Properties

Level $31$
Weight $0$
Character 31.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.343010459 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.826358522\) \(a_{3}=+1.171474302\) \(a_{4}=+2.335585451\) \(a_{5}=+0.882768560\)
\(a_{6}=-2.139532074\) \(a_{7}=+0.085020502\) \(a_{8}=-2.439257870\) \(a_{9}=+0.372352040\) \(a_{10}=-1.612251883\)
\(a_{11}=+0.479749022\) \(a_{12}=+2.736078335\) \(a_{13}=-0.480341608\) \(a_{14}=-0.155277918\) \(a_{15}=+1.034140682\)
\(a_{16}=+2.119373947\) \(a_{17}=-1.889739276\) \(a_{18}=-0.680048321\) \(a_{19}=+0.570225339\) \(a_{20}=+2.061781405\)
\(a_{21}=+0.099599333\) \(a_{22}=-0.876193714\) \(a_{23}=-0.282727258\) \(a_{24}=-2.857527910\) \(a_{25}=-0.220719669\)
\(a_{26}=+0.877275989\) \(a_{27}=-0.735273456\) \(a_{28}=+0.198572647\) \(a_{29}=+1.067452695\) \(a_{30}=-1.888711648\)
\(a_{31}=+0.179605302\) \(a_{32}=-1.431478800\) \(a_{33}=+0.562013650\) \(a_{34}=+3.451341431\) \(a_{35}=+0.075053426\)
\(a_{36}=+0.869660007\) \(a_{37}=+0.961633271\) \(a_{38}=-1.041435907\) \(a_{39}=-0.562707850\) \(a_{40}=-2.153300157\)
\(a_{41}=-0.749210742\) \(a_{42}=-0.181904091\) \(a_{43}=+0.203389151\) \(a_{44}=+1.120494835\) \(a_{45}=+0.328700674\)
\(a_{46}=+0.516361337\) \(a_{47}=-0.682060353\) \(a_{48}=+2.482792115\) \(a_{49}=-0.992771514\) \(a_{50}=+0.403113249\)
\(a_{51}=-2.213780999\) \(a_{52}=-1.121878871\) \(a_{53}=+0.257877402\) \(a_{54}=+1.342872942\) \(a_{55}=+0.423507353\)
\(a_{56}=-0.207386928\) \(a_{57}=+0.668004331\) \(a_{58}=-1.949551327\) \(a_{59}=+1.670301590\) \(a_{60}=+2.415323932\)
\(a_{61}=+1.580711820\) \(a_{62}=-0.328023674\) \(a_{63}=+0.031657557\) \(a_{64}=+0.495019558\) \(a_{65}=-0.424030470\)
\(a_{66}=-1.026438420\) \(a_{67}=-0.599439105\) \(a_{68}=-4.413647559\) \(a_{69}=-0.331207717\) \(a_{70}=-0.137074464\)
\(a_{71}=+0.049920007\) \(a_{72}=-0.908262643\) \(a_{73}=+0.679855486\) \(a_{74}=-1.756287120\) \(a_{75}=-0.258567421\)
\(a_{76}=+1.331810005\) \(a_{77}=+0.040788503\) \(a_{78}=+1.027706277\) \(a_{79}=+0.063073490\) \(a_{80}=+1.870916688\)
\(a_{81}=-1.233705998\) \(a_{82}=+1.368327424\) \(a_{83}=+1.258209151\) \(a_{84}=+0.232622753\) \(a_{85}=-1.668202419\)
\(a_{86}=-0.371461509\) \(a_{87}=+1.250493401\) \(a_{88}=-1.170231577\) \(a_{89}=+0.708813475\) \(a_{90}=-0.600325277\)
\(a_{91}=-0.040838885\) \(a_{92}=-0.660333670\) \(a_{93}=+0.210402996\) \(a_{94}=+1.245686739\) \(a_{95}=+0.503377001\)
\(a_{96}=-1.676940628\) \(a_{97}=+0.157622209\) \(a_{98}=+1.813156715\) \(a_{99}=+0.178635527\) \(a_{100}=-0.515509649\)

Showing 100 of 546 available coefficients

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