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: \( 27.1777919535 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.777427179\) \(a_{3}=+0.577350269\) \(a_{4}=-0.395606981\) \(a_{5}=+1.465859146\)
\(a_{6}=+0.448847791\) \(a_{7}=-1.383904003\) \(a_{8}=-1.084982799\) \(a_{9}=+0.333333333\) \(a_{10}=+1.139598740\)
\(a_{11}=+1.138330236\) \(a_{12}=-0.228403797\) \(a_{13}=+0.086707358\) \(a_{14}=-1.075884585\) \(a_{15}=+0.846314172\)
\(a_{16}=-0.447888135\) \(a_{17}=+1.516530007\) \(a_{18}=+0.259142393\) \(a_{19}=-0.338153144\) \(a_{20}=-0.579904112\)
\(a_{21}=-0.798997349\) \(a_{22}=+0.884968865\) \(a_{23}=+1.521248163\) \(a_{24}=-0.626415111\) \(a_{25}=+1.148743035\)
\(a_{26}=+0.067408657\) \(a_{27}=+0.192450090\) \(a_{28}=+0.547482085\) \(a_{29}=-1.055926006\) \(a_{30}=+0.657947640\)
\(a_{31}=+0.705263197\) \(a_{32}=+0.736782389\) \(a_{33}=+0.657215268\) \(a_{34}=+1.178991645\) \(a_{35}=-2.028608340\)
\(a_{36}=-0.131868994\) \(a_{37}=+0.515495150\) \(a_{38}=-0.262889445\) \(a_{39}=+0.050060517\) \(a_{40}=-1.590431958\)
\(a_{41}=-0.151812060\) \(a_{42}=-0.621162255\) \(a_{43}=+0.768865446\) \(a_{44}=-0.450331389\) \(a_{45}=+0.488619715\)
\(a_{46}=+1.182659668\) \(a_{47}=+0.446851105\) \(a_{48}=-0.258588335\) \(a_{49}=+0.915190290\) \(a_{50}=+0.893064057\)
\(a_{51}=+0.875569008\) \(a_{52}=-0.034302036\) \(a_{53}=+0.394827166\) \(a_{54}=+0.149615930\) \(a_{55}=+1.668631788\)
\(a_{56}=+1.501512038\) \(a_{57}=-0.195232809\) \(a_{58}=-0.820905576\) \(a_{59}=+0.371261642\) \(a_{60}=-0.334807795\)
\(a_{61}=+0.791166051\) \(a_{62}=+0.548290778\) \(a_{63}=-0.461301334\) \(a_{64}=+1.020682789\) \(a_{65}=+0.127100774\)
\(a_{66}=+0.510937012\) \(a_{67}=-0.260874563\) \(a_{68}=-0.599949858\) \(a_{69}=+0.878293036\) \(a_{70}=-1.577095259\)
\(a_{71}=+0.044588807\) \(a_{72}=-0.361660933\) \(a_{73}=+1.463200550\) \(a_{74}=+0.400759940\) \(a_{75}=+0.663227100\)
\(a_{76}=+0.133775745\) \(a_{77}=-1.575339771\) \(a_{78}=+0.038918406\) \(a_{79}=+0.724937818\) \(a_{80}=-0.656540919\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.118022822\) \(a_{83}=-1.361688580\) \(a_{84}=+0.316088929\) \(a_{85}=+2.223019380\)
\(a_{86}=+0.597736894\) \(a_{87}=-0.609639164\) \(a_{88}=-1.235068726\) \(a_{89}=+0.186179052\) \(a_{90}=+0.379866247\)
\(a_{91}=-0.119994660\) \(a_{92}=-0.601816393\) \(a_{93}=+0.407183897\) \(a_{94}=+0.347394194\) \(a_{95}=-0.495684879\)
\(a_{96}=+0.425381511\) \(a_{97}=-1.289810178\) \(a_{98}=+0.711493805\) \(a_{99}=+0.379443412\) \(a_{100}=-0.454450764\)

Showing 100 of 1228 available coefficients

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