0.333333333\) \(a_{10}=-0.271361126\)
\(a_{11}=+0.113829568\) \(a_{12}=+1.600384738\) \(a_{13}=-1.380398078\) \(a_{14}=+0.323841862\) \(a_{15}=-0.080668536\)
\(a_{16}=+3.911746248\) \(a_{17}=-1.168744063\) \(a_{18}=+0.647383424\) \(a_{19}=+0.229415734\) \(a_{20}=-0.387302081\)
\(a_{21}=+0.096269680\) \(a_{22}=+0.221074126\) \(a_{23}=-1.260776132\) \(a_{24}=+1.986886671\) \(a_{25}=-0.980477762\)
\(a_{26}=-2.680940502\) \(a_{27}=+0.192450090\) \(a_{28}=+0.462205582\) \(a_{29}=+1.731125077\) \(a_{30}=-0.156670419\)
\(a_{31}=+0.794557240\) \(a_{32}=+4.155810376\) \(a_{33}=+0.065719532\) \(a_{34}=-2.269876599\) \(a_{35}=-0.023297803\)
\(a_{36}=+0.923982559\) \(a_{37}=+0.232120452\) \(a_{38}=+0.445559830\) \(a_{39}=-0.796973202\) \(a_{40}=-0.480837716\)
\(a_{41}=-1.264295943\) \(a_{42}=+0.186970186\) \(a_{43}=+1.493402576\) \(a_{44}=+0.315529606\) \(a_{45}=-0.046574001\)
\(a_{46}=-2.448616707\) \(a_{47}=-0.633963292\) \(a_{48}=+2.258447750\) \(a_{49}=-0.972196446\) \(a_{50}=-1.904235152\)
\(a_{51}=-0.674774699\) \(a_{52}=-3.826391246\) \(a_{53}=-0.051598385\) \(a_{54}=+0.373766994\) \(a_{55}=-0.015904495\)
\(a_{56}=+0.573830834\) \(a_{57}=+0.132453236\) \(a_{58}=+3.362105039\) \(a_{59}=+0.601922776\) \(a_{60}=-0.223608961\)
\(a_{61}=-0.802762126\) \(a_{62}=+1.543149560\) \(a_{63}=+0.055581326\) \(a_{64}=+4.159462002\) \(a_{65}=+0.192871984\)
\(a_{66}=+0.127637206\) \(a_{67}=+0.059605273\) \(a_{68}=-3.239697391\) \(a_{69}=-0.727909439\) \(a_{70}=-0.045247833\)
\(a_{71}=+0.982354850\) \(a_{72}=+1.147129554\) \(a_{73}=+0.328088966\) \(a_{74}=+0.450812799\) \(a_{75}=-0.566079100\)
\(a_{76}=+0.635928411\) \(a_{77}=+0.018980395\) \(a_{78}=-1.547841720\) \(a_{79}=-0.562731828\) \(a_{80}=-0.546557020\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.455452709\) \(a_{83}=+1.833874917\) \(a_{84}=+0.266854517\) \(a_{85}=+0.163299261\)
\(a_{86}=+2.900412218\) \(a_{87}=+0.999465529\) \(a_{88}=+0.391731784\) \(a_{89}=-0.044648993\) \(a_{90}=-0.090453709\)
\(a_{91}=-0.230173066\) \(a_{92}=-3.494805470\) \(a_{93}=+0.458737837\) \(a_{94}=-1.231251979\) \(a_{95}=-0.032054426\)
\(a_{96}=+2.399358239\) \(a_{97}=+0.212518060\) \(a_{98}=-1.888151591\) \(a_{99}=+0.037943189\) \(a_{100}=-2.717833055\)

Showing 100 of 576 available coefficients

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