Properties

Level $14$
Weight $0$
Character 14.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.93985827196 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.552232642\) \(a_{4}=+0.500000000\) \(a_{5}=-1.170782528\)
\(a_{6}=-1.097594227\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=+1.409426176\) \(a_{10}=-0.827868265\)
\(a_{11}=-1.220285866\) \(a_{12}=-0.776116321\) \(a_{13}=-0.807508565\) \(a_{14}=+0.267261242\) \(a_{15}=+1.817326857\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.793961225\) \(a_{18}=+0.996614807\) \(a_{19}=+0.494892226\) \(a_{20}=-0.585391264\)
\(a_{21}=-0.586688793\) \(a_{22}=-0.862872411\) \(a_{23}=+1.316762438\) \(a_{24}=-0.548797114\) \(a_{25}=+0.370731728\)
\(a_{26}=-0.570994783\) \(a_{27}=-0.635524675\) \(a_{28}=+0.188982236\) \(a_{29}=-1.428184912\) \(a_{30}=+1.285044144\)
\(a_{31}=-0.192994966\) \(a_{32}=+0.176776695\) \(a_{33}=+1.894167554\) \(a_{34}=-0.561415366\) \(a_{35}=-0.442514201\)
\(a_{36}=+0.704713088\) \(a_{37}=-0.794332041\) \(a_{38}=+0.349941648\) \(a_{39}=+1.253441155\) \(a_{40}=-0.413934132\)
\(a_{41}=-0.569058503\) \(a_{42}=-0.414851628\) \(a_{43}=+0.502292852\) \(a_{44}=-0.610142915\) \(a_{45}=-1.650131552\)
\(a_{46}=+0.931091650\) \(a_{47}=-0.182859191\) \(a_{48}=-0.388058152\) \(a_{49}=+0.142857171\) \(a_{50}=+0.262146919\)
\(a_{51}=+1.232412530\) \(a_{52}=-0.403754283\) \(a_{53}=-0.610396911\) \(a_{54}=-0.449383807\) \(a_{55}=+1.428689371\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.768187868\) \(a_{58}=-1.009879237\) \(a_{59}=-1.013212928\) \(a_{60}=+0.908663428\)
\(a_{61}=+1.443399541\) \(a_{62}=-0.136468051\) \(a_{63}=+0.532713023\) \(a_{64}=+0.125000000\) \(a_{65}=+0.945416919\)
\(a_{66}=+1.339378721\) \(a_{67}=+0.775002364\) \(a_{68}=-0.396980614\) \(a_{69}=-2.043921637\) \(a_{70}=-0.312904796\)
\(a_{71}=-1.717188972\) \(a_{72}=+0.498307396\) \(a_{73}=-0.154211959\) \(a_{74}=-0.561677559\) \(a_{75}=-0.575461878\)
\(a_{76}=+0.247446093\) \(a_{77}=-0.461224806\) \(a_{78}=+0.886316762\) \(a_{79}=-0.905691617\) \(a_{80}=-0.292695765\)
\(a_{81}=-0.422944837\) \(a_{82}=-0.402385425\) \(a_{83}=+1.347078266\) \(a_{84}=-0.293344393\) \(a_{85}=+0.929555927\)
\(a_{86}=+0.355174690\) \(a_{87}=+2.216875237\) \(a_{88}=-0.431436203\) \(a_{89}=+1.386389647\) \(a_{90}=-1.166819200\)
\(a_{91}=-0.305209543\) \(a_{92}=+0.658381220\) \(a_{93}=+0.299573082\) \(a_{94}=-0.129300962\) \(a_{95}=-0.579411174\)
\(a_{96}=-0.274398570\) \(a_{97}=-0.179822068\) \(a_{98}=+0.101015254\) \(a_{99}=-1.719902794\) \(a_{100}=+0.185365888\)

Showing 100 of 2000 available coefficients

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