Properties

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

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 25.4442636432 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.954822698\) \(a_{3}=-0.577350269\) \(a_{4}=-0.088313616\) \(a_{5}=+0.590826414\)
\(a_{6}=+0.551267142\) \(a_{7}=-0.227326518\) \(a_{8}=+1.039146543\) \(a_{9}=+0.333333333\) \(a_{10}=-0.564134470\)
\(a_{11}=+1.385356033\) \(a_{12}=+0.050987890\) \(a_{13}=-1.126788108\) \(a_{14}=+0.217056519\) \(a_{15}=-0.341113789\)
\(a_{16}=-0.903887089\) \(a_{17}=+1.069445109\) \(a_{18}=-0.318274233\) \(a_{19}=-0.188742014\) \(a_{20}=-0.052178017\)
\(a_{21}=+0.131247026\) \(a_{22}=-1.322769384\) \(a_{23}=-1.455485670\) \(a_{24}=-0.599951536\) \(a_{25}=-0.650924149\)
\(a_{26}=+1.075882861\) \(a_{27}=-0.192450090\) \(a_{28}=+0.020076027\) \(a_{29}=-0.105496963\) \(a_{30}=+0.325703188\)
\(a_{31}=-0.178329010\) \(a_{32}=-0.176094633\) \(a_{33}=-0.799835678\) \(a_{34}=-1.021130464\) \(a_{35}=-0.134310511\)
\(a_{36}=-0.029437872\) \(a_{37}=-0.382599755\) \(a_{38}=+0.180215159\) \(a_{39}=+0.650551417\) \(a_{40}=+0.613955225\)
\(a_{41}=+0.532409035\) \(a_{42}=-0.125317640\) \(a_{43}=+1.436642875\) \(a_{44}=-0.122345800\) \(a_{45}=+0.196942138\)
\(a_{46}=+1.389730754\) \(a_{47}=+1.825229268\) \(a_{48}=+0.521859454\) \(a_{49}=-0.948322654\) \(a_{50}=+0.621517152\)
\(a_{51}=-0.617444421\) \(a_{52}=+0.099510732\) \(a_{53}=+1.629073513\) \(a_{54}=+0.183755714\) \(a_{55}=+0.818504936\)
\(a_{56}=-0.236225565\) \(a_{57}=+0.108970252\) \(a_{58}=+0.100730895\) \(a_{59}=-1.345616406\) \(a_{60}=+0.030124992\)
\(a_{61}=+0.801631037\) \(a_{62}=+0.170272587\) \(a_{63}=-0.075775506\) \(a_{64}=+1.072026242\) \(a_{65}=-0.665736177\)
\(a_{66}=+0.763701260\) \(a_{67}=-1.216183450\) \(a_{68}=-0.094446564\) \(a_{69}=+0.840325043\) \(a_{70}=+0.128242725\)
\(a_{71}=-1.612496839\) \(a_{72}=+0.346382181\) \(a_{73}=+0.483230120\) \(a_{74}=+0.365314931\) \(a_{75}=+0.375811233\)
\(a_{76}=+0.016668490\) \(a_{77}=-0.314928163\) \(a_{78}=-0.621161259\) \(a_{79}=+1.184439225\) \(a_{80}=-0.534040367\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.508356231\) \(a_{83}=-0.227362438\) \(a_{84}=-0.011590899\) \(a_{85}=+0.631856418\)
\(a_{86}=-1.371739226\) \(a_{87}=+0.060908700\) \(a_{88}=+1.439587932\) \(a_{89}=+0.510000962\) \(a_{90}=-0.188044823\)
\(a_{91}=+0.256148817\) \(a_{92}=+0.128539202\) \(a_{93}=+0.102958302\) \(a_{94}=-1.742770334\) \(a_{95}=-0.111513767\)
\(a_{96}=+0.101668284\) \(a_{97}=-1.156424006\) \(a_{98}=+0.905479995\) \(a_{99}=+0.461785344\) \(a_{100}=+0.057485465\)

Showing 100 of 1228 available coefficients

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