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: \( 5.82926875013 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.616429967\) \(a_{3}=-1.133407672\) \(a_{4}=+1.612845837\) \(a_{5}=-1.341652444\)
\(a_{6}=+1.832074125\) \(a_{7}=+0.377964473\) \(a_{8}=-0.990622376\) \(a_{9}=+0.284612951\) \(a_{10}=+2.168687215\)
\(a_{11}=-0.890623203\) \(a_{12}=-1.828011846\) \(a_{13}=+0.709339124\) \(a_{14}=-0.610953101\) \(a_{15}=+1.520639173\)
\(a_{16}=-0.011574142\) \(a_{17}=+1.090333476\) \(a_{18}=-0.460056903\) \(a_{19}=-0.244726691\) \(a_{20}=-2.163878559\)
\(a_{21}=-0.428387833\) \(a_{22}=+1.439630035\) \(a_{23}=-0.373623173\) \(a_{24}=+1.122779001\) \(a_{25}=+0.800031279\)
\(a_{26}=-1.146597016\) \(a_{27}=+0.810825170\) \(a_{28}=+0.609598427\) \(a_{29}=-0.887152364\) \(a_{30}=-2.458006727\)
\(a_{31}=+1.206808921\) \(a_{32}=+1.009331167\) \(a_{33}=+1.009439171\) \(a_{34}=-1.762447705\) \(a_{35}=-0.507096959\)
\(a_{36}=+0.459036813\) \(a_{37}=+0.150664915\) \(a_{38}=+0.395583557\) \(a_{39}=-0.803970405\) \(a_{40}=+1.329070932\)
\(a_{41}=-0.577515189\) \(a_{42}=+0.692458931\) \(a_{43}=+0.829428685\) \(a_{44}=-1.436437926\) \(a_{45}=-0.381851661\)
\(a_{46}=+0.603935693\) \(a_{47}=+0.382882587\) \(a_{48}=+0.013118222\) \(a_{49}=+0.142857143\) \(a_{50}=-1.293194534\)
\(a_{51}=-1.235792327\) \(a_{52}=+1.144054653\) \(a_{53}=-0.326792563\) \(a_{54}=-1.310642102\) \(a_{55}=+1.194906797\)
\(a_{56}=-0.374420064\) \(a_{57}=+0.277375109\) \(a_{58}=+1.434019667\) \(a_{59}=+1.262266512\) \(a_{60}=+2.452556560\)
\(a_{61}=-0.362946591\) \(a_{62}=-1.950722103\) \(a_{63}=+0.107573584\) \(a_{64}=-1.619939002\) \(a_{65}=-0.951686569\)
\(a_{66}=-1.631687726\) \(a_{67}=-1.473595433\) \(a_{68}=+1.758539808\) \(a_{69}=+0.423467371\) \(a_{70}=+0.819686720\)
\(a_{71}=+1.746389418\) \(a_{72}=-0.281943958\) \(a_{73}=+0.245882239\) \(a_{74}=-0.243539284\) \(a_{75}=-0.906761590\)
\(a_{76}=-0.394706424\) \(a_{77}=-0.336623930\) \(a_{78}=+1.299561855\) \(a_{79}=+1.071214578\) \(a_{80}=+0.015528477\)
\(a_{81}=-1.203608419\) \(a_{82}=+0.933512858\) \(a_{83}=+0.295904369\) \(a_{84}=-0.690923534\) \(a_{85}=-1.462848573\)
\(a_{86}=-1.340713381\) \(a_{87}=+1.005505296\) \(a_{88}=+0.882271274\) \(a_{89}=+0.872968054\) \(a_{90}=+0.617236468\)
\(a_{91}=+0.268104988\) \(a_{92}=-0.602596579\) \(a_{93}=-1.367806489\) \(a_{94}=-0.618902887\) \(a_{95}=+0.328338163\)
\(a_{96}=-1.143983688\) \(a_{97}=+0.675314244\) \(a_{98}=-0.230918567\) \(a_{99}=-0.253482898\) \(a_{100}=+1.290327119\)

Showing 100 of 1228 available coefficients

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