Properties

Level $509$
Weight $0$
Character 509.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 509 \)
Weight: \( 0 \)
Character: 509.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 0.43309736856 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.189617889\) \(a_{3}=-0.717078855\) \(a_{4}=-0.964045054\) \(a_{5}=-1.973834679\)
\(a_{6}=+0.135970977\) \(a_{7}=+0.251356465\) \(a_{8}=+0.372418072\) \(a_{9}=-0.485797914\) \(a_{10}=+0.374274369\)
\(a_{11}=-0.783053209\) \(a_{12}=+0.691296328\) \(a_{13}=-0.396446507\) \(a_{14}=-0.047661677\) \(a_{15}=+1.415395113\)
\(a_{16}=+0.893427923\) \(a_{17}=-0.678013639\) \(a_{18}=+0.092115978\) \(a_{19}=-1.701829423\) \(a_{20}=+1.902865553\)
\(a_{21}=-0.180242405\) \(a_{22}=+0.148480895\) \(a_{23}=+0.388083477\) \(a_{24}=-0.267053128\) \(a_{25}=+2.896023334\)
\(a_{26}=+0.075173347\) \(a_{27}=+1.065434266\) \(a_{28}=-0.242318958\) \(a_{29}=+0.516631471\) \(a_{30}=-0.268384233\)
\(a_{31}=+0.149529309\) \(a_{32}=-0.541827991\) \(a_{33}=+0.561510896\) \(a_{34}=+0.128563518\) \(a_{35}=-0.496136110\)
\(a_{36}=+0.468331073\) \(a_{37}=+1.648825153\) \(a_{38}=+0.322697298\) \(a_{39}=+0.284283414\) \(a_{40}=-0.735091703\)
\(a_{41}=-1.234952033\) \(a_{42}=+0.034177177\) \(a_{43}=-0.176941021\) \(a_{44}=+0.754898579\) \(a_{45}=+0.958884756\)
\(a_{46}=-0.073587577\) \(a_{47}=-0.926322647\) \(a_{48}=-0.640658267\) \(a_{49}=-0.936819924\) \(a_{50}=-0.549137840\)
\(a_{51}=+0.486189246\) \(a_{52}=+0.382192293\) \(a_{53}=-0.727625250\) \(a_{54}=-0.202025392\) \(a_{55}=+1.545617589\)
\(a_{56}=+0.093609699\) \(a_{57}=+1.220345905\) \(a_{58}=-0.097962576\) \(a_{59}=-0.888343136\) \(a_{60}=-1.364504677\)
\(a_{61}=-0.849910394\) \(a_{62}=-0.028353424\) \(a_{63}=-0.122108450\) \(a_{64}=-0.790687637\) \(a_{65}=+0.782519873\)
\(a_{66}=-0.106472503\) \(a_{67}=-0.025082999\) \(a_{68}=+0.653635702\) \(a_{69}=-0.278286455\) \(a_{70}=+0.094076277\)
\(a_{71}=-0.790610747\) \(a_{72}=-0.180919920\) \(a_{73}=-0.239426154\) \(a_{74}=-0.312646748\) \(a_{75}=-2.076677107\)
\(a_{76}=+1.640640242\) \(a_{77}=-0.196825487\) \(a_{78}=-0.053905219\) \(a_{79}=-0.898111076\) \(a_{80}=-1.763479034\)
\(a_{81}=-0.278202458\) \(a_{82}=+0.234168992\) \(a_{83}=-1.034354705\) \(a_{84}=+0.173761794\) \(a_{85}=+1.338286830\)
\(a_{86}=+0.033551197\) \(a_{87}=-0.370465526\) \(a_{88}=-0.291623174\) \(a_{89}=-0.722809829\) \(a_{90}=-0.181821680\)
\(a_{91}=-0.099649409\) \(a_{92}=-0.374129924\) \(a_{93}=-0.107224312\) \(a_{94}=+0.175647349\) \(a_{95}=+3.359129913\)
\(a_{96}=+0.388533387\) \(a_{97}=+1.630470664\) \(a_{98}=+0.177637822\) \(a_{99}=+0.380405639\) \(a_{100}=-2.791896958\)

Showing 100 of 1492 available coefficients

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