Properties

Level $68$
Weight $0$
Character 68.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.80201165803 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.045531371\) \(a_{4}=+0.000000000\) \(a_{5}=+0.887033970\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.481226389\) \(a_{8}=+0.000000000\) \(a_{9}=-0.997926894\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.059184776\) \(a_{12}=+0.000000000\) \(a_{13}=+1.150899508\) \(a_{14}=+0.000000000\) \(a_{15}=-0.040387872\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.023270172\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.067442268\) \(a_{22}=+0.000000000\) \(a_{23}=+1.402231377\) \(a_{24}=+0.000000000\) \(a_{25}=-0.213170735\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.090968350\) \(a_{28}=+0.000000000\) \(a_{29}=+0.488996845\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.599256908\) \(a_{32}=+0.000000000\) \(a_{33}=+0.048226135\) \(a_{34}=+0.000000000\) \(a_{35}=+1.313898125\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.987478116\) \(a_{38}=+0.000000000\) \(a_{39}=-0.052402032\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.815287740\) \(a_{42}=+0.000000000\) \(a_{43}=+0.430044077\) \(a_{44}=+0.000000000\) \(a_{45}=-0.885195055\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.300803810\) \(a_{48}=+0.000000000\) \(a_{49}=+1.194031614\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.011042979\) \(a_{52}=+0.000000000\) \(a_{53}=-1.381697684\) \(a_{54}=+0.000000000\) \(a_{55}=-0.939532877\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.001059523\) \(a_{58}=+0.000000000\) \(a_{59}=+1.035760789\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.407706799\) \(a_{62}=+0.000000000\) \(a_{63}=-1.478155650\) \(a_{64}=+0.000000000\) \(a_{65}=+1.020886960\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.188458876\) \(a_{68}=+0.000000000\) \(a_{69}=-0.063845516\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.709438338\) \(a_{72}=+0.000000000\) \(a_{73}=-1.190220993\) \(a_{74}=+0.000000000\) \(a_{75}=+0.009705956\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.568892440\) \(a_{78}=+0.000000000\) \(a_{79}=-0.547133603\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.993784980\) \(a_{82}=+0.000000000\) \(a_{83}=+1.233769249\) \(a_{84}=+0.000000000\) \(a_{85}=+0.215137338\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.022264697\) \(a_{88}=+0.000000000\) \(a_{89}=+1.588840641\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.704742721\) \(a_{92}=+0.000000000\) \(a_{93}=+0.027284988\) \(a_{94}=+0.000000000\) \(a_{95}=+0.020641433\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.910585313\) \(a_{98}=+0.000000000\) \(a_{99}=+1.056988974\) \(a_{100}=+0.000000000\)

Showing 100 of 640 available coefficients

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