Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 27.3156558458 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.787427750\) \(a_{3}=-0.577350269\) \(a_{4}=+2.194897961\) \(a_{5}=+0.501472122\)
\(a_{6}=+1.031971893\) \(a_{7}=+1.353710649\) \(a_{8}=-2.135793774\) \(a_{9}=+0.333333333\) \(a_{10}=-0.896345186\)
\(a_{11}=+0.494198515\) \(a_{12}=-1.267224929\) \(a_{13}=-1.746933534\) \(a_{14}=-2.419659980\) \(a_{15}=-0.289525065\)
\(a_{16}=+1.622679099\) \(a_{17}=+0.422900986\) \(a_{18}=-0.595809250\) \(a_{19}=-1.083730716\) \(a_{20}=+1.100680138\)
\(a_{21}=-0.781565208\) \(a_{22}=-0.883344139\) \(a_{23}=+1.435493775\) \(a_{24}=+1.233101110\) \(a_{25}=-0.748525711\)
\(a_{26}=+3.122517476\) \(a_{27}=-0.192450090\) \(a_{28}=+2.971256744\) \(a_{29}=-0.401846391\) \(a_{30}=+0.517505135\)
\(a_{31}=+0.824053214\) \(a_{32}=-0.764627877\) \(a_{33}=-0.285325645\) \(a_{34}=-0.755904958\) \(a_{35}=+0.678848152\)
\(a_{36}=+0.731632654\) \(a_{37}=-1.168353084\) \(a_{38}=+1.937090356\) \(a_{39}=+1.008592546\) \(a_{40}=-1.071041036\)
\(a_{41}=-0.319153520\) \(a_{42}=+1.396991341\) \(a_{43}=+0.256645940\) \(a_{44}=+1.084715312\) \(a_{45}=+0.167157374\)
\(a_{46}=-2.565841408\) \(a_{47}=-1.246253699\) \(a_{48}=-0.936854215\) \(a_{49}=+0.832532521\) \(a_{50}=+1.337935627\)
\(a_{51}=-0.244161998\) \(a_{52}=-3.834340852\) \(a_{53}=-0.389110644\) \(a_{54}=+0.343990631\) \(a_{55}=+0.247826778\)
\(a_{56}=-2.891246776\) \(a_{57}=+0.625692221\) \(a_{58}=+0.718271390\) \(a_{59}=-0.077834837\) \(a_{60}=-0.635477974\)
\(a_{61}=+0.037440077\) \(a_{62}=-1.472935582\) \(a_{63}=+0.451236883\) \(a_{64}=-0.255962014\) \(a_{65}=-0.876038466\)
\(a_{66}=+0.509998976\) \(a_{67}=+0.237606159\) \(a_{68}=+0.928224512\) \(a_{69}=-0.828782717\) \(a_{70}=-1.213392024\)
\(a_{71}=+1.212953401\) \(a_{72}=-0.711931258\) \(a_{73}=-0.539760629\) \(a_{74}=+2.088346725\) \(a_{75}=+0.432161521\)
\(a_{76}=-2.378678340\) \(a_{77}=+0.669001792\) \(a_{78}=-1.802786305\) \(a_{79}=+0.763127684\) \(a_{80}=+0.813728331\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.570463858\) \(a_{83}=+1.459781681\) \(a_{84}=-1.715455881\) \(a_{85}=+0.212073055\)
\(a_{86}=-0.458736075\) \(a_{87}=+0.232006122\) \(a_{88}=-1.055506111\) \(a_{89}=+0.491686791\) \(a_{90}=-0.298781729\)
\(a_{91}=-2.364842528\) \(a_{92}=+3.150762360\) \(a_{93}=-0.475767345\) \(a_{94}=+2.227588444\) \(a_{95}=-0.543460742\)
\(a_{96}=+0.441458110\) \(a_{97}=-0.623621676\) \(a_{98}=-1.488091732\) \(a_{99}=+0.164732838\) \(a_{100}=-1.642937557\)

Showing 100 of 1228 available coefficients

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