Properties

Level $15$
Weight $0$
Character 15.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.98505799392 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.143090293\) \(a_{3}=+0.577350269\) \(a_{4}=+0.306655417\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.659963488\) \(a_{7}=+1.514420775\) \(a_{8}=-0.792555463\) \(a_{9}=+0.333333333\) \(a_{10}=+0.511205520\)
\(a_{11}=+1.395175468\) \(a_{12}=+0.177047587\) \(a_{13}=+0.455882414\) \(a_{14}=+1.731119686\) \(a_{15}=+0.258198890\)
\(a_{16}=-1.212617873\) \(a_{17}=-0.095887830\) \(a_{18}=+0.381030098\) \(a_{19}=-1.559876733\) \(a_{20}=+0.137140471\)
\(a_{21}=+0.874351241\) \(a_{22}=+1.594811534\) \(a_{23}=-0.055897610\) \(a_{24}=-0.457582110\) \(a_{25}=+0.200000001\)
\(a_{26}=+0.521114762\) \(a_{27}=+0.192450090\) \(a_{28}=+0.464405333\) \(a_{29}=-1.434907011\) \(a_{30}=+0.295144644\)
\(a_{31}=-1.062215762\) \(a_{32}=-0.593576256\) \(a_{33}=+0.805504934\) \(a_{34}=-0.109608449\) \(a_{35}=+0.677269559\)
\(a_{36}=+0.102218471\) \(a_{37}=+1.277919360\) \(a_{38}=-1.783079947\) \(a_{39}=+0.263203835\) \(a_{40}=-0.354441573\)
\(a_{41}=-0.608142889\) \(a_{42}=+0.999462411\) \(a_{43}=-0.363611729\) \(a_{44}=+0.427838117\) \(a_{45}=+0.149071207\)
\(a_{46}=-0.063895996\) \(a_{47}=+0.249675386\) \(a_{48}=-0.700105303\) \(a_{49}=+1.293470284\) \(a_{50}=+0.228618050\)
\(a_{51}=-0.055360859\) \(a_{52}=+0.139798805\) \(a_{53}=-0.118428238\) \(a_{54}=+0.219987830\) \(a_{55}=+0.623941445\)
\(a_{56}=-1.200262464\) \(a_{57}=-0.900595271\) \(a_{58}=-1.640228254\) \(a_{59}=+0.222102542\) \(a_{60}=+0.079178155\)
\(a_{61}=+0.453318867\) \(a_{62}=-1.214208452\) \(a_{63}=+0.504806867\) \(a_{64}=+0.534106580\) \(a_{65}=+0.203876825\)
\(a_{66}=+0.920764826\) \(a_{67}=+0.277371799\) \(a_{68}=-0.029404510\) \(a_{69}=-0.032272478\) \(a_{70}=+0.774180202\)
\(a_{71}=-0.805890919\) \(a_{72}=-0.264185138\) \(a_{73}=-0.100093819\) \(a_{74}=+1.460777144\) \(a_{75}=+0.115470055\)
\(a_{76}=-0.478344463\) \(a_{77}=+2.112882574\) \(a_{78}=+0.300865744\) \(a_{79}=-1.027893330\) \(a_{80}=-0.542299008\)
\(a_{81}=+0.111110814\) \(a_{82}=-0.695162172\) \(a_{83}=-1.920115384\) \(a_{84}=+0.268124466\) \(a_{85}=-0.042882144\)
\(a_{86}=-0.415640979\) \(a_{87}=-0.828444053\) \(a_{88}=-1.105753967\) \(a_{89}=+1.297113288\) \(a_{90}=+0.170401869\)
\(a_{91}=+0.690397824\) \(a_{92}=-0.017141329\) \(a_{93}=-0.613270626\) \(a_{94}=+0.285401556\) \(a_{95}=-0.697597953\)
\(a_{96}=-0.342701508\) \(a_{97}=+1.545272170\) \(a_{98}=+1.478553478\) \(a_{99}=+0.465058614\) \(a_{100}=+0.061330876\)

Showing 100 of 1500 available coefficients

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