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: \( 28.3457877303 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.513110766\) \(a_{3}=+0.577350269\) \(a_{4}=-0.736717342\) \(a_{5}=-1.755303577\)
\(a_{6}=+0.296244639\) \(a_{7}=-1.439090195\) \(a_{8}=-0.891128366\) \(a_{9}=+0.333333333\) \(a_{10}=-0.900665163\)
\(a_{11}=-0.811864495\) \(a_{12}=-0.425343956\) \(a_{13}=-1.096197121\) \(a_{14}=-0.738412673\) \(a_{15}=-1.013424993\)
\(a_{16}=+0.279469783\) \(a_{17}=-0.111979227\) \(a_{18}=+0.171036922\) \(a_{19}=+0.520938153\) \(a_{20}=+1.293162585\)
\(a_{21}=-0.830859112\) \(a_{22}=-0.416576413\) \(a_{23}=-0.159669316\) \(a_{24}=-0.514493202\) \(a_{25}=+2.081090647\)
\(a_{26}=-0.562470545\) \(a_{27}=+0.192450090\) \(a_{28}=+1.060202703\) \(a_{29}=+0.389698053\) \(a_{30}=-0.519999274\)
\(a_{31}=-1.024145080\) \(a_{32}=+1.034527320\) \(a_{33}=-0.468730185\) \(a_{34}=-0.057457747\) \(a_{35}=+2.526040167\)
\(a_{36}=-0.245572447\) \(a_{37}=-0.570706191\) \(a_{38}=+0.267298975\) \(a_{39}=-0.632889703\) \(a_{40}=+1.564200808\)
\(a_{41}=-1.227646461\) \(a_{42}=-0.426322755\) \(a_{43}=-1.427251761\) \(a_{44}=+0.598114653\) \(a_{45}=-0.585101192\)
\(a_{46}=-0.081928045\) \(a_{47}=-0.877357427\) \(a_{48}=+0.161351955\) \(a_{49}=+1.070980590\) \(a_{50}=+1.067830016\)
\(a_{51}=-0.064651237\) \(a_{52}=+0.807587429\) \(a_{53}=-0.407378529\) \(a_{54}=+0.098748213\) \(a_{55}=+1.425068652\)
\(a_{56}=+1.282414094\) \(a_{57}=+0.300763783\) \(a_{58}=+0.199958266\) \(a_{59}=+1.268252166\) \(a_{60}=+0.746607767\)
\(a_{61}=+0.276224364\) \(a_{62}=-0.525499867\) \(a_{63}=-0.479696732\) \(a_{64}=+0.251357323\) \(a_{65}=+1.924158728\)
\(a_{66}=-0.240510504\) \(a_{67}=+0.409436982\) \(a_{68}=+0.082497038\) \(a_{69}=-0.092185122\) \(a_{70}=+1.296138406\)
\(a_{71}=-0.774534169\) \(a_{72}=-0.297042789\) \(a_{73}=-0.767243312\) \(a_{74}=-0.292835491\) \(a_{75}=+1.201518245\)
\(a_{76}=-0.383784171\) \(a_{77}=+1.168346235\) \(a_{78}=-0.324742520\) \(a_{79}=+0.616246150\) \(a_{80}=-0.490554310\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.629918616\) \(a_{83}=-0.545878868\) \(a_{84}=+0.612108316\) \(a_{85}=+0.196557537\)
\(a_{86}=-0.732338245\) \(a_{87}=+0.224992276\) \(a_{88}=+0.723475481\) \(a_{89}=-0.575252720\) \(a_{90}=-0.300221721\)
\(a_{91}=+1.577526529\) \(a_{92}=+0.117631154\) \(a_{93}=-0.591290438\) \(a_{94}=-0.450181542\) \(a_{95}=-0.914404603\)
\(a_{96}=+0.597284627\) \(a_{97}=+0.469878468\) \(a_{98}=+0.549531671\) \(a_{99}=-0.270621498\) \(a_{100}=-1.533175569\)

Showing 100 of 1228 available coefficients

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