Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 8.42175366822 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.845438305\) \(a_{3}=+0.217372886\) \(a_{4}=-0.285234073\) \(a_{5}=-0.683701002\)
\(a_{6}=+0.183775364\) \(a_{7}=+0.377964473\) \(a_{8}=-1.086586116\) \(a_{9}=-0.952749028\) \(a_{10}=-0.578027016\)
\(a_{11}=-0.410111612\) \(a_{12}=-0.062002154\) \(a_{13}=-1.072634044\) \(a_{14}=+0.319545643\) \(a_{15}=-0.148618060\)
\(a_{16}=-0.633407451\) \(a_{17}=-0.126580516\) \(a_{18}=-0.805490523\) \(a_{19}=+0.715884228\) \(a_{20}=+0.195014822\)
\(a_{21}=+0.082159228\) \(a_{22}=-0.346724066\) \(a_{23}=+1.086002693\) \(a_{24}=-0.236194360\) \(a_{25}=-0.532552939\)
\(a_{26}=-0.906845908\) \(a_{27}=-0.424474692\) \(a_{28}=-0.107808346\) \(a_{29}=+0.841145724\) \(a_{30}=-0.125647401\)
\(a_{31}=+0.884722630\) \(a_{32}=+0.551079194\) \(a_{33}=-0.089147145\) \(a_{34}=-0.107016017\) \(a_{35}=-0.258414689\)
\(a_{36}=+0.271756486\) \(a_{37}=-1.881650265\) \(a_{38}=+0.605235948\) \(a_{39}=-0.233161558\) \(a_{40}=+0.742900017\)
\(a_{41}=-1.439777557\) \(a_{42}=+0.069460559\) \(a_{43}=+1.343930216\) \(a_{44}=+0.116977805\) \(a_{45}=+0.651395466\)
\(a_{46}=+0.918148276\) \(a_{47}=-1.288764357\) \(a_{48}=-0.137685606\) \(a_{49}=+0.142857143\) \(a_{50}=-0.450240654\)
\(a_{51}=-0.027515172\) \(a_{52}=+0.305951777\) \(a_{53}=-0.322885050\) \(a_{54}=-0.358867164\) \(a_{55}=+0.280393720\)
\(a_{56}=-0.410690949\) \(a_{57}=+0.155613821\) \(a_{58}=+0.711136815\) \(a_{59}=-0.925846620\) \(a_{60}=+0.042390935\)
\(a_{61}=-0.458711568\) \(a_{62}=+0.747978401\) \(a_{63}=-0.360105284\) \(a_{64}=+1.099310911\) \(a_{65}=+0.733360971\)
\(a_{66}=-0.075368411\) \(a_{67}=-0.647887154\) \(a_{68}=+0.036105076\) \(a_{69}=+0.236067540\) \(a_{70}=-0.218473677\)
\(a_{71}=+0.616233153\) \(a_{72}=+1.035243866\) \(a_{73}=-1.907642781\) \(a_{74}=-1.590819210\) \(a_{75}=-0.115762569\)
\(a_{76}=-0.204194574\) \(a_{77}=-0.155007619\) \(a_{78}=-0.197123712\) \(a_{79}=+1.204063276\) \(a_{80}=+0.433061309\)
\(a_{81}=+0.860479739\) \(a_{82}=-1.217243097\) \(a_{83}=+1.009316545\) \(a_{84}=-0.023434611\) \(a_{85}=+0.086543225\)
\(a_{86}=+1.136210084\) \(a_{87}=+0.182842274\) \(a_{88}=+0.445621583\) \(a_{89}=-1.534943870\) \(a_{90}=+0.550714678\)
\(a_{91}=-0.405417561\) \(a_{92}=-0.309764971\) \(a_{93}=+0.192314712\) \(a_{94}=-1.089570753\) \(a_{95}=-0.489450765\)
\(a_{96}=+0.119789675\) \(a_{97}=-0.592228815\) \(a_{98}=+0.120776901\) \(a_{99}=+0.390733440\) \(a_{100}=+0.151902244\)

Showing 100 of 1228 available coefficients

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