Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 9.99016407004 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.393576658\) \(a_{3}=-0.653352455\) \(a_{4}=+0.942055901\) \(a_{5}=+0.001069574\)
\(a_{6}=-0.910496731\) \(a_{7}=-0.377964473\) \(a_{8}=-0.080749544\) \(a_{9}=-0.573130569\) \(a_{10}=+0.001490534\)
\(a_{11}=-0.184569743\) \(a_{12}=-0.615494536\) \(a_{13}=-0.757443584\) \(a_{14}=-0.526722467\) \(a_{15}=-0.000698809\)
\(a_{16}=-1.054586580\) \(a_{17}=-1.080776451\) \(a_{18}=-0.798701383\) \(a_{19}=+0.754287947\) \(a_{20}=+0.001007599\)
\(a_{21}=+0.246944017\) \(a_{22}=-0.257212085\) \(a_{23}=-0.544922111\) \(a_{24}=+0.052757913\) \(a_{25}=-0.999998856\)
\(a_{26}=-1.055555699\) \(a_{27}=+1.027808720\) \(a_{28}=-0.356063662\) \(a_{29}=+1.638884136\) \(a_{30}=-0.000973844\)
\(a_{31}=+1.200486681\) \(a_{32}=-1.388897698\) \(a_{33}=+0.120589095\) \(a_{34}=-1.506144835\) \(a_{35}=-0.000404261\)
\(a_{36}=-0.539921035\) \(a_{37}=-0.116557926\) \(a_{38}=+1.051158076\) \(a_{39}=+0.494877626\) \(a_{40}=-0.000086368\)
\(a_{41}=+1.040747816\) \(a_{42}=+0.344135417\) \(a_{43}=-1.532024295\) \(a_{44}=-0.173875015\) \(a_{45}=-0.000613006\)
\(a_{46}=-0.759390734\) \(a_{47}=+1.100391986\) \(a_{48}=+0.689016732\) \(a_{49}=+0.142857143\) \(a_{50}=-1.393575064\)
\(a_{51}=+0.706127948\) \(a_{52}=-0.713554198\) \(a_{53}=-1.341441383\) \(a_{54}=+1.432330241\) \(a_{55}=-0.000197411\)
\(a_{56}=+0.030520459\) \(a_{57}=-0.492815882\) \(a_{58}=+2.283910676\) \(a_{59}=-1.707709077\) \(a_{60}=-0.000658317\)
\(a_{61}=-0.260949485\) \(a_{62}=+1.672970217\) \(a_{63}=+0.216622993\) \(a_{64}=-0.880948832\) \(a_{65}=-0.000810142\)
\(a_{66}=+0.168050148\) \(a_{67}=-0.049468836\) \(a_{68}=-1.018151834\) \(a_{69}=+0.356026199\) \(a_{70}=-0.000563369\)
\(a_{71}=-1.737760600\) \(a_{72}=+0.046280032\) \(a_{73}=+0.187807286\) \(a_{74}=-0.162432404\) \(a_{75}=+0.653351708\)
\(a_{76}=+0.710581411\) \(a_{77}=+0.069760806\) \(a_{78}=+0.689649907\) \(a_{79}=+1.118791245\) \(a_{80}=-0.001127959\)
\(a_{81}=-0.098390782\) \(a_{82}=+1.450361863\) \(a_{83}=-1.704794845\) \(a_{84}=+0.232635068\) \(a_{85}=-0.001155971\)
\(a_{86}=-2.134993296\) \(a_{87}=-1.070768974\) \(a_{88}=+0.014903923\) \(a_{89}=+0.691884186\) \(a_{90}=-0.000854271\)
\(a_{91}=+0.286286765\) \(a_{92}=-0.513347090\) \(a_{93}=-0.784340921\) \(a_{94}=+1.533480586\) \(a_{95}=+0.000806767\)
\(a_{96}=+0.907439721\) \(a_{97}=+0.086168023\) \(a_{98}=+0.199082380\) \(a_{99}=+0.105782562\) \(a_{100}=-0.942054823\)

Showing 100 of 1228 available coefficients

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