Properties

Level $18$
Weight $0$
Character 18.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 18 = 2 \cdot 3^{2} \)
Weight: \( 0 \)
Character: 18.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 9.9613895766 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.000000000\) \(a_{4}=+0.500000000\) \(a_{5}=-0.096010841\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.054476595\) \(a_{8}=+0.353553391\) \(a_{9}=+0.000000000\) \(a_{10}=-0.067889916\)
\(a_{11}=-1.035537222\) \(a_{12}=+0.000000000\) \(a_{13}=+0.921989639\) \(a_{14}=+0.745627551\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.629733215\) \(a_{18}=+0.000000000\) \(a_{19}=-0.324991491\) \(a_{20}=-0.048005420\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.732235392\) \(a_{23}=+1.397476328\) \(a_{24}=+0.000000000\) \(a_{25}=-0.990781918\)
\(a_{26}=+0.651945126\) \(a_{27}=+0.000000000\) \(a_{28}=+0.527238297\) \(a_{29}=-0.771790796\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.488910683\) \(a_{32}=+0.176776695\) \(a_{33}=+0.000000000\) \(a_{34}=+0.445288627\) \(a_{35}=-0.101241184\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.537860498\) \(a_{38}=-0.229803687\) \(a_{39}=+0.000000000\) \(a_{40}=-0.033944958\)
\(a_{41}=+1.767516785\) \(a_{42}=+0.000000000\) \(a_{43}=+1.826518122\) \(a_{44}=-0.517768611\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.988164988\) \(a_{47}=-0.600190389\) \(a_{48}=+0.000000000\) \(a_{49}=+0.111920889\) \(a_{50}=-0.700588613\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.460994819\) \(a_{53}=-0.146512582\) \(a_{54}=+0.000000000\) \(a_{55}=+0.099422799\)
\(a_{56}=+0.372813775\) \(a_{57}=+0.000000000\) \(a_{58}=-0.545738505\) \(a_{59}=+0.227344857\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.234060585\) \(a_{62}=+1.052818841\) \(a_{63}=+0.000000000\) \(a_{64}=+0.125000000\) \(a_{65}=-0.088521000\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.316782367\) \(a_{68}=+0.314866608\) \(a_{69}=+0.000000000\) \(a_{70}=-0.071588328\)
\(a_{71}=-1.709106072\) \(a_{72}=+0.000000000\) \(a_{73}=-0.400382030\) \(a_{74}=+1.087431586\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.162495745\) \(a_{77}=-1.091949764\) \(a_{78}=+0.000000000\) \(a_{79}=-0.634597906\) \(a_{80}=-0.024002710\)
\(a_{81}=+0.000000000\) \(a_{82}=+1.249823105\) \(a_{83}=-1.111876221\) \(a_{84}=+0.000000000\) \(a_{85}=-0.060461215\)
\(a_{86}=+1.291543350\) \(a_{87}=+0.000000000\) \(a_{88}=-0.366117696\) \(a_{89}=+0.954680862\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.972216495\) \(a_{92}=+0.698738164\) \(a_{93}=+0.000000000\) \(a_{94}=-0.424398694\) \(a_{95}=+0.031202706\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.267792680\) \(a_{98}=+0.079140019\) \(a_{99}=+0.000000000\) \(a_{100}=-0.495390959\)

Showing 100 of 250 available coefficients

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